Mata kuliah : T0283 - Computer Vision
Tahun
: 2010
Lecture 07
Segmentation
Learning Objectives
After carefully listening this lecture, students will be able
to do the following :
Explain various segmentation techniques and demonstrate
their implementation (histogram based segmentation, kmeans) using MATLAB and OpenCV
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Motivation :
Recognition Using Region Properties
Training
For all training samples of each model object
Segment the image
Compute region properties (features)
Recognition
Given an image of unknown object,
Segment the image
Compute its feature vector
Compare with the training set
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Region Segmentation
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Segmentation
Find set of regions R1, R2, ….,Rn such that
n
R
i
i 1
I
i  j , Ri  R j  
All pixels in region i satisfy some similarity
constraint
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Similarity Constraints
All pixels in any sub-image musts have the same gray levels.
All pixels in any sub-image must not differ more than some
threshold
All pixels in any sub-image may not differ more than some
threshold from the mean of the gray of the region
The standard deviation of gray levels in any sub-image must
be small.
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Simple Segmentation
1
B ( x, y )  
0

if I ( x, y )  T
Otherwise
1
B( x, y )  
0
if T1  I ( x, y )  T2
Otherwise
1
B( x, y )  
0
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if I ( x, y )  Z
Otherwise
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Image Histogram
number of pixels
Histogram graphs the number of pixels with a
particular gray level as a function of the image of
gray levels.
gray
level
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Segmentation Using Histogram
Simple Case
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Segmentation Using Histogram
Simple Case
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1
B1 ( x, y )  
0
if 0  f ( x, y )  T1
Otherwise
1
B2 ( x, y )  
0
if T1  f ( x, y )  T2
Otherwise
1
B3 ( x, y )  
0
if T2  f ( x, y )  T3
Otherwise
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Realistic Histograms
Smooth out noise
Convolve hist. by averaging or 1D Gaussian filter
peak
peak
valley
peak
valley
valley
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Segmentation Using Histogram
Real image histograms
1.
2.
3.
4.
5.
Compute the histogram of a given image.
Smooth the histogram by averaging peaks and valleys in
the histogram.
Detect good peaks by applying thresholds at the valleys.
Segment the image into several binary images using
thresholds at the valleys.
Apply connected component algorithm to each binary image find
connected regions.
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Segmentation Using Histograms
Select the valleys as thresholds
Apply threshold to histogram
Label the pixels within the range of a threshold
with same label, i.e., a, b, c … or 1, 2, 3 …
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Connected Components
Disjoint segments with same labels need to be
split
0
1

0

0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0

0
0
0
b

0

0
0
0
b
0
0
d
0
0
0
c
0
a
a
0
c
c
0
a 
0

0
0 
may be added to segment c
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Recursive Connected Component Algorithm
1.
2.
3.
4.
Scan the binary image left to right, top to bottom.
If there is an unlabeled pixel with a value of “1”, assign a
new label to it.
Recursively check the neighbors of the pixel in step 2 and
assign the same label if they are unlabeled with value “1”.
Stop when all the pixels of value “1” have been labeled.
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Sequential Connected Component Algorithm
1.
2.
3.
4.
Scan the binary image left to right, top to bottom.
If an unlabeled pixel with a value of “1”, assign a new
label to it according to the following rules :
- 0
0 1
0
0
L
- L
0 1
0
L
L
- 0
L 1
L
0
L
- L
M 1
- L
(Set M=L)
M L
Determine equivalence classes of labels
In the second pass, assign the same label to all elements
in an equivalence class.
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Sequential Connected Component Algorithm
0
1

0

0
0
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0
1
0
0
1
0
0
0
1
1
1
1
0
1
1
0

1
0

0
0
0
b

0

0
0
0
b
0
0
d
T0283 - Computer Vision
0
0
0
c
c
a
a
0
c
c
0

a
0

0
0 
d=c
Equivalence
class
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Example
Detecting Finger Tips (marked white)
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Recaps : Steps in Seed Segmentation
1.
2.
3.
4.
Compute the histogram.
Smooth the histogram
Detect good peaks
Segment image into binary images using
thresholds at the valleys.
5. Apply connected component algorithm.
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Improving Seed Segmentation
Merge small neighboring regions
Region growing step
Split large regions
Region splitting
Remove weak boundaries between adjacent
regions
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Region Growing
Seed segmentation (histogram based seg.)
Region splitting and merging
Phagocyte algorithm
Likelihood ratio test
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Region Split and Merge
Splitting: split non uniform region into 4 adjacent
regions
Merging: merge similar regions
Stop when no splitting merging are possible
Uniformity/similarity function: P
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Example
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
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Phagocyte Algorithm
Boundary melting
Remove weak boundaries
Similar to region merging
Boundary weakness is based on color similarity
R2
S (x R1 , x R2 )  I (x R1 )  I (x R2 )
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x R1
x R2
R1
25
Phagocyte Algorithm
S (x R1 , x R2 )  I (x R1 )  I (x R2 )
1 S (x R1 , x R2 )  T
W (x R1 , x R2 )  
0 otherwise
W ( R1 , R2 ) 
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
R2
x R1
x R2
R1
W (x R1 , x R2 )
x R1 R1  x R2 R2
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Phagocyte Merging Heuristics
•
Merge two regions if
W ( Boundary )
T 2, 0  T2  1
min( P1 , P) 2
Phagocyte
where P1 and P2 are the perimeters of regions R1 and R2.
•
Merge regions if
W ( Boundary )
T 3, 0  T3  1
Total number of points on the border
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Weakness
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Likelihood Ratio Test
Two region hypothesis
There is only one region
There are indeed two regions
Intensity at every pixel is independent
Joint probability
Gaussian distribution
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Likelihood Ratio Test
p ( x) 
1
e
2 

( x )2
2 2
observing intensity under Gaussian model
Likelihood of region A
m1
 1   21
p( x1 , x2 ,, xm1 )  
 e
 2  
m
x1, x2, …,xm1A
Likelihood of region B
m2
 1   22
p( xm1 1 , xm1  2 ,, xm1  m2 )  
 e
 2  
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m
T0283 - Computer Vision
xm1+1, xm1+2, …,xm1+m2B
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Likelihood Ratio Test
There is 1 region hypothesis

1

P( H1 )  p( x1 , x2, , xm1 , xm1 1 , xm1  2 ,, xm1  m2 ) 
 2 
one region

There are 2 regions hypothesis
m1




m1  m2
e

m1  m2
2
m2
 1   m21  1   m22
 e 
 e
P( H 2 )  p( x1 , x2, , xm1 ) p( xm1 1 , xm1  2 ,, xm1  m2 )  



 2  A 
 2  B 
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Likelihood Ratio Test

1
P( H1 )  
 2 
one region





m1  m2
e
m1

m1  m2
2
m2
 1   m21  1   m22
 e 
 e
P( H 2 )  



 2  A 
 2  B 
( 0 ) m1  m2
P ( H1 )
LH 

P( H 2 ) ( A ) m1 ( B ) m2
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T0283 - Computer Vision
Merge regions if LH<T.
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Region Growing Methods
Different algorithms have different number of
thresholds
How much merging is required
Stopping criterion
Though simple, seed segmentation succeed by
region growing is usually successful
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Difference Between Segmentation and Edge
Detection
Closed boundary
Edges are usually open
Segmentation provides closed boundaries
Local or global
Edges are computed in the locality
Segmentation is global
Increasing feature vector dimensionality
Does not drastically improve edge detection
Improves segmentation (motion, texture information etc.)
Boundary position
Localized in edge detection
Usually not localized (recent advancements use locality as
well)
Especially contour based segmentation
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