segmentation of image sequences by mathematical morphologyjb/lectures/mathematical...
TRANSCRIPT
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Segmentation of Image
Sequences by
Mathematical Morphology
Franklin César Flores
Instituto de Matemática e Estatística - USP
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Outline
� Introduction
� Connected Filters
� Watershed
� Beucher-Meyer Segmentation Paradigm
� Aperture Operators
� Automatic Design of Morphological Operators
� Methodology and Applications
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Introduction
� Digital video edition is an important task nowadays.
� Some usual areas of applications are:
� Advertisement
� Special effects on movies
� Re-mastering of old movies
� Rotoscoping
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Introduction
� Computational tools are being used to help this task.
� Some applications are not easy, for instance:
composing (i.e. segmentation and mixing of video
sequences.)
� A known technique is called Chroma Keying.
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Introduction
� Some special cares have to be taken, though:
� The scene has to be photographed in front of a
bright, colored background.
� Objects to be substituted have to be covered by
a colored (green, blue, etc) cloth.
� The image processing technique applied in the
chroma keying is classical pattern recognition,
using pixel color intensities as attributes.
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Chroma Keying
� Photo Studio applications
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Chroma Keying
Forrest Gump and John Lennon being interviewed “together”
� Video sequence applications
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Rotoscoping
� Tracking live actions to create animation or an animated matte is usually called Rotoscoping
� It is applied mainly for short sequences
� The tracking is usually done manually with the help of a pointing device
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Connected Filters
� Connected filters are operators that act on the level
of the flat zones of an image, not on the level of the
pixels.
� They can not introduce new discontinuities, only
suppress existing ones.
� They are well suited for image segmentation because
they preserve the important desired borders.
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Connected Filters
Planning
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Areaopen Filter
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Homotopy Filter
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Levelings
� Levelings is a good methodology to simplify the
image before segmentation
� It creates and enlarges homogeneous (quasi-flat)
zones
� It can simplify the image before automatic
design of operators
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Levelings
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Levelings
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Levelings
Original
Marker
Result
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Watershed
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Oversegmentation
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Markers
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BeucherBeucherBeucherBeucher----Meyer ParadigmMeyer ParadigmMeyer ParadigmMeyer Paradigm
� A powerful segmentation method to find the bordersof specified objects in an image.
3D
2D
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BeucherBeucherBeucherBeucher----Meyer ParadigmMeyer ParadigmMeyer ParadigmMeyer Paradigm
Gradient
Marker
s
Filtered Gradient
Watershed lines
Composed Image
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Design of Image Operators
� A fundamental problem in Mathematical Morphology is the
design of function operators
� An approach for operators design is statistical optimization
in a space of operators
� In the optimization, it is fixed a family of useful operators
that have a standard representation
� The complexity of the optimization depends on the size of
the family of operators considered
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� In the binary case, the family of W-operators isusually considered
� The family of binary W-operators has
� In the gray-scale case, the family of W-operatorsis also usually considered
� The family of gray-scale W-operators has
� In ordinary applications l=m=256
22 ||W
lmW ||
Design of Image Operators
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� The family of Aperture operators depends on aspatial window W and a gray-scale window K
� The family of aperture filters has
� The complexity of the optimization problem iscontrolled by k and |W|
� The values of k and |W| depends on theproblem: k=3, 5, 7, ... and |W| = 9, 25, 49, ...
kk W ||
Design of Aperture Operators
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Characteristic Functions
MLW → : ψ
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Design of Aperture Operators
K-characteristic functions
� Gray-scale translation: (u + y)(z) = u(z) + y
� Gray-scale window:
−
−−
−2
1,...,1,0,1,...,
2
1 kk
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Design of Aperture Filters
Windowing in the space and range
( )( ) I U
−
−−
−=2
1,)(,
2
1/
kyzu
kzKu y
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� gray-scale t. i.: ψ (u + y) = ψ (u) + y
� locally defined in K:
� representation:
( ) ( ) ( ) ( )( )ouou Kuouu /βψ +=
( ) ( ) ( )( )ouKuouu /ψβψ +=
Design of Aperture Operators
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-2 1 2 2 2
-2 1 2 2 2
-2 1 2 2 2
-2 1 1 1 1
-2 -2 -2 -2 -2
-2 -1 0 1 2
2
1
0
-1
-2
ψβ
2 2 2 2 2
2 2 2 2 1
2 2 2 1 -2
2 2 1 -2 -2
2 1 -2 -2 -2
10 11 12 13 14
14
13
12
10
11
ψ
12 13 14 15 16
12 13 14 15 15
12 13 14 14 12
12 13 13 11 12
12 12 10 11 12
10 11 12 13 14
14
13
12
10
11
=
10 11 12 13 14
10 11 12 13 14
10 11 12 13 14
10 11 12 13 14
10 11 12 13 14
10 11 12 13 14
14
13
12
10
11
+
)(ou ψβ
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Aperture Operators
0000
5555
10101010
15151515
20202020
25252525
30303030
35353535
inputinputinputinput
outputoutputoutputoutput
-2 1 2 2 2
-2 1 2 2 2
-2 1 2 2 2
-2 1 1 1 1
-2 -2 -2 -2 -2
-2 -1 0 1 2
2
1
0
-1
-2
ψβ
W { }2,1,0,1,2 −−=K
Ψ
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Design of Aperture Operators
