representation and description - sharifee.sharif.edu/~dip/files/representationforview.pdf ·...
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![Page 1: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/1.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
1
Digital Image Processing
Representation and Description
1
• Representation and Description
– Representing regions in 2 ways:
• Based on their external characteristics (its boundary): – Shape characteristics
• Based on their internal characteristics (its region): – Regional properties: color, texture, and …
• Both
![Page 2: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/2.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
2
Digital Image Processing
Representation and Description
2
• Representation and Description
– Describes the region based on a selected representation:
• Representation boundary or textural features
• Description length, orientation, the number of concavities in the boundary, statistical measures of region.
![Page 3: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/3.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
3
Digital Image Processing
Representation and Description
3
• Invariant Description:
– Size (Scaling)
– Translation
– Rotation
![Page 4: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/4.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
4
Digital Image Processing
Representation and Description
4
• Boundary (Border) Following:
– We need the boundary as a ordered sequence of points.
![Page 5: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/5.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
5
Digital Image Processing
Representation and Description
5
• Moore Boundary Tracking Algorithm:
1. Let the starting point, b0 , be the uppermost, leftmost point in the image that is labeled 1. Denote by c0 the west neighbor of b0 . Clearly c0 always will be a background point. Then, examine the 8 neighbors of b0 , starting at c0 and proceeding in clockwise direction. Let b1 denote the first pixel encountered whose value is 1, and let c1 be the points immediately preceding b1 in the sequence. Store the location of b0 and b1.
2. Let b=b1 and c=c1.
3. Let the 8 neighbors of b , starting at c and proceeding in a clockwise direction be denoted by n1,n2,... , nk . Find the first nk whose value is 1.
4. Let b=nk and c=nk-1.
5. Repeat steps 3 and 4 until b=b0 and the next boundary point found is b1.
![Page 6: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/6.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
6
Digital Image Processing
Representation and Description
6
• Example:
![Page 7: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/7.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
7
Digital Image Processing
Representation and Description
7
• Freeman Chain Code:
– Code the 4 or 8 connectivity
![Page 8: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/8.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
8
Digital Image Processing
Representation and Description
8
• Chain Code Problems:
– Long Code
– Low noise Robustness • Solution: Resampling
– Starting Point: • Solution: Rotary/Circular shift until forms a minimum integer
– 10103322 01033221
– Angle normalization: • First difference (Counterclockwise)
– 10103322 3133030 or 33133030 (transition between last and first)
• Useful for integer multiple of used chain code (45° or 90°)
![Page 9: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/9.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
9
Digital Image Processing
Representation and Description
9
• Example: – Resampling
– 4 and 8 chain codes
![Page 10: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/10.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
10
Digital Image Processing
Representation and Description
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• Example:
![Page 11: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/11.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
11
Digital Image Processing
Representation and Description
11
• Polygon Approximation:
– Minimum-Perimeter Polygons • Read Pages 801-807.
![Page 12: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/12.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
12
Digital Image Processing
Representation and Description
12
• Example (Cont.):
![Page 13: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/13.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
13
Digital Image Processing
Representation and Description
13
• Example:
![Page 14: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/14.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
14
Digital Image Processing
Representation and Description
14
• Polygon Approximation:
– Merging: • Start from a seed point
• Continue on a line based on local average error (e.g. linear regression)
• Stop if error exceeds a threshold
• Continue from the last point
• ....
– No guarantee for corner detection
![Page 15: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/15.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
15
Digital Image Processing
Representation and Description
15
• Polygon Approximation:
– Splitting: • Segments to two parts based on a criteria (e.g. maximum internal
distance)
• Check each segment for splitting based on another criteria (e.g. linearity error)
• ….
