SEGMENTATION
ITERATIVE ALGORITHMS
HOUGH TRANSFORM
September 28, 1998
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ITERATIVE ALGORITHMS ON
IMAGES
• Start with an initial image.
• Apply a rule which transforms individual pixel
grey values according to neighboring grey values.
• At each step reapply this same rule.
• After ‘alot’ of iterations the effect of this rule on
the resulting image should be negligible and the
iterations are said to converge.
FOR k=0 to 999
IMAGE k+1 = F( IMAGE k)
September 28, 1998
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ITERATIVE ALGORITHMS ON
IMAGES
A general example of the form of an iterative rule at
the (k+1)st iteration:
I1 I2 I3
k+1
k
k
k
k
k
k
k
k
k
I0 = F(I1 ,I2 ,I3 ,I4 ,I5 ,I6 ,I7 ,I8 ,I0 )
I4
I0
I6
I7
I5
I8
Local
Image
Neighborhood
As a purely illustrative example, the convolution
operation is an example of an iterative rule
September 28, 1998
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DISCRETE CONVOLUTION
Template
‘Kernel’
T1 T2
T3
T4 T5
T6
3x3
Template
T7 T8 T9
Image
I = T1 x I1 + T2 x I2 + T3 x I3
+ T4 x I4 + T5 x I5 + T6 x I6
+ T7 x I7 + T8 x I8 + T9 x I9
September 28, 1998
I1
I2
I3
I4
I5
I6
I7
I8
I9
Local
Image
Neighborhood
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ITERATIVE ALGORITHMS ON
IMAGES
Specific simple example of an iterative procedure on an image
SUCCESSIVE CONVOLUTION AVERAGING
(Caveat: This is an illustrative example and not necessarily useful)
What Happens ??
ANSWER: Successive blurring at each iteration until eventually after a certain
number of iterations the image becomes a constant grey value equal to the average
of all pixels.
September 28, 1998
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ITERATIVE ALGORITHMS ON
IMAGES
SOMETHING MORE USEFUL
64
68
74
81
77
74
56
70
92
74
72
88
89
54
67
81
87
28
120
137
130
94
68
91
34 72 75
92 83 65
141 93 127
143 187 156
81 102 117
104 114 121
48 73 74
66 73 61
98
65
78
58
87
48
99
87
56
73
82
77
32
72
90
91
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
255
255
255
255
0
0
0 0
0 0
255 255
255 255
255 255
255 255
0 0
0 0
0
0
255
255
255
255
0
0
0
0
0
0
0
0
0
0
SIMULATED ANNEALING
RELAXATION LABELING
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0
0
0
0
0
0
0
0
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GRAYLEVEL HISTOGRAM
# OF
PIXELS
PIXEL GRAYVALUE
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HOUGH ALGORITHM
• Choose an analytic form f(x,y,a1,a2,…,an)
and choose a range of values for parameters
a1, a2, a3,….,an.
• Create accumulator array A(a1,a2,…,an)
which represents direct match of
f(x,y,a1,a2,…,an) with binary image.
• Local for local maximum which exceeds
certain threshold.
September 28, 1998
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GENERALIZED HOUGH
ALGORITHM
R-TABLE
f 1
f2
(Xc,Yc)
f
September 28, 1998
f
n
r1,r2,…,,rn
r1,r2,…,,rn
r1,r2,…,,rn
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