insensitive to the finite size of the images (wrap-around errors) and 
also to noise. 
As the effect of image projection is not quite clear in this case, the 
testing of this matching procedure has been performed in two 
dimensions. Due to the limited computer means at hand, the images used 
were chosen to have a size of 32 times 32 pixels. First the effects of 
wrap-around were investigated by determining the phase correlation 
function for 9 different image pairs constructed by  noncyclical 
displacements y = 1,3,5,...,31 in the x-direction. For translations uy 
less than half the image size, 70 out of 72 determinations of y were 
correct within one pixel. For translations greater than half the image 
size, the method rapidly breaks down. Figure 5 shows the relative 
energy in the largest spike, the location of which was chosen for the 
estimated translation y. As indicated in Kuglin and Hines, the method 
is found to be superior to the methods discussed in this paper. 
The procedure discussed above is in fact so insensitive to wrap- 
around, that it is interesting to test it on image pairs consisting 
of two different images. 225 image pairs were sampled from two aerial 
photographs in such a way that the displacements were small (of the 
order of a few pixels). The difference between the images is therefore 
almost completely due to noise (i.e. a priori unspecified effects of 
differences in projection, reflection dependent on direction , etc.). 
The phase correlation function was then computed and the matching 
parameter u obtained by thresholding. The results of the test can be 
summarized in the following points: 
1) Only 10 of the 225 determinations give a relative energy 
greater than 0.1 in the main spike. 
2) All these 10 matchings give the same result. 
3) Main spikes with a relative energy only slightly smaller than 
0.1 generally give incorrect results. 
4) When the test was rerun with one of the images displaced 2 
pixels, only 2 of the 10 matchings mentioned in point 1) 
turned up again. In the precence of noise, even spikes of 
large relative energy are apparently unstable. 
It is concluded, that the noise results in, an almost complete 
breakdown of the method. Even 1f the phase correlation function 
apparently is remarkably insensitive to effects of finite image size, 
much remains to be done before image pairs consisting of aerial 
photographies can be matched with this method. 
MAXIMUM ENTROPY METHODS 
As shown earlier, wrap-around effects on Fourier transforms are so 
strong that these cannot be used for matching image pairs. As this is 
due to the very unrealistic assumption of cyclic extrapolation outside 
the image boundaries, a possible method is to use estimates of cross 
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