![Page 16: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/16.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
16
Digital Image Processing
Representation and Description
16
• Signatures:
– A 1-D functional representation of a boundary • Distance vs. Angle (in the polar representation):
– Invariant to translation
– Non-Invariant to rotation (may be achieved by start point selection)
» Farthest point from centroid
» The point on eigen axis
» Use chain code solution for the start point
• Line tangent angle
• Histogram of tangent angle
![Page 17: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/17.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
17
Digital Image Processing
Representation and Description
17
• Example:
![Page 18: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/18.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
18
Digital Image Processing
Representation and Description
18
• Example:
![Page 19: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/19.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
19
Digital Image Processing
Representation and Description
19
• Boundary Segments:
– Convex Hull: Smallest convex set containing the S
– Convex Deficiency: The set difference D=H-S
– Problem of noise: • Smoothing (K-neighbour average)
• Polygon approximation
– Convex Hull of Polygon
![Page 20: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/20.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
20
Digital Image Processing
Representation and Description
20
• Boundary Segments:
• Skeletonization / Thinning:
– Medial Axis Transform (MAT)
• Point p is belong to medial (Region R and Border B): – Has more than one closest neighbor in B
– Chapter 9 and Page 813
![Page 21: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/21.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
21
Digital Image Processing
Representation and Description
21
• Example of Thinning:
![Page 22: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/22.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
22
Digital Image Processing
Representation and Description
22
• Boundary Descriptor:
– Simple one:
• Diameter: – Lead to Major axis and minor axis (Perpendicular to major)
– Basic Rectangle
• Curvature
,
Diam max ,i ji j
B D p q
1.5
2 2
1 x y x yk
R x y
![Page 23: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/23.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
23
Digital Image Processing
Representation and Description
23
• Shape Number
– Smallest integers of first difference circular chain code.
![Page 24: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/24.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
24
Digital Image Processing
Representation and Description
24
• Example:
![Page 25: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/25.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
25
Digital Image Processing
Representation and Description
25
• Fourier Descriptors:
1
1
0
1
0
0
exp 2
1exp 2
1ˆ exp 2
K
k
K
u
u
P
s k x k jy k
uka u s k j
K
uks k a u j
K K
uks k a
KPu j
![Page 26: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/26.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
26
Digital Image Processing
Representation and Description
26
• Example:
![Page 27: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/27.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
27
Digital Image Processing
Representation and Description
27
• Problem of invariance:
– Rotation
– Normalization will solve!
1
0
1exp 2
Kj j
r
k
uka u s k e j a u e
K K
2
0
ˆ , , ,....s s s
s
s s is ii
i
a u a u a ua u
a u a u a u
![Page 28: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/28.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
28
Digital Image Processing
Representation and Description
28
• Problem of invariance:
– Translation
– Translation to centroid will solve!
xy x x
t xy x y
t xy
j
s k s k x k j y k
a u u
![Page 29: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/29.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
29
Digital Image Processing
Representation and Description
29
• Problem of invariance:
– Scaling
– Normalization will solve
s ss k s k a u a u
2
0
ˆ , , ,....s s s
s
s s is ii
i
a u a u a ua u
a u a u a u
![Page 30: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/30.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
30
Digital Image Processing
Representation and Description
30
• Problem of invariance:
– Starting Point
– Normalization will solve
0 0 0
0
,
2exp
p
p
s k s k k x k k y k k
j k ua u a u
K
2
0
ˆ , , ,....p p p
p
p p ip ii
i
a u a u a ua u
a u a ua u
![Page 31: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/31.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
31
Digital Image Processing
Representation and Description
31
• Properties in a single table:
![Page 32: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/32.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
32
Digital Image Processing
Representation and Description
32
• Statistical Moments:
– Boundary Representation
1
0
1
0
,
v as random variable
A
i i
i
An
n i i
i
r v g r
m v p v
v v m p v
1
0
1
0
,
normalized ( ) as histogram
A
i i
i
An
n i i
i
r v g r
g r
m r g r
v r m g r
![Page 33: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/33.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
33
Digital Image Processing
Representation and Description
33
• Regional Descriptor:
– The simple one: • Area (Number of pixels)
• Perimeter (Length of boundary)
• Compactness (Perimeter2/Area)
• Circularity: Ratio of the area to the area of a circle with same perimeter
• Mean, median, max, min, ratio pixels above/below … from intensity data.
