The other functions are placed in the middle: in fig. 8 the intensity coeffi- 
cient c) shows less distortions against low SNR whereas in fig. 9 the corre- 
lation function a) is of greater accuracy with lower SNR than b) and c). 
But both images together show that the choice of good correlation points may 
have as great influences as the choice of a good correlation function. Fig. 10 
shows the dependency of correlation maximum (here of function a)) on the 
variances in the pattern matrix (SNR = 2.6). 
  
A KORRELATIONSMAXIMUM 
  
0.2 
  
  
ay 
0 S 40 1% 26 25 
  
  
  
Fig. 10: Correlation maximum versus standard deviation of pattern matrix 
Combining these results we can say that high variances in the correlation point 
environment and the phase correlation method have the greatest probability for 
exact correlation even in images with a SNR in the near of 1.0. 
CONCLUSIONS 
Naturally this study cannot treat all aspects of the problem 'accuracy in 
digital correlation'. Rotation and change of scale is not discussed here. 
Only normal and uniform distribution of random noise have been tested. Other 
distributions may have more relations to natural problems and shall be taken 
into account likewise. 
Reference and search images have not been digitized independently and no other 
features as variance in the pattern matrix has been taken into account. Never- 
theless a correlation concept for rectification of remote sensing imagery with 
low SNR (like we have in those of tidal lands) should consider the phase and 
not only the amplitude of image signals. 
Indeed phase correlation requires more computation time than 'normal' correla- 
tion (depending on the number of prime factors in pattern matrix size), but 
still less than the method of complex exponentiation. 
Time factors (normalized on the fastest objective function, the Laplace- 
coefficient). are given in table 2. 
76 
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