Learning System
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Design of Aperture Operators
ObservedIdeal
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Design of Aperture Operators
Windowing observedThe center of the window
seen at the sameposition in the Ideal
![Page 34: Segmentation of Image Sequences by Mathematical Morphologyjb/lectures/mathematical morphology/Qualify.pdf · Design of Image Operators A fundamental problem in Mathematical Morphology](https://reader030.vdocuments.us/reader030/viewer/2022040308/5eda011528db2d5ca2493c9a/html5/thumbnails/34.jpg)
One representation
of Aperture
Operators
Lattice representation
of the kernel of the
operator
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The proposed technique
Automatic design of morphological operators for Motion Segmentation
![Page 36: Segmentation of Image Sequences by Mathematical Morphologyjb/lectures/mathematical morphology/Qualify.pdf · Design of Image Operators A fundamental problem in Mathematical Morphology](https://reader030.vdocuments.us/reader030/viewer/2022040308/5eda011528db2d5ca2493c9a/html5/thumbnails/36.jpg)
The proposed technique
Some frames are segmented and used to train an operator
Observed Ideal
![Page 37: Segmentation of Image Sequences by Mathematical Morphologyjb/lectures/mathematical morphology/Qualify.pdf · Design of Image Operators A fundamental problem in Mathematical Morphology](https://reader030.vdocuments.us/reader030/viewer/2022040308/5eda011528db2d5ca2493c9a/html5/thumbnails/37.jpg)
Applying the proposed
technique
The first frame of the sequence is segmented manually
The speed of the object is also a parameter
![Page 38: Segmentation of Image Sequences by Mathematical Morphologyjb/lectures/mathematical morphology/Qualify.pdf · Design of Image Operators A fundamental problem in Mathematical Morphology](https://reader030.vdocuments.us/reader030/viewer/2022040308/5eda011528db2d5ca2493c9a/html5/thumbnails/38.jpg)
Applying the proposed
technique
The position of the object in the first frame plus its speed determine the application mask for the next frame
Possible
position
of the
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Applying the proposed
technique
The operator is applied inside the application mask
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Applying the proposed
technique
The result is filtered (area opening)
![Page 41: Segmentation of Image Sequences by Mathematical Morphologyjb/lectures/mathematical morphology/Qualify.pdf · Design of Image Operators A fundamental problem in Mathematical Morphology](https://reader030.vdocuments.us/reader030/viewer/2022040308/5eda011528db2d5ca2493c9a/html5/thumbnails/41.jpg)
The proposed technique
Beucher-Meyer paradigm is applied
![Page 42: Segmentation of Image Sequences by Mathematical Morphologyjb/lectures/mathematical morphology/Qualify.pdf · Design of Image Operators A fundamental problem in Mathematical Morphology](https://reader030.vdocuments.us/reader030/viewer/2022040308/5eda011528db2d5ca2493c9a/html5/thumbnails/42.jpg)
The proposed technique
The segmented object can be substituted or analysed
![Page 43: Segmentation of Image Sequences by Mathematical Morphologyjb/lectures/mathematical morphology/Qualify.pdf · Design of Image Operators A fundamental problem in Mathematical Morphology](https://reader030.vdocuments.us/reader030/viewer/2022040308/5eda011528db2d5ca2493c9a/html5/thumbnails/43.jpg)
Applications - simulation
Tracking disks
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Applications
Mask Result of the application
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Applications
Result of the connected filter Composition
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Applications
Watershed regions Composed Result
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Applications - tracking one disk
![Page 48: Segmentation of Image Sequences by Mathematical Morphologyjb/lectures/mathematical morphology/Qualify.pdf · Design of Image Operators A fundamental problem in Mathematical Morphology](https://reader030.vdocuments.us/reader030/viewer/2022040308/5eda011528db2d5ca2493c9a/html5/thumbnails/48.jpg)
Applications
Tracking a table tennis ball
Two problems have been
explored in this sequence
• Track the ball
• Track the racquet
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Applications - Tracking the ballTracking the ballTracking the ballTracking the ball
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Applications - Tracking the racquetTracking the racquetTracking the racquetTracking the racquet
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Future Research
Design of Aperture Operators for Image Simplification by
Connected Filters
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Future Research
Design of Adaptative Filters
![Page 53: Segmentation of Image Sequences by Mathematical Morphologyjb/lectures/mathematical morphology/Qualify.pdf · Design of Image Operators A fundamental problem in Mathematical Morphology](https://reader030.vdocuments.us/reader030/viewer/2022040308/5eda011528db2d5ca2493c9a/html5/thumbnails/53.jpg)
Future Research
Detection of Abrupt Changes in the Scene
![Page 54: Segmentation of Image Sequences by Mathematical Morphologyjb/lectures/mathematical morphology/Qualify.pdf · Design of Image Operators A fundamental problem in Mathematical Morphology](https://reader030.vdocuments.us/reader030/viewer/2022040308/5eda011528db2d5ca2493c9a/html5/thumbnails/54.jpg)
Future Research
( )( )
( ) ( ) ( ){ }xNyyxdxG
bad
xxN
∈=∇ :,max
metric a :,
of oodneighbourh :
Design of Aperture Operators for Color Image
![Page 55: Segmentation of Image Sequences by Mathematical Morphologyjb/lectures/mathematical morphology/Qualify.pdf · Design of Image Operators A fundamental problem in Mathematical Morphology](https://reader030.vdocuments.us/reader030/viewer/2022040308/5eda011528db2d5ca2493c9a/html5/thumbnails/55.jpg)
Future Research
Design of Aperture Operators for Color Image
![Page 56: Segmentation of Image Sequences by Mathematical Morphologyjb/lectures/mathematical morphology/Qualify.pdf · Design of Image Operators A fundamental problem in Mathematical Morphology](https://reader030.vdocuments.us/reader030/viewer/2022040308/5eda011528db2d5ca2493c9a/html5/thumbnails/56.jpg)
Correlation