digital image processing j. shanbehzadeh, m. mahdijo j. shanbehzadeh, m. mahdijo...
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DIGITAL IMAGE PROCESSING
J Shanbehzadeh M MahdijoShanbehzadehgmailcom
Khwarizmi University of Tehran
Chapter 9 ndash Morphological Image Processing
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Table of Contents2
Preview
91 Preliminaries
92 Erosion and Dilation
bull 921 Erosionbull 922 Dilationbull 923 Duality
93 Opening and Closing
94 Hit-or-Miss Transformation
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Preview3
Morphology form and structure Extracting image components for
representation and description of region shape From
Image processing methods
Input Image Output Image To
Image processing methods
Input Image Output Attributes
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91 Preliminaries4
Reflection and Translation
Translation
(B)z = c | c = b + z for b є B
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91 Preliminaries5
Structuring Elements
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91 Preliminaries6
Structuring Elements
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92 Erosion and Dilation7
Erosion
(B)z = c | c = b + z for b є B
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92 Erosion and Dilation8
Computing the Erosion of a Binary Image
9
For each foreground pixel we superimpose the structuring element on top of the input image so that the origin of the structuring element coincides with the input pixel coordinates
If for every pixel in the structuring element
the corresponding pixel in the image underneath is a foreground pixel then the input pixel is left as it
is Otherwise it is set to background value
The effect of Erosion10
removing any foreground pixel that is not completely surrounded by other white pixels (assuming 8-connectedness)
Such pixels must lie at the edges of white regions and so the practical upshot is that foreground regions shrink (and holes inside a region grow)
11
Effect of Erosion Using a 3times3 Square Structuring Element
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92 Erosion12
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92 Erosion13
Erosion (More examples)
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92 Erosion14
Erosion (More examples)
1515
Erosion in removing salt noise15
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92 Dilation16
Dilation
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92 Dilation17
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92 Dilation18
Dilation19
The basic effect of the operator on a binary image is to gradually enlarge the boundaries of regions of foreground pixels
Thus areas of foreground pixels grow in size while holes within those regions become smaller
Dilation Example20
21
Gray level erosion dilation22
1048708 Erosion
1048708 Chose the local minimum over the region defined by the structure element
1048708 Put the minimums value in the same pixel position in the out image Results in darker images and light details are removed
23
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Dilation in noise reduction24
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Dilation in edge detection25
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92 Erosion and Dilation26
Duality
Proof
27
ClosingOpening
93 Opening and Closing
28
ErosionDilation
Opening Closing
Isthmus29
An isthmus (ˈɪsθməs or ˈɪsməs plural isthmuses from Ancient Greekἰσθμός isthmos ldquoneckrdquo) is a narrow strip of land connecting two larger land areas usually with water on either side[1] A tombolo is an isthmus where the strip of land consists of a spit or bar
The Isthmus of PanamaThe Suez Canal goes across the western side of the Sinai Peninsula
30
promiddottrude (prō-troD oD dprime)v promiddottrudmiddoted promiddottrudmiddoting promiddottrudesvtrTo push or thrust outwardvintrTo jut out project See Synonyms at bulge
Example sentencesThe air-conditioner does not protrude into the alleyThey are large-bodied and display a mouthful ofsharp teeth that protrude in Samanthas face and paws protrude from thecutout doorScrub the mussels and use a paring knife toremove any beards that protrude
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93 Opening and Closing31
Opening smoothes the contour of an object breaks narrow
isthmuses and eliminates thin protrusions
Erosion Dilation
Opening is defined as an erosion followed by a dilation using the same structuring element for both operations
Opening32
Opening removes some of the foreground (bright) pixels from the edges of regions of foreground pixels
Opening is less destructive than erosion in general
The exact operation is determined by a
structuring element
Opening33
The effect of the operator is to preserve foreground regions that
have a similar shape to this structuring element
or can completely contain the structuring element
Eliminating all other regions of foreground pixels
Opening34
Effect of opening using a 3times3 square structuring element
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
56
5757
ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
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Table of Contents2
Preview
91 Preliminaries
92 Erosion and Dilation
bull 921 Erosionbull 922 Dilationbull 923 Duality
93 Opening and Closing
94 Hit-or-Miss Transformation
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Preview3
Morphology form and structure Extracting image components for
representation and description of region shape From
Image processing methods
Input Image Output Image To
Image processing methods
Input Image Output Attributes
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91 Preliminaries4
Reflection and Translation
Translation
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91 Preliminaries5
Structuring Elements
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91 Preliminaries6
Structuring Elements
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92 Erosion and Dilation7
Erosion
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92 Erosion and Dilation8
Computing the Erosion of a Binary Image
9
For each foreground pixel we superimpose the structuring element on top of the input image so that the origin of the structuring element coincides with the input pixel coordinates
If for every pixel in the structuring element
the corresponding pixel in the image underneath is a foreground pixel then the input pixel is left as it
is Otherwise it is set to background value
The effect of Erosion10
removing any foreground pixel that is not completely surrounded by other white pixels (assuming 8-connectedness)
Such pixels must lie at the edges of white regions and so the practical upshot is that foreground regions shrink (and holes inside a region grow)
11
Effect of Erosion Using a 3times3 Square Structuring Element
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92 Erosion12
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92 Erosion13
Erosion (More examples)
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92 Erosion14
Erosion (More examples)
1515
Erosion in removing salt noise15
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92 Dilation16
Dilation
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92 Dilation17
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92 Dilation18
Dilation19
The basic effect of the operator on a binary image is to gradually enlarge the boundaries of regions of foreground pixels
Thus areas of foreground pixels grow in size while holes within those regions become smaller
Dilation Example20
21
Gray level erosion dilation22
1048708 Erosion
1048708 Chose the local minimum over the region defined by the structure element
1048708 Put the minimums value in the same pixel position in the out image Results in darker images and light details are removed
23
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Dilation in noise reduction24
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Dilation in edge detection25
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92 Erosion and Dilation26
Duality
Proof
27
ClosingOpening
93 Opening and Closing
28
ErosionDilation
Opening Closing
Isthmus29
An isthmus (ˈɪsθməs or ˈɪsməs plural isthmuses from Ancient Greekἰσθμός isthmos ldquoneckrdquo) is a narrow strip of land connecting two larger land areas usually with water on either side[1] A tombolo is an isthmus where the strip of land consists of a spit or bar
The Isthmus of PanamaThe Suez Canal goes across the western side of the Sinai Peninsula
30
promiddottrude (prō-troD oD dprime)v promiddottrudmiddoted promiddottrudmiddoting promiddottrudesvtrTo push or thrust outwardvintrTo jut out project See Synonyms at bulge
Example sentencesThe air-conditioner does not protrude into the alleyThey are large-bodied and display a mouthful ofsharp teeth that protrude in Samanthas face and paws protrude from thecutout doorScrub the mussels and use a paring knife toremove any beards that protrude
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93 Opening and Closing31
Opening smoothes the contour of an object breaks narrow
isthmuses and eliminates thin protrusions
Erosion Dilation
Opening is defined as an erosion followed by a dilation using the same structuring element for both operations
Opening32
Opening removes some of the foreground (bright) pixels from the edges of regions of foreground pixels
Opening is less destructive than erosion in general
The exact operation is determined by a
structuring element
Opening33
The effect of the operator is to preserve foreground regions that
have a similar shape to this structuring element
or can completely contain the structuring element
Eliminating all other regions of foreground pixels
Opening34
Effect of opening using a 3times3 square structuring element
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
56
5757
ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
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Preview3
Morphology form and structure Extracting image components for
representation and description of region shape From
Image processing methods
Input Image Output Image To
Image processing methods
Input Image Output Attributes
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91 Preliminaries4
Reflection and Translation
Translation
(B)z = c | c = b + z for b є B
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91 Preliminaries5
Structuring Elements
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91 Preliminaries6
Structuring Elements
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92 Erosion and Dilation7
Erosion
(B)z = c | c = b + z for b є B
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92 Erosion and Dilation8
Computing the Erosion of a Binary Image
9
For each foreground pixel we superimpose the structuring element on top of the input image so that the origin of the structuring element coincides with the input pixel coordinates
If for every pixel in the structuring element
the corresponding pixel in the image underneath is a foreground pixel then the input pixel is left as it
is Otherwise it is set to background value
The effect of Erosion10
removing any foreground pixel that is not completely surrounded by other white pixels (assuming 8-connectedness)
Such pixels must lie at the edges of white regions and so the practical upshot is that foreground regions shrink (and holes inside a region grow)
11
Effect of Erosion Using a 3times3 Square Structuring Element
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92 Erosion12
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92 Erosion13
Erosion (More examples)
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92 Erosion14
Erosion (More examples)
1515
Erosion in removing salt noise15
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92 Dilation16
Dilation
(B)z = c | c = b + z for b є B
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92 Dilation17
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92 Dilation18
Dilation19
The basic effect of the operator on a binary image is to gradually enlarge the boundaries of regions of foreground pixels
Thus areas of foreground pixels grow in size while holes within those regions become smaller
Dilation Example20
21
Gray level erosion dilation22
1048708 Erosion
1048708 Chose the local minimum over the region defined by the structure element
1048708 Put the minimums value in the same pixel position in the out image Results in darker images and light details are removed
23
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Dilation in noise reduction24
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Dilation in edge detection25
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92 Erosion and Dilation26
Duality
Proof
27
ClosingOpening
93 Opening and Closing
28
ErosionDilation
Opening Closing
Isthmus29
An isthmus (ˈɪsθməs or ˈɪsməs plural isthmuses from Ancient Greekἰσθμός isthmos ldquoneckrdquo) is a narrow strip of land connecting two larger land areas usually with water on either side[1] A tombolo is an isthmus where the strip of land consists of a spit or bar
The Isthmus of PanamaThe Suez Canal goes across the western side of the Sinai Peninsula
30
promiddottrude (prō-troD oD dprime)v promiddottrudmiddoted promiddottrudmiddoting promiddottrudesvtrTo push or thrust outwardvintrTo jut out project See Synonyms at bulge
Example sentencesThe air-conditioner does not protrude into the alleyThey are large-bodied and display a mouthful ofsharp teeth that protrude in Samanthas face and paws protrude from thecutout doorScrub the mussels and use a paring knife toremove any beards that protrude
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93 Opening and Closing31
Opening smoothes the contour of an object breaks narrow
isthmuses and eliminates thin protrusions
Erosion Dilation
Opening is defined as an erosion followed by a dilation using the same structuring element for both operations
Opening32
Opening removes some of the foreground (bright) pixels from the edges of regions of foreground pixels
Opening is less destructive than erosion in general
The exact operation is determined by a
structuring element
Opening33
The effect of the operator is to preserve foreground regions that
have a similar shape to this structuring element
or can completely contain the structuring element
Eliminating all other regions of foreground pixels
Opening34
Effect of opening using a 3times3 square structuring element
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
56
5757
ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
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91 Preliminaries4
Reflection and Translation
Translation
(B)z = c | c = b + z for b є B
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91 Preliminaries5
Structuring Elements
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91 Preliminaries6
Structuring Elements
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92 Erosion and Dilation7
Erosion
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92 Erosion and Dilation8
Computing the Erosion of a Binary Image
9
For each foreground pixel we superimpose the structuring element on top of the input image so that the origin of the structuring element coincides with the input pixel coordinates
If for every pixel in the structuring element
the corresponding pixel in the image underneath is a foreground pixel then the input pixel is left as it
is Otherwise it is set to background value
The effect of Erosion10
removing any foreground pixel that is not completely surrounded by other white pixels (assuming 8-connectedness)
Such pixels must lie at the edges of white regions and so the practical upshot is that foreground regions shrink (and holes inside a region grow)
11
Effect of Erosion Using a 3times3 Square Structuring Element
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92 Erosion12
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92 Erosion13
Erosion (More examples)
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92 Erosion14
Erosion (More examples)
1515
Erosion in removing salt noise15
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92 Dilation16
Dilation
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92 Dilation17
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92 Dilation18
Dilation19
The basic effect of the operator on a binary image is to gradually enlarge the boundaries of regions of foreground pixels
Thus areas of foreground pixels grow in size while holes within those regions become smaller
Dilation Example20
21
Gray level erosion dilation22
1048708 Erosion
1048708 Chose the local minimum over the region defined by the structure element
1048708 Put the minimums value in the same pixel position in the out image Results in darker images and light details are removed
23
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Dilation in noise reduction24
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Dilation in edge detection25
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92 Erosion and Dilation26
Duality
Proof
27
ClosingOpening
93 Opening and Closing
28
ErosionDilation
Opening Closing
Isthmus29
An isthmus (ˈɪsθməs or ˈɪsməs plural isthmuses from Ancient Greekἰσθμός isthmos ldquoneckrdquo) is a narrow strip of land connecting two larger land areas usually with water on either side[1] A tombolo is an isthmus where the strip of land consists of a spit or bar
The Isthmus of PanamaThe Suez Canal goes across the western side of the Sinai Peninsula
30
promiddottrude (prō-troD oD dprime)v promiddottrudmiddoted promiddottrudmiddoting promiddottrudesvtrTo push or thrust outwardvintrTo jut out project See Synonyms at bulge
Example sentencesThe air-conditioner does not protrude into the alleyThey are large-bodied and display a mouthful ofsharp teeth that protrude in Samanthas face and paws protrude from thecutout doorScrub the mussels and use a paring knife toremove any beards that protrude
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93 Opening and Closing31
Opening smoothes the contour of an object breaks narrow
isthmuses and eliminates thin protrusions
Erosion Dilation
Opening is defined as an erosion followed by a dilation using the same structuring element for both operations
Opening32
Opening removes some of the foreground (bright) pixels from the edges of regions of foreground pixels
Opening is less destructive than erosion in general
The exact operation is determined by a
structuring element
Opening33
The effect of the operator is to preserve foreground regions that
have a similar shape to this structuring element
or can completely contain the structuring element
Eliminating all other regions of foreground pixels
Opening34
Effect of opening using a 3times3 square structuring element
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
56
5757
ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
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91 Preliminaries5
Structuring Elements
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91 Preliminaries6
Structuring Elements
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92 Erosion and Dilation7
Erosion
(B)z = c | c = b + z for b є B
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92 Erosion and Dilation8
Computing the Erosion of a Binary Image
9
For each foreground pixel we superimpose the structuring element on top of the input image so that the origin of the structuring element coincides with the input pixel coordinates
If for every pixel in the structuring element
the corresponding pixel in the image underneath is a foreground pixel then the input pixel is left as it
is Otherwise it is set to background value
The effect of Erosion10
removing any foreground pixel that is not completely surrounded by other white pixels (assuming 8-connectedness)
Such pixels must lie at the edges of white regions and so the practical upshot is that foreground regions shrink (and holes inside a region grow)
11
Effect of Erosion Using a 3times3 Square Structuring Element
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92 Erosion12
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92 Erosion13
Erosion (More examples)
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92 Erosion14
Erosion (More examples)
1515
Erosion in removing salt noise15
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92 Dilation16
Dilation
(B)z = c | c = b + z for b є B
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92 Dilation17
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92 Dilation18
Dilation19
The basic effect of the operator on a binary image is to gradually enlarge the boundaries of regions of foreground pixels
Thus areas of foreground pixels grow in size while holes within those regions become smaller
Dilation Example20
21
Gray level erosion dilation22
1048708 Erosion
1048708 Chose the local minimum over the region defined by the structure element
1048708 Put the minimums value in the same pixel position in the out image Results in darker images and light details are removed
23
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Dilation in noise reduction24
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Dilation in edge detection25
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92 Erosion and Dilation26
Duality
Proof
27
ClosingOpening
93 Opening and Closing
28
ErosionDilation
Opening Closing
Isthmus29
An isthmus (ˈɪsθməs or ˈɪsməs plural isthmuses from Ancient Greekἰσθμός isthmos ldquoneckrdquo) is a narrow strip of land connecting two larger land areas usually with water on either side[1] A tombolo is an isthmus where the strip of land consists of a spit or bar
The Isthmus of PanamaThe Suez Canal goes across the western side of the Sinai Peninsula
30
promiddottrude (prō-troD oD dprime)v promiddottrudmiddoted promiddottrudmiddoting promiddottrudesvtrTo push or thrust outwardvintrTo jut out project See Synonyms at bulge
Example sentencesThe air-conditioner does not protrude into the alleyThey are large-bodied and display a mouthful ofsharp teeth that protrude in Samanthas face and paws protrude from thecutout doorScrub the mussels and use a paring knife toremove any beards that protrude
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93 Opening and Closing31
Opening smoothes the contour of an object breaks narrow
isthmuses and eliminates thin protrusions
Erosion Dilation
Opening is defined as an erosion followed by a dilation using the same structuring element for both operations
Opening32
Opening removes some of the foreground (bright) pixels from the edges of regions of foreground pixels
Opening is less destructive than erosion in general
The exact operation is determined by a
structuring element
Opening33
The effect of the operator is to preserve foreground regions that
have a similar shape to this structuring element
or can completely contain the structuring element
Eliminating all other regions of foreground pixels
Opening34
Effect of opening using a 3times3 square structuring element
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
56
5757
ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
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91 Preliminaries6
Structuring Elements
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92 Erosion and Dilation7
Erosion
(B)z = c | c = b + z for b є B
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92 Erosion and Dilation8
Computing the Erosion of a Binary Image
9
For each foreground pixel we superimpose the structuring element on top of the input image so that the origin of the structuring element coincides with the input pixel coordinates
If for every pixel in the structuring element
the corresponding pixel in the image underneath is a foreground pixel then the input pixel is left as it
is Otherwise it is set to background value
The effect of Erosion10
removing any foreground pixel that is not completely surrounded by other white pixels (assuming 8-connectedness)
Such pixels must lie at the edges of white regions and so the practical upshot is that foreground regions shrink (and holes inside a region grow)
11
Effect of Erosion Using a 3times3 Square Structuring Element
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92 Erosion12
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92 Erosion13
Erosion (More examples)
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92 Erosion14
Erosion (More examples)
1515
Erosion in removing salt noise15
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92 Dilation16
Dilation
(B)z = c | c = b + z for b є B
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92 Dilation17
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92 Dilation18
Dilation19
The basic effect of the operator on a binary image is to gradually enlarge the boundaries of regions of foreground pixels
Thus areas of foreground pixels grow in size while holes within those regions become smaller
Dilation Example20
21
Gray level erosion dilation22
1048708 Erosion
1048708 Chose the local minimum over the region defined by the structure element
1048708 Put the minimums value in the same pixel position in the out image Results in darker images and light details are removed
23
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Dilation in noise reduction24
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Dilation in edge detection25
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92 Erosion and Dilation26
Duality
Proof
27
ClosingOpening
93 Opening and Closing
28
ErosionDilation
Opening Closing
Isthmus29
An isthmus (ˈɪsθməs or ˈɪsməs plural isthmuses from Ancient Greekἰσθμός isthmos ldquoneckrdquo) is a narrow strip of land connecting two larger land areas usually with water on either side[1] A tombolo is an isthmus where the strip of land consists of a spit or bar
The Isthmus of PanamaThe Suez Canal goes across the western side of the Sinai Peninsula
30
promiddottrude (prō-troD oD dprime)v promiddottrudmiddoted promiddottrudmiddoting promiddottrudesvtrTo push or thrust outwardvintrTo jut out project See Synonyms at bulge
Example sentencesThe air-conditioner does not protrude into the alleyThey are large-bodied and display a mouthful ofsharp teeth that protrude in Samanthas face and paws protrude from thecutout doorScrub the mussels and use a paring knife toremove any beards that protrude
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93 Opening and Closing31
Opening smoothes the contour of an object breaks narrow
isthmuses and eliminates thin protrusions
Erosion Dilation
Opening is defined as an erosion followed by a dilation using the same structuring element for both operations
Opening32
Opening removes some of the foreground (bright) pixels from the edges of regions of foreground pixels
Opening is less destructive than erosion in general
The exact operation is determined by a
structuring element
Opening33
The effect of the operator is to preserve foreground regions that
have a similar shape to this structuring element
or can completely contain the structuring element
Eliminating all other regions of foreground pixels
Opening34
Effect of opening using a 3times3 square structuring element
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
56
5757
ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
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92 Erosion and Dilation7
Erosion
(B)z = c | c = b + z for b є B
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92 Erosion and Dilation8
Computing the Erosion of a Binary Image
9
For each foreground pixel we superimpose the structuring element on top of the input image so that the origin of the structuring element coincides with the input pixel coordinates
If for every pixel in the structuring element
the corresponding pixel in the image underneath is a foreground pixel then the input pixel is left as it
is Otherwise it is set to background value
The effect of Erosion10
removing any foreground pixel that is not completely surrounded by other white pixels (assuming 8-connectedness)
Such pixels must lie at the edges of white regions and so the practical upshot is that foreground regions shrink (and holes inside a region grow)
11
Effect of Erosion Using a 3times3 Square Structuring Element
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92 Erosion12
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92 Erosion13
Erosion (More examples)
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92 Erosion14
Erosion (More examples)
1515
Erosion in removing salt noise15
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92 Dilation16
Dilation
(B)z = c | c = b + z for b є B
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92 Dilation17
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92 Dilation18
Dilation19
The basic effect of the operator on a binary image is to gradually enlarge the boundaries of regions of foreground pixels
Thus areas of foreground pixels grow in size while holes within those regions become smaller
Dilation Example20
21
Gray level erosion dilation22
1048708 Erosion
1048708 Chose the local minimum over the region defined by the structure element
1048708 Put the minimums value in the same pixel position in the out image Results in darker images and light details are removed
23
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Dilation in noise reduction24
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Dilation in edge detection25
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92 Erosion and Dilation26
Duality
Proof
27
ClosingOpening
93 Opening and Closing
28
ErosionDilation
Opening Closing
Isthmus29
An isthmus (ˈɪsθməs or ˈɪsməs plural isthmuses from Ancient Greekἰσθμός isthmos ldquoneckrdquo) is a narrow strip of land connecting two larger land areas usually with water on either side[1] A tombolo is an isthmus where the strip of land consists of a spit or bar
The Isthmus of PanamaThe Suez Canal goes across the western side of the Sinai Peninsula
30
promiddottrude (prō-troD oD dprime)v promiddottrudmiddoted promiddottrudmiddoting promiddottrudesvtrTo push or thrust outwardvintrTo jut out project See Synonyms at bulge
Example sentencesThe air-conditioner does not protrude into the alleyThey are large-bodied and display a mouthful ofsharp teeth that protrude in Samanthas face and paws protrude from thecutout doorScrub the mussels and use a paring knife toremove any beards that protrude
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93 Opening and Closing31
Opening smoothes the contour of an object breaks narrow
isthmuses and eliminates thin protrusions
Erosion Dilation
Opening is defined as an erosion followed by a dilation using the same structuring element for both operations
Opening32
Opening removes some of the foreground (bright) pixels from the edges of regions of foreground pixels
Opening is less destructive than erosion in general
The exact operation is determined by a
structuring element
Opening33
The effect of the operator is to preserve foreground regions that
have a similar shape to this structuring element
or can completely contain the structuring element
Eliminating all other regions of foreground pixels
Opening34
Effect of opening using a 3times3 square structuring element
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
56
5757
ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
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92 Erosion and Dilation8
Computing the Erosion of a Binary Image
9
For each foreground pixel we superimpose the structuring element on top of the input image so that the origin of the structuring element coincides with the input pixel coordinates
If for every pixel in the structuring element
the corresponding pixel in the image underneath is a foreground pixel then the input pixel is left as it
is Otherwise it is set to background value
The effect of Erosion10
removing any foreground pixel that is not completely surrounded by other white pixels (assuming 8-connectedness)
Such pixels must lie at the edges of white regions and so the practical upshot is that foreground regions shrink (and holes inside a region grow)
11
Effect of Erosion Using a 3times3 Square Structuring Element
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92 Erosion12
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92 Erosion13
Erosion (More examples)
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92 Erosion14
Erosion (More examples)
1515
Erosion in removing salt noise15
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92 Dilation16
Dilation
(B)z = c | c = b + z for b є B
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92 Dilation17
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92 Dilation18
Dilation19
The basic effect of the operator on a binary image is to gradually enlarge the boundaries of regions of foreground pixels
Thus areas of foreground pixels grow in size while holes within those regions become smaller
Dilation Example20
21
Gray level erosion dilation22
1048708 Erosion
1048708 Chose the local minimum over the region defined by the structure element
1048708 Put the minimums value in the same pixel position in the out image Results in darker images and light details are removed
23
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Dilation in noise reduction24
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Dilation in edge detection25
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92 Erosion and Dilation26
Duality
Proof
27
ClosingOpening
93 Opening and Closing
28
ErosionDilation
Opening Closing
Isthmus29
An isthmus (ˈɪsθməs or ˈɪsməs plural isthmuses from Ancient Greekἰσθμός isthmos ldquoneckrdquo) is a narrow strip of land connecting two larger land areas usually with water on either side[1] A tombolo is an isthmus where the strip of land consists of a spit or bar
The Isthmus of PanamaThe Suez Canal goes across the western side of the Sinai Peninsula
30
promiddottrude (prō-troD oD dprime)v promiddottrudmiddoted promiddottrudmiddoting promiddottrudesvtrTo push or thrust outwardvintrTo jut out project See Synonyms at bulge
Example sentencesThe air-conditioner does not protrude into the alleyThey are large-bodied and display a mouthful ofsharp teeth that protrude in Samanthas face and paws protrude from thecutout doorScrub the mussels and use a paring knife toremove any beards that protrude
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93 Opening and Closing31
Opening smoothes the contour of an object breaks narrow
isthmuses and eliminates thin protrusions
Erosion Dilation
Opening is defined as an erosion followed by a dilation using the same structuring element for both operations
Opening32
Opening removes some of the foreground (bright) pixels from the edges of regions of foreground pixels
Opening is less destructive than erosion in general
The exact operation is determined by a
structuring element
Opening33
The effect of the operator is to preserve foreground regions that
have a similar shape to this structuring element
or can completely contain the structuring element
Eliminating all other regions of foreground pixels
Opening34
Effect of opening using a 3times3 square structuring element
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
56
5757
ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
Computing the Erosion of a Binary Image
9
For each foreground pixel we superimpose the structuring element on top of the input image so that the origin of the structuring element coincides with the input pixel coordinates
If for every pixel in the structuring element
the corresponding pixel in the image underneath is a foreground pixel then the input pixel is left as it
is Otherwise it is set to background value
The effect of Erosion10
removing any foreground pixel that is not completely surrounded by other white pixels (assuming 8-connectedness)
Such pixels must lie at the edges of white regions and so the practical upshot is that foreground regions shrink (and holes inside a region grow)
11
Effect of Erosion Using a 3times3 Square Structuring Element
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92 Erosion12
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92 Erosion13
Erosion (More examples)
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92 Erosion14
Erosion (More examples)
1515
Erosion in removing salt noise15
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92 Dilation16
Dilation
(B)z = c | c = b + z for b є B
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92 Dilation17
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92 Dilation18
Dilation19
The basic effect of the operator on a binary image is to gradually enlarge the boundaries of regions of foreground pixels
Thus areas of foreground pixels grow in size while holes within those regions become smaller
Dilation Example20
21
Gray level erosion dilation22
1048708 Erosion
1048708 Chose the local minimum over the region defined by the structure element
1048708 Put the minimums value in the same pixel position in the out image Results in darker images and light details are removed
23
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Dilation in noise reduction24
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Dilation in edge detection25
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92 Erosion and Dilation26
Duality
Proof
27
ClosingOpening
93 Opening and Closing
28
ErosionDilation
Opening Closing
Isthmus29
An isthmus (ˈɪsθməs or ˈɪsməs plural isthmuses from Ancient Greekἰσθμός isthmos ldquoneckrdquo) is a narrow strip of land connecting two larger land areas usually with water on either side[1] A tombolo is an isthmus where the strip of land consists of a spit or bar
The Isthmus of PanamaThe Suez Canal goes across the western side of the Sinai Peninsula
30
promiddottrude (prō-troD oD dprime)v promiddottrudmiddoted promiddottrudmiddoting promiddottrudesvtrTo push or thrust outwardvintrTo jut out project See Synonyms at bulge
Example sentencesThe air-conditioner does not protrude into the alleyThey are large-bodied and display a mouthful ofsharp teeth that protrude in Samanthas face and paws protrude from thecutout doorScrub the mussels and use a paring knife toremove any beards that protrude
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93 Opening and Closing31
Opening smoothes the contour of an object breaks narrow
isthmuses and eliminates thin protrusions
Erosion Dilation
Opening is defined as an erosion followed by a dilation using the same structuring element for both operations
Opening32
Opening removes some of the foreground (bright) pixels from the edges of regions of foreground pixels
Opening is less destructive than erosion in general
The exact operation is determined by a
structuring element
Opening33
The effect of the operator is to preserve foreground regions that
have a similar shape to this structuring element
or can completely contain the structuring element
Eliminating all other regions of foreground pixels
Opening34
Effect of opening using a 3times3 square structuring element
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
56
5757
ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
The effect of Erosion10
removing any foreground pixel that is not completely surrounded by other white pixels (assuming 8-connectedness)
Such pixels must lie at the edges of white regions and so the practical upshot is that foreground regions shrink (and holes inside a region grow)
11
Effect of Erosion Using a 3times3 Square Structuring Element
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92 Erosion12
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92 Erosion13
Erosion (More examples)
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92 Erosion14
Erosion (More examples)
1515
Erosion in removing salt noise15
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92 Dilation16
Dilation
(B)z = c | c = b + z for b є B
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92 Dilation17
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92 Dilation18
Dilation19
The basic effect of the operator on a binary image is to gradually enlarge the boundaries of regions of foreground pixels
Thus areas of foreground pixels grow in size while holes within those regions become smaller
Dilation Example20
21
Gray level erosion dilation22
1048708 Erosion
1048708 Chose the local minimum over the region defined by the structure element
1048708 Put the minimums value in the same pixel position in the out image Results in darker images and light details are removed
23
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Dilation in noise reduction24
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Dilation in edge detection25
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92 Erosion and Dilation26
Duality
Proof
27
ClosingOpening
93 Opening and Closing
28
ErosionDilation
Opening Closing
Isthmus29
An isthmus (ˈɪsθməs or ˈɪsməs plural isthmuses from Ancient Greekἰσθμός isthmos ldquoneckrdquo) is a narrow strip of land connecting two larger land areas usually with water on either side[1] A tombolo is an isthmus where the strip of land consists of a spit or bar
The Isthmus of PanamaThe Suez Canal goes across the western side of the Sinai Peninsula
30
promiddottrude (prō-troD oD dprime)v promiddottrudmiddoted promiddottrudmiddoting promiddottrudesvtrTo push or thrust outwardvintrTo jut out project See Synonyms at bulge
Example sentencesThe air-conditioner does not protrude into the alleyThey are large-bodied and display a mouthful ofsharp teeth that protrude in Samanthas face and paws protrude from thecutout doorScrub the mussels and use a paring knife toremove any beards that protrude
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93 Opening and Closing31
Opening smoothes the contour of an object breaks narrow
isthmuses and eliminates thin protrusions
Erosion Dilation
Opening is defined as an erosion followed by a dilation using the same structuring element for both operations
Opening32
Opening removes some of the foreground (bright) pixels from the edges of regions of foreground pixels
Opening is less destructive than erosion in general
The exact operation is determined by a
structuring element
Opening33
The effect of the operator is to preserve foreground regions that
have a similar shape to this structuring element
or can completely contain the structuring element
Eliminating all other regions of foreground pixels
Opening34
Effect of opening using a 3times3 square structuring element
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
56
5757
ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
11
Effect of Erosion Using a 3times3 Square Structuring Element
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92 Erosion12
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92 Erosion13
Erosion (More examples)
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92 Erosion14
Erosion (More examples)
1515
Erosion in removing salt noise15
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92 Dilation16
Dilation
(B)z = c | c = b + z for b є B
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92 Dilation17
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92 Dilation18
Dilation19
The basic effect of the operator on a binary image is to gradually enlarge the boundaries of regions of foreground pixels
Thus areas of foreground pixels grow in size while holes within those regions become smaller
Dilation Example20
21
Gray level erosion dilation22
1048708 Erosion
1048708 Chose the local minimum over the region defined by the structure element
1048708 Put the minimums value in the same pixel position in the out image Results in darker images and light details are removed
23
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Dilation in noise reduction24
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Dilation in edge detection25
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92 Erosion and Dilation26
Duality
Proof
27
ClosingOpening
93 Opening and Closing
28
ErosionDilation
Opening Closing
Isthmus29
An isthmus (ˈɪsθməs or ˈɪsməs plural isthmuses from Ancient Greekἰσθμός isthmos ldquoneckrdquo) is a narrow strip of land connecting two larger land areas usually with water on either side[1] A tombolo is an isthmus where the strip of land consists of a spit or bar
The Isthmus of PanamaThe Suez Canal goes across the western side of the Sinai Peninsula
30
promiddottrude (prō-troD oD dprime)v promiddottrudmiddoted promiddottrudmiddoting promiddottrudesvtrTo push or thrust outwardvintrTo jut out project See Synonyms at bulge
Example sentencesThe air-conditioner does not protrude into the alleyThey are large-bodied and display a mouthful ofsharp teeth that protrude in Samanthas face and paws protrude from thecutout doorScrub the mussels and use a paring knife toremove any beards that protrude
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93 Opening and Closing31
Opening smoothes the contour of an object breaks narrow
isthmuses and eliminates thin protrusions
Erosion Dilation
Opening is defined as an erosion followed by a dilation using the same structuring element for both operations
Opening32
Opening removes some of the foreground (bright) pixels from the edges of regions of foreground pixels
Opening is less destructive than erosion in general
The exact operation is determined by a
structuring element
Opening33
The effect of the operator is to preserve foreground regions that
have a similar shape to this structuring element
or can completely contain the structuring element
Eliminating all other regions of foreground pixels
Opening34
Effect of opening using a 3times3 square structuring element
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
56
5757
ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
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92 Erosion12
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92 Erosion13
Erosion (More examples)
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92 Erosion14
Erosion (More examples)
1515
Erosion in removing salt noise15
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92 Dilation16
Dilation
(B)z = c | c = b + z for b є B
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92 Dilation17
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92 Dilation18
Dilation19
The basic effect of the operator on a binary image is to gradually enlarge the boundaries of regions of foreground pixels
Thus areas of foreground pixels grow in size while holes within those regions become smaller
Dilation Example20
21
Gray level erosion dilation22
1048708 Erosion
1048708 Chose the local minimum over the region defined by the structure element
1048708 Put the minimums value in the same pixel position in the out image Results in darker images and light details are removed
23
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Dilation in noise reduction24
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Dilation in edge detection25
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92 Erosion and Dilation26
Duality
Proof
27
ClosingOpening
93 Opening and Closing
28
ErosionDilation
Opening Closing
Isthmus29
An isthmus (ˈɪsθməs or ˈɪsməs plural isthmuses from Ancient Greekἰσθμός isthmos ldquoneckrdquo) is a narrow strip of land connecting two larger land areas usually with water on either side[1] A tombolo is an isthmus where the strip of land consists of a spit or bar
The Isthmus of PanamaThe Suez Canal goes across the western side of the Sinai Peninsula
30
promiddottrude (prō-troD oD dprime)v promiddottrudmiddoted promiddottrudmiddoting promiddottrudesvtrTo push or thrust outwardvintrTo jut out project See Synonyms at bulge
Example sentencesThe air-conditioner does not protrude into the alleyThey are large-bodied and display a mouthful ofsharp teeth that protrude in Samanthas face and paws protrude from thecutout doorScrub the mussels and use a paring knife toremove any beards that protrude
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93 Opening and Closing31
Opening smoothes the contour of an object breaks narrow
isthmuses and eliminates thin protrusions
Erosion Dilation
Opening is defined as an erosion followed by a dilation using the same structuring element for both operations
Opening32
Opening removes some of the foreground (bright) pixels from the edges of regions of foreground pixels
Opening is less destructive than erosion in general
The exact operation is determined by a
structuring element
Opening33
The effect of the operator is to preserve foreground regions that
have a similar shape to this structuring element
or can completely contain the structuring element
Eliminating all other regions of foreground pixels
Opening34
Effect of opening using a 3times3 square structuring element
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
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5757
ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
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92 Erosion13
Erosion (More examples)
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92 Erosion14
Erosion (More examples)
1515
Erosion in removing salt noise15
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92 Dilation16
Dilation
(B)z = c | c = b + z for b є B
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92 Dilation17
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92 Dilation18
Dilation19
The basic effect of the operator on a binary image is to gradually enlarge the boundaries of regions of foreground pixels
Thus areas of foreground pixels grow in size while holes within those regions become smaller
Dilation Example20
21
Gray level erosion dilation22
1048708 Erosion
1048708 Chose the local minimum over the region defined by the structure element
1048708 Put the minimums value in the same pixel position in the out image Results in darker images and light details are removed
23
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Dilation in noise reduction24
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Dilation in edge detection25
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92 Erosion and Dilation26
Duality
Proof
27
ClosingOpening
93 Opening and Closing
28
ErosionDilation
Opening Closing
Isthmus29
An isthmus (ˈɪsθməs or ˈɪsməs plural isthmuses from Ancient Greekἰσθμός isthmos ldquoneckrdquo) is a narrow strip of land connecting two larger land areas usually with water on either side[1] A tombolo is an isthmus where the strip of land consists of a spit or bar
The Isthmus of PanamaThe Suez Canal goes across the western side of the Sinai Peninsula
30
promiddottrude (prō-troD oD dprime)v promiddottrudmiddoted promiddottrudmiddoting promiddottrudesvtrTo push or thrust outwardvintrTo jut out project See Synonyms at bulge
Example sentencesThe air-conditioner does not protrude into the alleyThey are large-bodied and display a mouthful ofsharp teeth that protrude in Samanthas face and paws protrude from thecutout doorScrub the mussels and use a paring knife toremove any beards that protrude
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93 Opening and Closing31
Opening smoothes the contour of an object breaks narrow
isthmuses and eliminates thin protrusions
Erosion Dilation
Opening is defined as an erosion followed by a dilation using the same structuring element for both operations
Opening32
Opening removes some of the foreground (bright) pixels from the edges of regions of foreground pixels
Opening is less destructive than erosion in general
The exact operation is determined by a
structuring element
Opening33
The effect of the operator is to preserve foreground regions that
have a similar shape to this structuring element
or can completely contain the structuring element
Eliminating all other regions of foreground pixels
Opening34
Effect of opening using a 3times3 square structuring element
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
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5757
ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
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92 Erosion14
Erosion (More examples)
1515
Erosion in removing salt noise15
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92 Dilation16
Dilation
(B)z = c | c = b + z for b є B
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92 Dilation17
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92 Dilation18
Dilation19
The basic effect of the operator on a binary image is to gradually enlarge the boundaries of regions of foreground pixels
Thus areas of foreground pixels grow in size while holes within those regions become smaller
Dilation Example20
21
Gray level erosion dilation22
1048708 Erosion
1048708 Chose the local minimum over the region defined by the structure element
1048708 Put the minimums value in the same pixel position in the out image Results in darker images and light details are removed
23
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Dilation in noise reduction24
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Dilation in edge detection25
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92 Erosion and Dilation26
Duality
Proof
27
ClosingOpening
93 Opening and Closing
28
ErosionDilation
Opening Closing
Isthmus29
An isthmus (ˈɪsθməs or ˈɪsməs plural isthmuses from Ancient Greekἰσθμός isthmos ldquoneckrdquo) is a narrow strip of land connecting two larger land areas usually with water on either side[1] A tombolo is an isthmus where the strip of land consists of a spit or bar
The Isthmus of PanamaThe Suez Canal goes across the western side of the Sinai Peninsula
30
promiddottrude (prō-troD oD dprime)v promiddottrudmiddoted promiddottrudmiddoting promiddottrudesvtrTo push or thrust outwardvintrTo jut out project See Synonyms at bulge
Example sentencesThe air-conditioner does not protrude into the alleyThey are large-bodied and display a mouthful ofsharp teeth that protrude in Samanthas face and paws protrude from thecutout doorScrub the mussels and use a paring knife toremove any beards that protrude
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93 Opening and Closing31
Opening smoothes the contour of an object breaks narrow
isthmuses and eliminates thin protrusions
Erosion Dilation
Opening is defined as an erosion followed by a dilation using the same structuring element for both operations
Opening32
Opening removes some of the foreground (bright) pixels from the edges of regions of foreground pixels
Opening is less destructive than erosion in general
The exact operation is determined by a
structuring element
Opening33
The effect of the operator is to preserve foreground regions that
have a similar shape to this structuring element
or can completely contain the structuring element
Eliminating all other regions of foreground pixels
Opening34
Effect of opening using a 3times3 square structuring element
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
56
5757
ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
1515
Erosion in removing salt noise15
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92 Dilation16
Dilation
(B)z = c | c = b + z for b є B
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92 Dilation17
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92 Dilation18
Dilation19
The basic effect of the operator on a binary image is to gradually enlarge the boundaries of regions of foreground pixels
Thus areas of foreground pixels grow in size while holes within those regions become smaller
Dilation Example20
21
Gray level erosion dilation22
1048708 Erosion
1048708 Chose the local minimum over the region defined by the structure element
1048708 Put the minimums value in the same pixel position in the out image Results in darker images and light details are removed
23
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Dilation in noise reduction24
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Dilation in edge detection25
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92 Erosion and Dilation26
Duality
Proof
27
ClosingOpening
93 Opening and Closing
28
ErosionDilation
Opening Closing
Isthmus29
An isthmus (ˈɪsθməs or ˈɪsməs plural isthmuses from Ancient Greekἰσθμός isthmos ldquoneckrdquo) is a narrow strip of land connecting two larger land areas usually with water on either side[1] A tombolo is an isthmus where the strip of land consists of a spit or bar
The Isthmus of PanamaThe Suez Canal goes across the western side of the Sinai Peninsula
30
promiddottrude (prō-troD oD dprime)v promiddottrudmiddoted promiddottrudmiddoting promiddottrudesvtrTo push or thrust outwardvintrTo jut out project See Synonyms at bulge
Example sentencesThe air-conditioner does not protrude into the alleyThey are large-bodied and display a mouthful ofsharp teeth that protrude in Samanthas face and paws protrude from thecutout doorScrub the mussels and use a paring knife toremove any beards that protrude
R
C
Gon
zale
z a
nd R
E
W
oods
D
igita
l Im
age
Pro
cess
ing
New
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sey
Pre
ntic
e H
all
3rd e
ditio
n 2
008
93 Opening and Closing31
Opening smoothes the contour of an object breaks narrow
isthmuses and eliminates thin protrusions
Erosion Dilation
Opening is defined as an erosion followed by a dilation using the same structuring element for both operations
Opening32
Opening removes some of the foreground (bright) pixels from the edges of regions of foreground pixels
Opening is less destructive than erosion in general
The exact operation is determined by a
structuring element
Opening33
The effect of the operator is to preserve foreground regions that
have a similar shape to this structuring element
or can completely contain the structuring element
Eliminating all other regions of foreground pixels
Opening34
Effect of opening using a 3times3 square structuring element
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
R
C
Gon
zale
z a
nd R
E
W
oods
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
R
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nd R
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D
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
R
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nd R
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
R
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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nd R
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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cess
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
R
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z a
nd R
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94 The Hit-or-Miss Transformation
56
5757
ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
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92 Dilation16
Dilation
(B)z = c | c = b + z for b є B
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92 Dilation17
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92 Dilation18
Dilation19
The basic effect of the operator on a binary image is to gradually enlarge the boundaries of regions of foreground pixels
Thus areas of foreground pixels grow in size while holes within those regions become smaller
Dilation Example20
21
Gray level erosion dilation22
1048708 Erosion
1048708 Chose the local minimum over the region defined by the structure element
1048708 Put the minimums value in the same pixel position in the out image Results in darker images and light details are removed
23
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Dilation in noise reduction24
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Dilation in edge detection25
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92 Erosion and Dilation26
Duality
Proof
27
ClosingOpening
93 Opening and Closing
28
ErosionDilation
Opening Closing
Isthmus29
An isthmus (ˈɪsθməs or ˈɪsməs plural isthmuses from Ancient Greekἰσθμός isthmos ldquoneckrdquo) is a narrow strip of land connecting two larger land areas usually with water on either side[1] A tombolo is an isthmus where the strip of land consists of a spit or bar
The Isthmus of PanamaThe Suez Canal goes across the western side of the Sinai Peninsula
30
promiddottrude (prō-troD oD dprime)v promiddottrudmiddoted promiddottrudmiddoting promiddottrudesvtrTo push or thrust outwardvintrTo jut out project See Synonyms at bulge
Example sentencesThe air-conditioner does not protrude into the alleyThey are large-bodied and display a mouthful ofsharp teeth that protrude in Samanthas face and paws protrude from thecutout doorScrub the mussels and use a paring knife toremove any beards that protrude
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93 Opening and Closing31
Opening smoothes the contour of an object breaks narrow
isthmuses and eliminates thin protrusions
Erosion Dilation
Opening is defined as an erosion followed by a dilation using the same structuring element for both operations
Opening32
Opening removes some of the foreground (bright) pixels from the edges of regions of foreground pixels
Opening is less destructive than erosion in general
The exact operation is determined by a
structuring element
Opening33
The effect of the operator is to preserve foreground regions that
have a similar shape to this structuring element
or can completely contain the structuring element
Eliminating all other regions of foreground pixels
Opening34
Effect of opening using a 3times3 square structuring element
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
56
5757
ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
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92 Dilation17
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92 Dilation18
Dilation19
The basic effect of the operator on a binary image is to gradually enlarge the boundaries of regions of foreground pixels
Thus areas of foreground pixels grow in size while holes within those regions become smaller
Dilation Example20
21
Gray level erosion dilation22
1048708 Erosion
1048708 Chose the local minimum over the region defined by the structure element
1048708 Put the minimums value in the same pixel position in the out image Results in darker images and light details are removed
23
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Dilation in noise reduction24
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Dilation in edge detection25
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92 Erosion and Dilation26
Duality
Proof
27
ClosingOpening
93 Opening and Closing
28
ErosionDilation
Opening Closing
Isthmus29
An isthmus (ˈɪsθməs or ˈɪsməs plural isthmuses from Ancient Greekἰσθμός isthmos ldquoneckrdquo) is a narrow strip of land connecting two larger land areas usually with water on either side[1] A tombolo is an isthmus where the strip of land consists of a spit or bar
The Isthmus of PanamaThe Suez Canal goes across the western side of the Sinai Peninsula
30
promiddottrude (prō-troD oD dprime)v promiddottrudmiddoted promiddottrudmiddoting promiddottrudesvtrTo push or thrust outwardvintrTo jut out project See Synonyms at bulge
Example sentencesThe air-conditioner does not protrude into the alleyThey are large-bodied and display a mouthful ofsharp teeth that protrude in Samanthas face and paws protrude from thecutout doorScrub the mussels and use a paring knife toremove any beards that protrude
R
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zale
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nd R
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oods
D
igita
l Im
age
Pro
cess
ing
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sey
Pre
ntic
e H
all
3rd e
ditio
n 2
008
93 Opening and Closing31
Opening smoothes the contour of an object breaks narrow
isthmuses and eliminates thin protrusions
Erosion Dilation
Opening is defined as an erosion followed by a dilation using the same structuring element for both operations
Opening32
Opening removes some of the foreground (bright) pixels from the edges of regions of foreground pixels
Opening is less destructive than erosion in general
The exact operation is determined by a
structuring element
Opening33
The effect of the operator is to preserve foreground regions that
have a similar shape to this structuring element
or can completely contain the structuring element
Eliminating all other regions of foreground pixels
Opening34
Effect of opening using a 3times3 square structuring element
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
R
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nd R
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
R
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nd R
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94 The Hit-or-Miss Transformation
56
5757
ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
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92 Dilation18
Dilation19
The basic effect of the operator on a binary image is to gradually enlarge the boundaries of regions of foreground pixels
Thus areas of foreground pixels grow in size while holes within those regions become smaller
Dilation Example20
21
Gray level erosion dilation22
1048708 Erosion
1048708 Chose the local minimum over the region defined by the structure element
1048708 Put the minimums value in the same pixel position in the out image Results in darker images and light details are removed
23
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all
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008
Dilation in noise reduction24
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Dilation in edge detection25
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92 Erosion and Dilation26
Duality
Proof
27
ClosingOpening
93 Opening and Closing
28
ErosionDilation
Opening Closing
Isthmus29
An isthmus (ˈɪsθməs or ˈɪsməs plural isthmuses from Ancient Greekἰσθμός isthmos ldquoneckrdquo) is a narrow strip of land connecting two larger land areas usually with water on either side[1] A tombolo is an isthmus where the strip of land consists of a spit or bar
The Isthmus of PanamaThe Suez Canal goes across the western side of the Sinai Peninsula
30
promiddottrude (prō-troD oD dprime)v promiddottrudmiddoted promiddottrudmiddoting promiddottrudesvtrTo push or thrust outwardvintrTo jut out project See Synonyms at bulge
Example sentencesThe air-conditioner does not protrude into the alleyThey are large-bodied and display a mouthful ofsharp teeth that protrude in Samanthas face and paws protrude from thecutout doorScrub the mussels and use a paring knife toremove any beards that protrude
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93 Opening and Closing31
Opening smoothes the contour of an object breaks narrow
isthmuses and eliminates thin protrusions
Erosion Dilation
Opening is defined as an erosion followed by a dilation using the same structuring element for both operations
Opening32
Opening removes some of the foreground (bright) pixels from the edges of regions of foreground pixels
Opening is less destructive than erosion in general
The exact operation is determined by a
structuring element
Opening33
The effect of the operator is to preserve foreground regions that
have a similar shape to this structuring element
or can completely contain the structuring element
Eliminating all other regions of foreground pixels
Opening34
Effect of opening using a 3times3 square structuring element
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
R
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
56
5757
ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
Dilation19
The basic effect of the operator on a binary image is to gradually enlarge the boundaries of regions of foreground pixels
Thus areas of foreground pixels grow in size while holes within those regions become smaller
Dilation Example20
21
Gray level erosion dilation22
1048708 Erosion
1048708 Chose the local minimum over the region defined by the structure element
1048708 Put the minimums value in the same pixel position in the out image Results in darker images and light details are removed
23
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Dilation in noise reduction24
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Dilation in edge detection25
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92 Erosion and Dilation26
Duality
Proof
27
ClosingOpening
93 Opening and Closing
28
ErosionDilation
Opening Closing
Isthmus29
An isthmus (ˈɪsθməs or ˈɪsməs plural isthmuses from Ancient Greekἰσθμός isthmos ldquoneckrdquo) is a narrow strip of land connecting two larger land areas usually with water on either side[1] A tombolo is an isthmus where the strip of land consists of a spit or bar
The Isthmus of PanamaThe Suez Canal goes across the western side of the Sinai Peninsula
30
promiddottrude (prō-troD oD dprime)v promiddottrudmiddoted promiddottrudmiddoting promiddottrudesvtrTo push or thrust outwardvintrTo jut out project See Synonyms at bulge
Example sentencesThe air-conditioner does not protrude into the alleyThey are large-bodied and display a mouthful ofsharp teeth that protrude in Samanthas face and paws protrude from thecutout doorScrub the mussels and use a paring knife toremove any beards that protrude
R
C
Gon
zale
z a
nd R
E
W
oods
D
igita
l Im
age
Pro
cess
ing
New
Jer
sey
Pre
ntic
e H
all
3rd e
ditio
n 2
008
93 Opening and Closing31
Opening smoothes the contour of an object breaks narrow
isthmuses and eliminates thin protrusions
Erosion Dilation
Opening is defined as an erosion followed by a dilation using the same structuring element for both operations
Opening32
Opening removes some of the foreground (bright) pixels from the edges of regions of foreground pixels
Opening is less destructive than erosion in general
The exact operation is determined by a
structuring element
Opening33
The effect of the operator is to preserve foreground regions that
have a similar shape to this structuring element
or can completely contain the structuring element
Eliminating all other regions of foreground pixels
Opening34
Effect of opening using a 3times3 square structuring element
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
R
C
Gon
zale
z a
nd R
E
W
oods
D
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l Im
age
Pro
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
R
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nd R
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oods
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
R
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nd R
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ntic
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93 Opening and Closing40
Opening in removing salt noise
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cess
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ntic
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008
93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
R
C
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zale
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nd R
E
W
oods
D
igita
l Im
age
Pro
cess
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ntic
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
R
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nd R
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cess
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all
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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nd R
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age
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cess
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ntic
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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008
93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
R
C
Gon
zale
z a
nd R
E
W
oods
D
igita
l Im
age
Pro
cess
ing
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sey
Pre
ntic
e H
all
3rd e
ditio
n 2
008
94 The Hit-or-Miss Transformation
56
5757
ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
R
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
Dilation Example20
21
Gray level erosion dilation22
1048708 Erosion
1048708 Chose the local minimum over the region defined by the structure element
1048708 Put the minimums value in the same pixel position in the out image Results in darker images and light details are removed
23
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Dilation in noise reduction24
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Dilation in edge detection25
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008
92 Erosion and Dilation26
Duality
Proof
27
ClosingOpening
93 Opening and Closing
28
ErosionDilation
Opening Closing
Isthmus29
An isthmus (ˈɪsθməs or ˈɪsməs plural isthmuses from Ancient Greekἰσθμός isthmos ldquoneckrdquo) is a narrow strip of land connecting two larger land areas usually with water on either side[1] A tombolo is an isthmus where the strip of land consists of a spit or bar
The Isthmus of PanamaThe Suez Canal goes across the western side of the Sinai Peninsula
30
promiddottrude (prō-troD oD dprime)v promiddottrudmiddoted promiddottrudmiddoting promiddottrudesvtrTo push or thrust outwardvintrTo jut out project See Synonyms at bulge
Example sentencesThe air-conditioner does not protrude into the alleyThey are large-bodied and display a mouthful ofsharp teeth that protrude in Samanthas face and paws protrude from thecutout doorScrub the mussels and use a paring knife toremove any beards that protrude
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93 Opening and Closing31
Opening smoothes the contour of an object breaks narrow
isthmuses and eliminates thin protrusions
Erosion Dilation
Opening is defined as an erosion followed by a dilation using the same structuring element for both operations
Opening32
Opening removes some of the foreground (bright) pixels from the edges of regions of foreground pixels
Opening is less destructive than erosion in general
The exact operation is determined by a
structuring element
Opening33
The effect of the operator is to preserve foreground regions that
have a similar shape to this structuring element
or can completely contain the structuring element
Eliminating all other regions of foreground pixels
Opening34
Effect of opening using a 3times3 square structuring element
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
56
5757
ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
21
Gray level erosion dilation22
1048708 Erosion
1048708 Chose the local minimum over the region defined by the structure element
1048708 Put the minimums value in the same pixel position in the out image Results in darker images and light details are removed
23
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Dilation in noise reduction24
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Dilation in edge detection25
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92 Erosion and Dilation26
Duality
Proof
27
ClosingOpening
93 Opening and Closing
28
ErosionDilation
Opening Closing
Isthmus29
An isthmus (ˈɪsθməs or ˈɪsməs plural isthmuses from Ancient Greekἰσθμός isthmos ldquoneckrdquo) is a narrow strip of land connecting two larger land areas usually with water on either side[1] A tombolo is an isthmus where the strip of land consists of a spit or bar
The Isthmus of PanamaThe Suez Canal goes across the western side of the Sinai Peninsula
30
promiddottrude (prō-troD oD dprime)v promiddottrudmiddoted promiddottrudmiddoting promiddottrudesvtrTo push or thrust outwardvintrTo jut out project See Synonyms at bulge
Example sentencesThe air-conditioner does not protrude into the alleyThey are large-bodied and display a mouthful ofsharp teeth that protrude in Samanthas face and paws protrude from thecutout doorScrub the mussels and use a paring knife toremove any beards that protrude
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008
93 Opening and Closing31
Opening smoothes the contour of an object breaks narrow
isthmuses and eliminates thin protrusions
Erosion Dilation
Opening is defined as an erosion followed by a dilation using the same structuring element for both operations
Opening32
Opening removes some of the foreground (bright) pixels from the edges of regions of foreground pixels
Opening is less destructive than erosion in general
The exact operation is determined by a
structuring element
Opening33
The effect of the operator is to preserve foreground regions that
have a similar shape to this structuring element
or can completely contain the structuring element
Eliminating all other regions of foreground pixels
Opening34
Effect of opening using a 3times3 square structuring element
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
56
5757
ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
Gray level erosion dilation22
1048708 Erosion
1048708 Chose the local minimum over the region defined by the structure element
1048708 Put the minimums value in the same pixel position in the out image Results in darker images and light details are removed
23
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Dilation in noise reduction24
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Dilation in edge detection25
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92 Erosion and Dilation26
Duality
Proof
27
ClosingOpening
93 Opening and Closing
28
ErosionDilation
Opening Closing
Isthmus29
An isthmus (ˈɪsθməs or ˈɪsməs plural isthmuses from Ancient Greekἰσθμός isthmos ldquoneckrdquo) is a narrow strip of land connecting two larger land areas usually with water on either side[1] A tombolo is an isthmus where the strip of land consists of a spit or bar
The Isthmus of PanamaThe Suez Canal goes across the western side of the Sinai Peninsula
30
promiddottrude (prō-troD oD dprime)v promiddottrudmiddoted promiddottrudmiddoting promiddottrudesvtrTo push or thrust outwardvintrTo jut out project See Synonyms at bulge
Example sentencesThe air-conditioner does not protrude into the alleyThey are large-bodied and display a mouthful ofsharp teeth that protrude in Samanthas face and paws protrude from thecutout doorScrub the mussels and use a paring knife toremove any beards that protrude
R
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zale
z a
nd R
E
W
oods
D
igita
l Im
age
Pro
cess
ing
New
Jer
sey
Pre
ntic
e H
all
3rd e
ditio
n 2
008
93 Opening and Closing31
Opening smoothes the contour of an object breaks narrow
isthmuses and eliminates thin protrusions
Erosion Dilation
Opening is defined as an erosion followed by a dilation using the same structuring element for both operations
Opening32
Opening removes some of the foreground (bright) pixels from the edges of regions of foreground pixels
Opening is less destructive than erosion in general
The exact operation is determined by a
structuring element
Opening33
The effect of the operator is to preserve foreground regions that
have a similar shape to this structuring element
or can completely contain the structuring element
Eliminating all other regions of foreground pixels
Opening34
Effect of opening using a 3times3 square structuring element
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
R
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
56
5757
ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
23
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Dilation in noise reduction24
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Dilation in edge detection25
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92 Erosion and Dilation26
Duality
Proof
27
ClosingOpening
93 Opening and Closing
28
ErosionDilation
Opening Closing
Isthmus29
An isthmus (ˈɪsθməs or ˈɪsməs plural isthmuses from Ancient Greekἰσθμός isthmos ldquoneckrdquo) is a narrow strip of land connecting two larger land areas usually with water on either side[1] A tombolo is an isthmus where the strip of land consists of a spit or bar
The Isthmus of PanamaThe Suez Canal goes across the western side of the Sinai Peninsula
30
promiddottrude (prō-troD oD dprime)v promiddottrudmiddoted promiddottrudmiddoting promiddottrudesvtrTo push or thrust outwardvintrTo jut out project See Synonyms at bulge
Example sentencesThe air-conditioner does not protrude into the alleyThey are large-bodied and display a mouthful ofsharp teeth that protrude in Samanthas face and paws protrude from thecutout doorScrub the mussels and use a paring knife toremove any beards that protrude
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93 Opening and Closing31
Opening smoothes the contour of an object breaks narrow
isthmuses and eliminates thin protrusions
Erosion Dilation
Opening is defined as an erosion followed by a dilation using the same structuring element for both operations
Opening32
Opening removes some of the foreground (bright) pixels from the edges of regions of foreground pixels
Opening is less destructive than erosion in general
The exact operation is determined by a
structuring element
Opening33
The effect of the operator is to preserve foreground regions that
have a similar shape to this structuring element
or can completely contain the structuring element
Eliminating all other regions of foreground pixels
Opening34
Effect of opening using a 3times3 square structuring element
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
R
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zale
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nd R
E
W
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D
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Pro
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94 The Hit-or-Miss Transformation
56
5757
ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
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Dilation in noise reduction24
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Dilation in edge detection25
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92 Erosion and Dilation26
Duality
Proof
27
ClosingOpening
93 Opening and Closing
28
ErosionDilation
Opening Closing
Isthmus29
An isthmus (ˈɪsθməs or ˈɪsməs plural isthmuses from Ancient Greekἰσθμός isthmos ldquoneckrdquo) is a narrow strip of land connecting two larger land areas usually with water on either side[1] A tombolo is an isthmus where the strip of land consists of a spit or bar
The Isthmus of PanamaThe Suez Canal goes across the western side of the Sinai Peninsula
30
promiddottrude (prō-troD oD dprime)v promiddottrudmiddoted promiddottrudmiddoting promiddottrudesvtrTo push or thrust outwardvintrTo jut out project See Synonyms at bulge
Example sentencesThe air-conditioner does not protrude into the alleyThey are large-bodied and display a mouthful ofsharp teeth that protrude in Samanthas face and paws protrude from thecutout doorScrub the mussels and use a paring knife toremove any beards that protrude
R
C
Gon
zale
z a
nd R
E
W
oods
D
igita
l Im
age
Pro
cess
ing
New
Jer
sey
Pre
ntic
e H
all
3rd e
ditio
n 2
008
93 Opening and Closing31
Opening smoothes the contour of an object breaks narrow
isthmuses and eliminates thin protrusions
Erosion Dilation
Opening is defined as an erosion followed by a dilation using the same structuring element for both operations
Opening32
Opening removes some of the foreground (bright) pixels from the edges of regions of foreground pixels
Opening is less destructive than erosion in general
The exact operation is determined by a
structuring element
Opening33
The effect of the operator is to preserve foreground regions that
have a similar shape to this structuring element
or can completely contain the structuring element
Eliminating all other regions of foreground pixels
Opening34
Effect of opening using a 3times3 square structuring element
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
R
C
Gon
zale
z a
nd R
E
W
oods
D
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
R
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nd R
E
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D
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Pro
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
R
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nd R
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
56
5757
ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
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Dilation in edge detection25
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92 Erosion and Dilation26
Duality
Proof
27
ClosingOpening
93 Opening and Closing
28
ErosionDilation
Opening Closing
Isthmus29
An isthmus (ˈɪsθməs or ˈɪsməs plural isthmuses from Ancient Greekἰσθμός isthmos ldquoneckrdquo) is a narrow strip of land connecting two larger land areas usually with water on either side[1] A tombolo is an isthmus where the strip of land consists of a spit or bar
The Isthmus of PanamaThe Suez Canal goes across the western side of the Sinai Peninsula
30
promiddottrude (prō-troD oD dprime)v promiddottrudmiddoted promiddottrudmiddoting promiddottrudesvtrTo push or thrust outwardvintrTo jut out project See Synonyms at bulge
Example sentencesThe air-conditioner does not protrude into the alleyThey are large-bodied and display a mouthful ofsharp teeth that protrude in Samanthas face and paws protrude from thecutout doorScrub the mussels and use a paring knife toremove any beards that protrude
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93 Opening and Closing31
Opening smoothes the contour of an object breaks narrow
isthmuses and eliminates thin protrusions
Erosion Dilation
Opening is defined as an erosion followed by a dilation using the same structuring element for both operations
Opening32
Opening removes some of the foreground (bright) pixels from the edges of regions of foreground pixels
Opening is less destructive than erosion in general
The exact operation is determined by a
structuring element
Opening33
The effect of the operator is to preserve foreground regions that
have a similar shape to this structuring element
or can completely contain the structuring element
Eliminating all other regions of foreground pixels
Opening34
Effect of opening using a 3times3 square structuring element
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
56
5757
ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
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92 Erosion and Dilation26
Duality
Proof
27
ClosingOpening
93 Opening and Closing
28
ErosionDilation
Opening Closing
Isthmus29
An isthmus (ˈɪsθməs or ˈɪsməs plural isthmuses from Ancient Greekἰσθμός isthmos ldquoneckrdquo) is a narrow strip of land connecting two larger land areas usually with water on either side[1] A tombolo is an isthmus where the strip of land consists of a spit or bar
The Isthmus of PanamaThe Suez Canal goes across the western side of the Sinai Peninsula
30
promiddottrude (prō-troD oD dprime)v promiddottrudmiddoted promiddottrudmiddoting promiddottrudesvtrTo push or thrust outwardvintrTo jut out project See Synonyms at bulge
Example sentencesThe air-conditioner does not protrude into the alleyThey are large-bodied and display a mouthful ofsharp teeth that protrude in Samanthas face and paws protrude from thecutout doorScrub the mussels and use a paring knife toremove any beards that protrude
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008
93 Opening and Closing31
Opening smoothes the contour of an object breaks narrow
isthmuses and eliminates thin protrusions
Erosion Dilation
Opening is defined as an erosion followed by a dilation using the same structuring element for both operations
Opening32
Opening removes some of the foreground (bright) pixels from the edges of regions of foreground pixels
Opening is less destructive than erosion in general
The exact operation is determined by a
structuring element
Opening33
The effect of the operator is to preserve foreground regions that
have a similar shape to this structuring element
or can completely contain the structuring element
Eliminating all other regions of foreground pixels
Opening34
Effect of opening using a 3times3 square structuring element
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
56
5757
ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
27
ClosingOpening
93 Opening and Closing
28
ErosionDilation
Opening Closing
Isthmus29
An isthmus (ˈɪsθməs or ˈɪsməs plural isthmuses from Ancient Greekἰσθμός isthmos ldquoneckrdquo) is a narrow strip of land connecting two larger land areas usually with water on either side[1] A tombolo is an isthmus where the strip of land consists of a spit or bar
The Isthmus of PanamaThe Suez Canal goes across the western side of the Sinai Peninsula
30
promiddottrude (prō-troD oD dprime)v promiddottrudmiddoted promiddottrudmiddoting promiddottrudesvtrTo push or thrust outwardvintrTo jut out project See Synonyms at bulge
Example sentencesThe air-conditioner does not protrude into the alleyThey are large-bodied and display a mouthful ofsharp teeth that protrude in Samanthas face and paws protrude from thecutout doorScrub the mussels and use a paring knife toremove any beards that protrude
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93 Opening and Closing31
Opening smoothes the contour of an object breaks narrow
isthmuses and eliminates thin protrusions
Erosion Dilation
Opening is defined as an erosion followed by a dilation using the same structuring element for both operations
Opening32
Opening removes some of the foreground (bright) pixels from the edges of regions of foreground pixels
Opening is less destructive than erosion in general
The exact operation is determined by a
structuring element
Opening33
The effect of the operator is to preserve foreground regions that
have a similar shape to this structuring element
or can completely contain the structuring element
Eliminating all other regions of foreground pixels
Opening34
Effect of opening using a 3times3 square structuring element
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
56
5757
ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
28
ErosionDilation
Opening Closing
Isthmus29
An isthmus (ˈɪsθməs or ˈɪsməs plural isthmuses from Ancient Greekἰσθμός isthmos ldquoneckrdquo) is a narrow strip of land connecting two larger land areas usually with water on either side[1] A tombolo is an isthmus where the strip of land consists of a spit or bar
The Isthmus of PanamaThe Suez Canal goes across the western side of the Sinai Peninsula
30
promiddottrude (prō-troD oD dprime)v promiddottrudmiddoted promiddottrudmiddoting promiddottrudesvtrTo push or thrust outwardvintrTo jut out project See Synonyms at bulge
Example sentencesThe air-conditioner does not protrude into the alleyThey are large-bodied and display a mouthful ofsharp teeth that protrude in Samanthas face and paws protrude from thecutout doorScrub the mussels and use a paring knife toremove any beards that protrude
R
C
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zale
z a
nd R
E
W
oods
D
igita
l Im
age
Pro
cess
ing
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sey
Pre
ntic
e H
all
3rd e
ditio
n 2
008
93 Opening and Closing31
Opening smoothes the contour of an object breaks narrow
isthmuses and eliminates thin protrusions
Erosion Dilation
Opening is defined as an erosion followed by a dilation using the same structuring element for both operations
Opening32
Opening removes some of the foreground (bright) pixels from the edges of regions of foreground pixels
Opening is less destructive than erosion in general
The exact operation is determined by a
structuring element
Opening33
The effect of the operator is to preserve foreground regions that
have a similar shape to this structuring element
or can completely contain the structuring element
Eliminating all other regions of foreground pixels
Opening34
Effect of opening using a 3times3 square structuring element
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
R
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zale
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nd R
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
R
C
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zale
z a
nd R
E
W
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94 The Hit-or-Miss Transformation
56
5757
ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
Isthmus29
An isthmus (ˈɪsθməs or ˈɪsməs plural isthmuses from Ancient Greekἰσθμός isthmos ldquoneckrdquo) is a narrow strip of land connecting two larger land areas usually with water on either side[1] A tombolo is an isthmus where the strip of land consists of a spit or bar
The Isthmus of PanamaThe Suez Canal goes across the western side of the Sinai Peninsula
30
promiddottrude (prō-troD oD dprime)v promiddottrudmiddoted promiddottrudmiddoting promiddottrudesvtrTo push or thrust outwardvintrTo jut out project See Synonyms at bulge
Example sentencesThe air-conditioner does not protrude into the alleyThey are large-bodied and display a mouthful ofsharp teeth that protrude in Samanthas face and paws protrude from thecutout doorScrub the mussels and use a paring knife toremove any beards that protrude
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93 Opening and Closing31
Opening smoothes the contour of an object breaks narrow
isthmuses and eliminates thin protrusions
Erosion Dilation
Opening is defined as an erosion followed by a dilation using the same structuring element for both operations
Opening32
Opening removes some of the foreground (bright) pixels from the edges of regions of foreground pixels
Opening is less destructive than erosion in general
The exact operation is determined by a
structuring element
Opening33
The effect of the operator is to preserve foreground regions that
have a similar shape to this structuring element
or can completely contain the structuring element
Eliminating all other regions of foreground pixels
Opening34
Effect of opening using a 3times3 square structuring element
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
56
5757
ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
30
promiddottrude (prō-troD oD dprime)v promiddottrudmiddoted promiddottrudmiddoting promiddottrudesvtrTo push or thrust outwardvintrTo jut out project See Synonyms at bulge
Example sentencesThe air-conditioner does not protrude into the alleyThey are large-bodied and display a mouthful ofsharp teeth that protrude in Samanthas face and paws protrude from thecutout doorScrub the mussels and use a paring knife toremove any beards that protrude
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008
93 Opening and Closing31
Opening smoothes the contour of an object breaks narrow
isthmuses and eliminates thin protrusions
Erosion Dilation
Opening is defined as an erosion followed by a dilation using the same structuring element for both operations
Opening32
Opening removes some of the foreground (bright) pixels from the edges of regions of foreground pixels