![Page 34: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/34.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
34
Digital Image Processing
Representation and Description
34
• Example:
– Normalized area: • Ratio of light pixels to total light pixels
![Page 35: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/35.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
35
Digital Image Processing
Representation and Description
35
• Topology Descriptor:
– Number of holes (H): • Invariants to several operators.
![Page 36: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/36.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
36
Digital Image Processing
Representation and Description
36
• Topology Descriptor:
– Number of connected components (C) : • Invariants to several operators.
![Page 37: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/37.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
37
Digital Image Processing
Representation and Description
37
• Topology Descriptor:
– Euler number (E=C-H) : • Invariants to several operators.
0 -1
![Page 38: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/38.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
38
Digital Image Processing
Representation and Description
38
• Topology Descriptor:
– Polygonal net: • V: # of vertices (7)
• Q: # of edges (11)
• F: # of faces (2)
• E=C-H=V-Q+F
– C=1 , H=3
– E=-2
![Page 39: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/39.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
39
Digital Image Processing
Representation and Description
39
Original Threshold
Largest Connected Region Skeleton
• Example:
![Page 40: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/40.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
40
Digital Image Processing
Representation and Description
40
• Texture:
– No formal definition
Smooth Coarse Regular
![Page 41: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/41.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
41
Digital Image Processing
Representation and Description
41
• Statistical Approaches – 1st order grey level statistics
• From normalised histogram – One pixel gray level repeat n times
– 2nd order grey level statistics • From GLCM (Grey Level Co-ocurrence Matrix)
– Repeatation of two pixels in a pre-defined neighbourhood
• Needs: – A Positioning Operator, P.
– GLCM(i,j): # of times that points with gray level Zi occure relative to points with gray level Zj
![Page 42: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/42.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
42
Digital Image Processing
Representation and Description
42
• Texture feature from 1st order statistics:
1 1
0 0
2
3
4
12
0
1
0
,
11 : Gray Level Contrast (Normalized)
1
:Skewness
: Kurtosis, Flatness
: Uniformity
log : Entropy
L Ln
n i i i i
i i
z
L
i
i
L
i i
i
z z m P z m z P z
R z
z
z
U z p z
e z p z p z
![Page 43: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/43.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2011
43
Digital Image Processing
Representation and Description
43
• Example: Smooth Coarse Regular
![Page 44: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/44.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
44
Digital Image Processing
Representation and Description
44
• Problem with 1st order histogram
– Lack of spatial information
![Page 45: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/45.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
45
Digital Image Processing
Representation and Description
45
• Gray Level Co-Occurence Matrix (GLCM):
1 2 3
0 0 0 1 2
1 1 1 1
, 0 1 2 ,2 2 1 0
1 1 0 2
0 0 1 1
0 0 0
0 1 1 : one pixel to right one below
0 1 0
2
0
0
0
0
1 2 11
2 3 2 2 3 216
0 2 0 0 2 0
4 4
z z z z
G = P
![Page 46: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/46.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
46
Digital Image Processing
Representation and Description
46
• Gray Level Co-Occurence Matrix (GLCM):
![Page 47: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/47.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
47
Digital Image Processing
Representation and Description
47
• Gray Level Co-Occurence Matrix (GLCM):
1 1
1 1 1 1
2 22 2
1 1 1 1
: # of gray levels
,
,
g g
g g g g
g g g g
g
N N
ij
ij ij
i j
N N N N
r ij c ij
i j j i
N N N N
r r ij c c ij
i j j i
N
gn g p
n
m i p m j p
i m p j m p
![Page 48: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/48.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
48
Digital Image Processing
Representation and Description
48
• Texture feature from GLCM
,
2
2
2
( ) : Maximum probability (G1)
: Correlation (G2)
( ) : Contrast (G3)
: Uniformity
: Homogeneity1
log ( ) : Entropy
iji j
r c
