Transcript Image Segmentation © 2002-2003 by Yu Hen Hu ECE533 Digital Image Processing What is Image Segmentation?  Segmentation: » Split or separate an image into regions » To.

Image
Segmentation
© 2002-2003 by Yu Hen Hu
ECE533 Digital Image Processing
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What is Image Segmentation?

Segmentation:
» Split or separate an image into
regions
» To facilitate recognition,
understanding, and region of
interests (ROI) processing

20
40
60
20
40
60
Ill-defined problem
» The definition of a region is contextdependent
© 2002-2003 by Yu Hen Hu
ECE533 Digital Image Processing
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Outline

Discontinuity Detection
» Point, edge, line
Edge Linking and boundary detection
 Thresholding
 Region based segmentation
 Segmentation by morphological
watersheds
 Motion segmentation

© 2002-2003 by Yu Hen Hu
ECE533 Digital Image Processing
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Point Detection
Apply detection mask, followed
by threshold detection
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ECE533 Digital Image Processing
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Line Detection
Useful for
detecting lines
with width = 1.
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ECE533 Digital Image Processing
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Edge Detection
Points and lines are special cases of
edges.
 Edge detection is difficult since it is not
clear what amounts to an edge!

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ECE533 Digital Image Processing
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Edge Detection
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ECE533 Digital Image Processing
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Impact of Noise
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First & Second Derivatives of Edges
Gx  f / x 
f     

G y  f / y 
f  Gx2  G y2  Gx  G y : magnitudeof gradient
 Gy 
 : directionof gradient,
 Gx 
 ( x, y )  tan1 
© 2002-2003 by Yu Hen Hu
ECE533 Digital Image Processing
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Edge Detection Operators
Figure 10.8, 10.9
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ECE533 Digital Image Processing
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Approximate Gradient with L1 Norm
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ECE533 Digital Image Processing
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Effects of Smoothing
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Emphasizing Diagonal Edges
Use diagonal
Sobel operator
shown in figure
10.9(d)
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ECE533 Digital Image Processing
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Laplacian and Mexican Hat
2 f 2 f
 f  2  2
x
y
2
LoG operator
© 2002-2003 by Yu Hen Hu

 h( r )    e
2
2

 r 2 / 2 2
ECE533 Digital Image Processing

2
2
    r e r / 2 
4
2
2
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Comparison of Edge Detection
original
Sobel
LoG
Threshold LoG
Zero-crossing
Gradient method:
suitable for abrupt gray level
transition, sensitive to noise
2nd order derivative:
good for smooth edges
Gaussian smooth
operator
© 2002-2003 by Yu Hen Hu
Laplacian
operator
ECE533 Digital Image Processing
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Boundary Extraction



Edge detection
classifies individual
pixels to be on an edge
or not.
Isolated edge pixels is
more likely to be noise
rather than a true edge.
Adjacent or connected
edge pixels should be
linked together to form
boundary of regions that
segment the image.
© 2002-2003 by Yu Hen Hu

Edge linking methods:
»
»
»
»
Local processing
Hough transform
Graphic theoretic method
Dynamic programming
ECE533 Digital Image Processing
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Local Processing Edge Linking
An edge pixel will be
linked to another
edge pixel within its
own neighborhood if
they meet two
criteria:
f ( x, y )  f ( xo , yo )  E
 ( x, y )   ( xo , yo )  A
© 2002-2003 by Yu Hen Hu
ECE533 Digital Image Processing
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Global Processing Edge Linking:
Hough Transform
Find a subset of n points on an
image that lie on the same straight
line.
Write each line formed by a pair of
these points as
yi = axi + b
Then plot them on the parameter
space (a, b):
b = xi a + yi
All points (xi, yi) on the same line will
pass the same parameter space
point (a, b).
Quantize the parameter space and
tally # of times each points fall into
the same accumulator cell. The cell
count = # of points in the same line.
© 2002-2003 by Yu Hen Hu
ECE533 Digital Image Processing
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Hough Transform in (r, ) plane
To avoid infinity slope,
use polar coordinate to
represent a line.
x cos  y sin   r
Q points on the same
straight line gives Q
sinusoidal curves in (r,
) plane intersecting at
the same (ri, i) cell.
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ECE533 Digital Image Processing
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Example
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Example
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Threshold Segmentation
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ECE533 Digital Image Processing
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Effect of Illumination on Thresholding
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Threshold Example
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Needs of Adaptive Threshold
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ECE533 Digital Image Processing
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Needs of Local Threshold
Properly and improperly segmented
subimages from Fig. 10.30.
Further division of the sub-image,
and result of adaptive thresholding
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ECE533 Digital Image Processing
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Threshold: Hypothesis Testing

Question:

» Does this pixel with
intensity z belong to a
region (edge) or not?

Hypothesis
» H0: Null. It does not
» H1: Alt. It does

Likelihood
Maximum likelihood:
» Pixel z belongs to a region if
p(z|H1) > p(z|H0)

Bayesian:
P2 p(z|H1) > P1 p(z|H0)

Sufficient statistic:
z>T
» p(z|zH0) = p1(z)
» p(z| z H1) = p2(z)

Prior
» P1 = p(zH0) ,
» P2 = p(zH1)
© 2002-2003 by Yu Hen Hu
ECE533 Digital Image Processing
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Uni-model Gaussian Example

Given
pi ( z ) 

   z   i 2 
1

exp
2

2 
 2 i

Set
P1 p1(T) = P2 p2(T)
and solve for T.
Take log on both sides
and simplify to
AT2 + BT + C = 0
© 2002-2003 by Yu Hen Hu
A   12   22

B  2 1 22   2 12

 P 
C   12  22   22 12  2 12 22 ln 2 1 
  1 P2 
If  1   2   , then
T
1   2
2
 P2 
2

 ln 
1   2  P1 
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Clustering Problem Statement

Given a set of vectors {xk; 1  k  K}, find a set of
M clustering centers {w(i); 1  i  c} such that
each xk is assigned to a cluster, say, w(i*),
according to a distance (distortion, similarity)
measure d(xk, w(i)) such that the average
distortion
1 c K
D   I ( xk , i)d ( xk ,W (i))
K i 1 k 1

is minimized.
I(xk,i) = 1 if x is assigned to cluster i with cluster
center w(I); and = 0 otherwise -- indicator function.
© 2002-2003 by Yu Hen Hu
ECE533 Digital Image Processing
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k-means Clustering Algorithm
Initialization: Initial cluster center w(i); 1  i  c, D(–1)= 0, I(xk,i)
= 0, 1  i  c, 1  k  K;
Repeat
(A) Assign cluster membership (Expectation step)
Evaluate d(xk, w(i));
1  i  c, 1  k  K
I(xk,i) = 1 if d(xk, w(i)) < d(xk, w(j)), j  i;
= 0; otherwise.
1kK
N
(B) Evaluate distortion D:
D(iter)   I ( xk , i)d ( xk , w(i)) 1  k  K
k 1
(C) Update code words according to new assignment
(Maximization)
N
W (i)   I ( xk , i) xk ,
k 1
N
N i   I ( xk , i),
1 i  c
k 1
(D) Check for convergence
if 1–D(Iter–1)/D(Iter) < e , then convergent = TRUE,
© 2002-2003 by Yu Hen Hu
ECE533 Digital Image Processing
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A Numerical Example
x = {1, 2,0,2,3,4},
W={2.1, 2.3}
Assign membership
2.1: {1, 2, 0, 2}
2.3: {3, 4}
Distortion
D = (1 2.1)2 + (22.1)2
+ (0 2.1)2 + (2 2.1)2 +
(3 2.3)2 + (4 2.3)2
© 2002-2003 by Yu Hen Hu
3. Update W to minimize
distortion
W1 = (12+0+2)/4 = .25
W2 = (3+4)/2 = 3.5
4. Reassign membership
.25: {1, 2, 0}
3.5: {2, 3, 4}
5. Update W:
w1 = (1 2+0)/3 = 1
w2 = (2+3+4)/3 = 3.
Converged.
ECE533 Digital Image Processing
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Thresholding Example
Threshdemo.m
© 2002-2003 by Yu Hen Hu
ECE533 Digital Image Processing
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