Chain Code can be assigned to it (Fig.1), 
  
Fig.1 Chain code 
then we transform the chain code and length to be y-s 
curve (Fig.2), 
$ 
368 
313 
270 
225 
188 
135 
9e 
45 
° CTTTTTITTITLóL- 
  
Fig.2 The shape description by wy-s curve 
then the shape of two regions can be compared by the 
curves, because the qy-s curve has three characters: 
(1) If the corresponding region pair has a different 
orientation, their y-s curve has a different shift in the 
vertical direction. 
(2) If the corresponding region pair has a different 
starting point, their §-s curve has a different shift in the 
horizontal direction. 
(3) If the corresponding region pair has a scale difference 
their y-s curve has a different length. 
Therefore, during the shape comparison, we need to 
interpolate all the y-s curves into a uniform length, and 
extend the curve by repeating the y-s curve once; then 
during the comparison, we treat the w-s curve of left 
region as target window, and treat the extended y-s curve 
as search window, then compare/ search vertically and 
horizontally as we do in the matching procedure. The 
minimum difference.between these two curves is the 
result of shape comparison. Because the resolution of the 
chain code is 45 degree only, we can smooth the curve 
with [0.1, 0.2, 0.4, 0.2, 0.1] operator for getting better 
resolution and better result of shape comparison. 
42 Initial matching probability 
The property of region can be used for region matching, 
such as the shape, the area, the grey value, the gravity 
centre etc.. For initial matching probability, the shape 
and area of regions in image 1 and image 2 are selected 
for Minimum Cost Function and the region difference 
M(i,j) can be calculated : 
M(i,j) =[shape1(i) - shape2(j)]" (2) 
+[ Area1(i) - Area2(j) J? 
The similarity measure S(i,j) is inversely proportional to 
M(i,j) and is defined as: 
S(i,j)=1 /(1+Cm * Máj), 0 «Sj «1 (3) 
Cm =2 /( Max(M(i,j)) + Min.(M(i,j)) ) (4) 
where Cm is a scale factor, if image 1 (left image) has n 
regions, image 2 (right image) has m regions, then i= 
1,2....n and j=1,2.....m. The smaller the value Cm is, the 
more sensitive the similarity measure bécomes. The 
selection of Cm depends on the image quality. For 
478 
occlusion or imperfect segmentation or change of land 
use, some regions can not get the corresponding region 
in another image, a pseudo region called null region with 
index 0 is used, the similarity measure of i region of left 
image with its null region is define as: 
S(i,0) =1 - Max(S(j),i =1,2...n, j =12..m. (5) 
The estimated matching probability P(i,j) can be obtained 
by normalizing the similarity: 
n 
P(i,j) -S(üj/zSük,i-12.nj-142.m. (6) 
k=0 
4.3 Compatibility of regions 
If the matching of region is not independent on each 
other, we can use the compatibility, which is denoted as 
C(i,jh,k), to show the relationship of their dependency. 
If A match B denote as A;eB; and their matching prob- 
ability P;. is strongly influenced by A, eB,, We say capabil- 
ity C(i,j;hk) >1. If C(i,jh,k) < 1, it means A,eB, has 
negative influence to A;eB; If C(ijh,k)=0, it means 
there is irrelevance between A, eB, and A;cB; 
For region matching, we can compare the interior angles 
of triangles which are constructed by three region gravity 
centers of two images each, as the compatibility [Lee & 
Lei, 1990], or we can simplify the angles into vectors 
(Fig.3) : 
Right Image Regions Left Image Regions 
Sl a 
Fig.3 The vector of gravity centre of region 
  
  
  
  
  
  
  
  
in Fig.3, if A;eB; , and the vector ih is the same as vector 
jk, then we say C(i,j;h,k)=1 and the P,, would influence 
P, ; if the vectors (e.g. ih and jl) are completely different, 
we assign C(i,j;h,1) =0, it means A;eB; has irrelevance with 
A,€B, and P, has no influence to P;. If the matching 
probability P,, is high and C(i,j;h,k) is positive, we want 
to increase P,,, since it is compatible with the high proba- 
bility matching A,eB,. Similarly, if P,, is high and 
C(ijh,k) is negative or zero, we want to decrease Pj , 
since it is incompatible with A,eB, even it has high 
probability. A very simple way to define an influence to 
P, that has desired properties is to use the product 
C(ijh,k) P, . 
44 Refinement of matching pairs 
During the iteration for region matching refinement, the 
matching probability P;; is adjusted by reinforce quantity 
O(i,j): 
Q(ij -z (zx C(ijh,k) * P(h,k) ) (7) 
the Q(i,j) should be greater than 0 except when C(i,j;h,k) 
=0, the increment Q is used in refinement procedure: 
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