i j r c
ij
i i
ij
i j
ij
i i
ij ij
i j
Max p
i m j m
i j p
p
p
i j
p p
![Page 49: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/49.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
49
Digital Image Processing
Representation and Description
49
• Example:
– One pixel immediately to he right
![Page 50: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/50.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
50
Digital Image Processing
Representation and Description
50
• Example:
![Page 51: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/51.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
51
Digital Image Processing
Representation and Description
51
• Effect of Horizontal offset: – Correlation index
– Horizontal distance between neighbors
Noisy Sin Circuit board
![Page 52: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/52.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
52
Digital Image Processing
Representation and Description
52
• Spectral approaches:
– Peaks and Frequencies related to periodicity:
– S(r,θ), Sr(θ),Sθ(r):
0
1
R
r
r
S r S r
S r S
S S
![Page 53: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/53.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
53
Digital Image Processing
Representation and Description
53
• Spectral approaches:
![Page 54: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/54.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
54
Digital Image Processing
Representation and Description
54
• Spectral approach:
![Page 55: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/55.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
55
Digital Image Processing
Representation and Description
55
• Moments of Image as a 2D pdf:
10 01
00 00
Moments of order of (p+q)
,
Central moments of order of (p+q)
,
;
p q
pq
p q
pq
m x y f x y dxdy
x x y y f x y dxdy
m mx y
m m
![Page 56: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/56.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
56
Digital Image Processing
Representation and Description
56
• Digital Data:
10 01
00 00
00 00
1 0 1010 10 00
00
0 1 0101 01 00
00
Moments of order of (p+q)
( , )
( ) ( ) ( , ), ;
( , )
( ) ( ) ( , ) 0
( ) ( ) ( , ) 0
p q
pq
x y
p q
pq
x y
x y
x y
x y
m x y f x y
m mx x y y f x y x y
m m
f x y m
mx x y y f x y m m
m
mx x y y f x y m m
m
![Page 57: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/57.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
57
Digital Image Processing
Representation and Description
57
• Moments:
• A set of invariant moments (7 by Hu)
11 20 02
21 12 30 03
00
2nd ordens centrale momenter 2
, ,
3rd ordens centrale momenter 3
, , ,
Normalized central momens
and 12
pq
pq
p q
p q
p q
![Page 58: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/58.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
58
Digital Image Processing
Representation and Description
58
• Hu Moments:
1 20 02
2 2
2 20 02 11
2 2
3 30 12 12 03
2 2
4 30 12 21 03
2 2
5 30 12 30 12 30 12 21 03
2 2
21 03 21 03 30 12 21 03
2 2
6 20 02 30 12 21 03 11 30 12 21 0
4
3 3
3 3
3 3
4
3
2 2
7 21 03 30 12 30 12 30 12
2 2
30 12 21 0
2 2
8 11 30 12 0
3 30 12
3 21 20 02 30
2
12 03
1 0
21
3
3 3
3 3
![Page 59: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/59.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
59
Digital Image Processing
Representation and Description
59
• Example:
![Page 60: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/60.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
60
Digital Image Processing
Representation and Description
60
• Results of invariant moments:
![Page 61: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/61.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
61
Digital Image Processing
Representation and Description
61
• Complex Zernike Moments:
• Where Vmn are Zernike polynomials:
2 2 1
0
1, ,
, , ,
mn mn
x y
mA f x y V x y dxdy
m n m n even n m
2
0
2
, , , : over unit disc
1 , , ,
!, , ,
! ! !2 2
jn
mn mn
m n
s
mn
s
m s
V r R r e r
R r F m n s r
m sF m n s r r
m n m ns s s
![Page 62: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/62.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
62
Digital Image Processing
Representation and Description
62
• Some Zernike Polynomials:
, ,
0,0
1,1
2
2,0
2
2,2
3
3,1
3
3,3
1
2 1
3 2
m n m nR R
R
R r
R r
R r
R r r
R r
![Page 63: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/63.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
63
Digital Image Processing
Representation and Description
63
• How to Compute Zernike Polynomials:
– Scale and Translation invariance transform: • Shift to center of gravity (m10 = m01= 0)
• Fix m00 at a predetermined value (= b):
– Map Image to the unit disc using polar coordinates.
