ty 
ed 
red 
e. 
The simulation was based on 20 points with low and 2C points with high contrast, selected from 
one image which was taken as true object and contaminated by Gaussian noise of different variance. 
The signal to noise ratio varied between 0.8 and 20. The result of a match was accepted if the 
estimated shift was 1 pixel or less giving an estimate for the reliability of the procedures in 
dependency of the SNE. 
The results for points with high and low contrast demonstrate the influence of the texture of the 
object, namely the gradient In The highest reliability in both cases is reached with the phase 
correlation (e.). For good points the SNR might even be below 7, still yielding a reliability 
of 0.8 or better. The dominance of the phase correlation, being representative for whitening 
filters becomes clear from fig. 7b for the points with low contrast. The worst reliability is (d.) 
obtained with the least sum method, which should be robust against noise. The reason for this be- 
havior is not quite clear, it might be caused by the type of distribution of the noise. The com- 
plex exponentiation (b.) with local adaption to the variance proves to be as reliable as cross- 
correlation (a.). For small signal to noise ratios however there is a slight difference in favour 
of the complex exponentiation. 
The investigation clearly demonstrates that for low signal to noise ratios the reliability of 
correlation can be increased significantly by sharpening the peak of the correlation function. 
3.7 The effect of quantization and.data compression 
Multi-image correlation as discussed in sect. 2.3 requires the storage of a large number of 
image patches. In order to reduce the necessary storage the data have to be compressed. A pure 
redundancy reduction where the original image can be restored without loss is not efficient enough. 
But information reduction will cause quantization errors and thus increase the noise component in 
the images. Consequently the reliability and the precision will be worse. 
1. Table 5 is taken from Bailey et.al. (1976) and shows the effect of quantization on the relia- 
bility for 5 different scenes using 25 points in each scene. The data are digitized pictures. The 
reliability values are given for the median absolute deviation (MAD) and the normal product cova- 
riance (NProd). 4 different quantization levels are investigated. The patch sizes of g. and Zn 
were 20x20 and 5x5 resp.. n E 
Table 5 Effect of Quantization on the probability of Correlation 
(from Bailey et. al. 1976) 
  
Quantization Scheme 
  
Continuous | 8-level 4-level Binary 
  
Scene Type MAD | NProd | MAD | NProd | MAD | NProd | MAD | NProd 
  
  
  
  
  
  
  
  
  
  
  
Random .90 95 .78 .87 .65 74 .30 .30 
Agricultural| .72 «i72 . 64 „52 .36 .40 36 36 
Mountains „75 „72 .60 .60 .36 32 .28 „28 
Desert .92 92 „80 „80 ‚48 .56 36 „36 
Suburban „80 „92 72 .80 .68 42 36 . 36 
  
Obviously the reliability decreases monotonically with decreasing quantization level. A quanti- 
zation with only 4 levels on an average seems to be not sufficient. Also the MAD clearly gives 
worse results than the covariance (NProd), which does not quite follow the expections, as the 
MAD is a robust measure. The results are based on unmodified data, where not all 64 grey levels 
are present in some of the regions. This should be kept in mind when analysing the results.