Opening is less destructive than erosion in general
The exact operation is determined by a
structuring element
Opening33
The effect of the operator is to preserve foreground regions that
have a similar shape to this structuring element
or can completely contain the structuring element
Eliminating all other regions of foreground pixels
Opening34
Effect of opening using a 3times3 square structuring element
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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zale
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nd R
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94 The Hit-or-Miss Transformation
56
5757
ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
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93 Opening and Closing31
Opening smoothes the contour of an object breaks narrow
isthmuses and eliminates thin protrusions
Erosion Dilation
Opening is defined as an erosion followed by a dilation using the same structuring element for both operations
Opening32
Opening removes some of the foreground (bright) pixels from the edges of regions of foreground pixels
Opening is less destructive than erosion in general
The exact operation is determined by a
structuring element
Opening33
The effect of the operator is to preserve foreground regions that
have a similar shape to this structuring element
or can completely contain the structuring element
Eliminating all other regions of foreground pixels
Opening34
Effect of opening using a 3times3 square structuring element
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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Closing for pepper noise
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Closing for salt noise
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
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ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
Opening32
Opening removes some of the foreground (bright) pixels from the edges of regions of foreground pixels
Opening is less destructive than erosion in general
The exact operation is determined by a
structuring element
Opening33
The effect of the operator is to preserve foreground regions that
have a similar shape to this structuring element
or can completely contain the structuring element
Eliminating all other regions of foreground pixels
Opening34
Effect of opening using a 3times3 square structuring element
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
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93 Opening37
Opening
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Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
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ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
Opening33
The effect of the operator is to preserve foreground regions that
have a similar shape to this structuring element
or can completely contain the structuring element
Eliminating all other regions of foreground pixels
Opening34
Effect of opening using a 3times3 square structuring element
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
56
5757
ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
Opening34
Effect of opening using a 3times3 square structuring element
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
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93 Opening37
Opening
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Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
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ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
Opening35
opening can be very useful for separating out particularly shaped objects from the background
opening is far from being a universal 2-D object recognizersegmenter
Eg if we use a long thin structuring element to locate a pencils in our image any one such element will only find pencils at a particular orientation
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
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ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
Opening36
If it is necessary to find pencils at other orientations then differently oriented elements must be used to look for each desired orientation
It is also necessary to be very careful that the structuring element chosen does not eliminate too many desirable objects or retain too many undesirable ones and sometimes this can be a delicate or even impossible balance
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
56
5757
ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
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93 Opening37
Opening
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
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ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
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93 Opening38
Opening
Separate out the circles from the lines so that they can be counted Opening with a disk shaped structuring element 11
pixels in diameter gives
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
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ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
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93 Opening39
Opening
Extracting the horizontal and vertical lines The results of an Opening with a 3times9 vertically and 9x3
horizontally oriented structuring element is shown
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
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ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
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93 Opening and Closing40
Opening in removing salt noise
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
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ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
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93 Opening and Closing41
Opening in removing pepper noise
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
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ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
42
93 Closing42
bull Closing
Smooth sections of contours but as opposed to Opening it generally fuses narrow breaks and long thin gulfs eliminates small holes and fills gaps in the contour
ErosionDilation
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
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ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
Closing43
Closing is opening performed in reverse Closing is the dual of opening
ie closing the foreground pixels with a particular structuring element is equivalent to closing the background with the same element
a dilation followed by an erosion using the same structuring element for both operations
The closing operator requires two inputs an image to be closed a structuring element
Closing44
Effect of closing using a 3times3 square structuring element
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing50
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
56
5757
ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
Closing44
Effect of closing using a 3times3 square structuring element
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Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
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ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
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93 Closing45
Closing
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
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ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
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93 Closing exapmles46
Removing the small holes while retaining the large holes
Closing with a disk-shaped structuring element with a diameter larger than the
smaller holes
Closingwith a 22
pixel diameter
disk
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
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ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
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93 Closing examples47
Enhance binary images of objects obtained from thresholding
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
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5757
ErosionDilation
Opening Closing
The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
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93 Closing48
Closing for pepper noise
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93 Closing49
Closing for salt noise
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(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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94 The Hit-or-Miss Transformation
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The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation58
Erosion
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- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
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93 Closing49
Closing for salt noise
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(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
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(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
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ErosionDilation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
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93 Opening and Closing51
(a) A o B is a subset (subimage) of A(b) If C is a subset of D then C o B is a subset of D o B(c) (A o B) o B = A o B
(a) A is a subset (subimage) of A bull B(b) If C is a subset of D then C bull B is a subset of D bull B(c) (AbullB)bullB=AbullB
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
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ErosionDilation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
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93 Opening and Closing52
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
94 The Hit-or-Miss Transformation
53
The hit-and-miss transform is a general binary morphological operation that can be used to look for particular patterns of foreground and background pixels in an image It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
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ErosionDilation
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The Hit-or-Miss Transformation
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
-
94 The Hit-or-Miss Transformation
54
The structuring element used in the hit-and-miss is a slight extension to the type that has been introduced for erosion and dilation in that it can contain both foreground and background pixels rather than just foreground pixels
Example of the extended type of structuring element used in hit-and-miss operations This particular element can be used to find corner points
94 The Hit-or-Miss Transformation
55
Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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94 The Hit-or-Miss Transformation
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ErosionDilation
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94 The Hit-or-Miss Transformation58
Erosion
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- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
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94 The Hit-or-Miss Transformation
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Four structuring elements used for corner finding in binary images using the hit-and-miss transform Note that they are really all the same element but rotated by different amounts
After obtaining the locations of corners in each orientation We can then simply OR all these images together to get the final result showing the locations of all right angle convex corners in any orientation
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- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
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94 The Hit-or-Miss Transformation58
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- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
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94 The Hit-or-Miss Transformation58
Erosion
Dilation
- DIGITAL IMAGE PROCESSING
- Table of Contents
- Preview
- 91 Preliminaries
- 91 Preliminaries (2)
- 91 Preliminaries (3)
- 92 Erosion and Dilation
- 92 Erosion and Dilation (2)
- Computing the Erosion of a Binary Image
- The effect of Erosion
- Slide 11
- 92 Erosion
- 92 Erosion (2)
- 92 Erosion (3)
- Slide 15
- 92 Dilation
- 92 Dilation (2)
- 92 Dilation (3)
- Dilation
- Dilation Example
- Slide 21
- Gray level erosion dilation
- Slide 23
- Dilation in noise reduction
- Dilation in edge detection
- 92 Erosion and Dilation (3)
- 93 Opening and Closing
- Slide 28
- Isthmus
- Slide 30
- 93 Opening and Closing (2)
- Opening
- Opening (2)
- Opening (3)
- Opening (4)
- Opening (5)
- 93 Opening
- 93 Opening (2)
- 93 Opening (3)
- 93 Opening and Closing (3)
- 93 Opening and Closing (4)
- Slide 42
- Closing
- Closing (2)
- 93 Closing
- 93 Closing exapmles
- 93 Closing examples
- 93 Closing (2)
- 93 Closing (3)
- 93 Opening and Closing (5)
- 93 Opening and Closing (6)
- 93 Opening and Closing (7)
- 94 The Hit-or-Miss Transformation
- 94 The Hit-or-Miss Transformation (2)
- 94 The Hit-or-Miss Transformation (3)
- 94 The Hit-or-Miss Transformation (4)
- Slide 57
- 94 The Hit-or-Miss Transformation (5)
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