– The center of the image is the origin of the unit disc
– Those pixels falling outside the unit disc are not used in the computation.
2 2 1, tany
r x yx
00
, , ,x y
g x y f x ym
b
![Page 64: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/64.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
64
Digital Image Processing
Representation and Description
64
• How to Compute Zernike Polynomials:
, ,
1, ,m n m n
x y
mA g x y V x y
![Page 65: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/65.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
65
Digital Image Processing
Representation and Description
65
• Legendre Moments:
1 1
, 0
1 1
2
2 1 2 1, ,
4
11
2 !
m n m n
kk
k k k
m nP x P y dxdy m n
dP r x
k dx
![Page 66: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/66.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
66
Digital Image Processing
Representation and Description
66
• Fourier-Mellin Moments:
– Fourier-Mellin Transform:
– Fourier-Mellin Moments:
2
,
0 0
( , ) , ,m in
m nF r f r e rdrd m n
2
,
0 0
1
0
1( , ) , ,
2
: orthogonal polynomial of degree m over the raneg 0 1
in
m n m
m
m
m l m
f r Q r e rdrd m na
Q r r
Q r Q r rdr a m k
![Page 67: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/67.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
67
Digital Image Processing
Representation and Description
67
• Principal Component Analysis:
– Consider a multi (value/Channel/Spectral) images:
1 2
1
1
1
1 2 1 2
1, : # of observations
1
: Real Positive Definiter Matrix
: 0, ,
,
T
n
K
x k
k
KT T T
x x x k k x x
k
x
x i i j
T T
n n
x x x
E KK
EK
v v v v i j
v v v A A
x
m x x
C x m x m x x m m
C
C
A
![Page 68: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/68.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
68
Digital Image Processing
Representation and Description
68
• Karhunen–Loève or Hotelling Transform:
– Analysis:
– Complete Synthesis:
– Optimal Synthesis:
1 2, ndiag T
X y y xy = A x -m m = 0 C = AC A
T X
x = A y m
2
1 1 1
Form Using eigenvectors correspondinf to -largest eigenvalues
ˆ
ˆ
PCA Analysis
k
T
k
n k n
rms j j j
j j j k
k k
e E
X
A
x = A y m
x x
![Page 69: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/69.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
69
Digital Image Processing
Representation and Description
69
• Example:
![Page 70: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/70.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
70
Digital Image Processing
Representation and Description
70
• Data Preparation:
![Page 71: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/71.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
71
Digital Image Processing
Representation and Description
71
• Eigenvalues Analysis:
![Page 72: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/72.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
72
Digital Image Processing
Representation and Description
72
• PCA Analysis:
– Eigneimages
![Page 73: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/73.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
73
Digital Image Processing
Representation and Description
73
• Example: – Using 2 components
![Page 74: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/74.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
74
Digital Image Processing
Representation and Description
74
• Example:
– Difference
![Page 75: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/75.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2011
75
Digital Image Processing
Representation and Description
75
• PCA in Boundary description:
![Page 76: Representation and Description - Sharifee.sharif.edu/~dip/Files/RepresentationForView.pdf · Digital Image Processing Representation and Description 5 •Moore Boundary Tracking Algorithm:](https://reader034.vdocument.in/reader034/viewer/2022051809/60158dad735944778c647c7d/html5/thumbnails/76.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2011
76
Digital Image Processing
Representation and Description
76
• PCA in Boundary description: