= p "n 2: 
V = 2 (A,-Bi) =llc’ll =(||Al| sin §) =min (21) 
1,5 
ea Er [0| =min (22) 
It is eauivalence to correlation coefficient (Fig. 2). 
The difference betwen A and B can also be defined by the 
absolute norm of vector C, i.e. 
pim 321A; Bi 321€; Lo min (23) 
Fig.3 shows that all points along square sides 1234, which 
has symmetric centre at point A and diagonals paralle to 
axis u or v, is equal in norm P. 
Analysis of the algorithms with derivative preprocessing is 
more complete. However for finding the discrepancy among the 
criterions only, we may take a simple example to make easy. 
Considering the sum of absolute differences with first de- 
rivative processing, the following expression can be derived 
from (10.1) 
"n-1 n-] 
D,72 ZA: Ar) (Bi Bi0] 2 2214; B2 Art Bin) 
i21 i21 
-$316,-6,.l -E3l4C;l o min (24) 
It will be seen from Fig. 3, that points along the line lo 
passing through point A and spreading 45'angle from axis u, 
have \aCu|=0; and all points on line ltparallel to le, have 
làcuv'lconstant, that is in proportion to the distance from 
l4 to lo. 
  
  
  
  
  
  
  
  
  
  
Fig. 4 Discrepancy of the criterions 
The expressions (15),(19), (180, (222, (24) demonstrat various 
criterions in the same vector space and shows all the crite- 
rions are not identical.When the target vector A is given and 
several match vectors (such as I,1.IL,IV.V shown in Fig.4) ap- 
pear in a sertain searching area of the right image, the dif- 
ferent criterion may result different correlation. For ins- 
tance, vector 1 may be selected as the correspondence of A by 
correlation coeffient criterion and vectors I.IX.1V or V may 
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