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)

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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)

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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

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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)

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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

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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)

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91 Preliminaries5

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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)

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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

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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)

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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

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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)

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92 Erosion and Dilation8

Computing the Erosion of a Binary Image

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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)

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)

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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Erosion (More examples)

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Erosion in removing salt noise15

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92 Dilation16

Dilation

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92 Dilation17

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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

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Erosion (More examples)

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Erosion (More examples)

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Erosion in removing salt noise15

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Dilation

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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

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92 Erosion13

Erosion (More examples)

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Erosion (More examples)

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Erosion in removing salt noise15

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92 Dilation16

Dilation

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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

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92 Erosion14

Erosion (More examples)

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Erosion in removing salt noise15

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92 Dilation16

Dilation

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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

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

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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

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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

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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

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

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

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

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

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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

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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

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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

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

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

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

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

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

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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zale

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nd R

E

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oods

D

igita

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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

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 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 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 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 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 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

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

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

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 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 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 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

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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

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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

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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

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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

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

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)

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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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)