EFFECTS OF WINDOW CHOICE 
When matching two images using (18), the wrap-around error has been 
shown to dominate the result. The effects obtained when standard 
methods for repressing wrap-around error are used will be investigated 
in this section. 
The simplest method of handling wrap-around effects is to augment the 
images with zeros. Instead of (7) and (8), we therefore define £ and q 
as N-dimensional vectors: 
  
  
fond Genio qrr. qi 
2 = S10) 4g, ge On (26) 
alu) = (9 +1 942 IM 0...09,3, ... 2 
f 
all rill] il 
à ^ Te 
g 
tes il 
[ T T + x 
0 M N 
Figure 3: fix) z«gílne4), 090. 2 Y,2o 4L.) Wes 
(Ox) atcgUx) 230i x 22804,8425... N. 
f and g are periodic with period À = N. 
When the matching is performed according to (18) using N components of 
the vectors instead of M, it is found that yu « O independently of the 
translation between the images. The reason for this is that when f 
and g are defined according to (26), the translation between the 
images is a secondary effect, while the dominating property is 
f(x) 2-0; g(x) 
fix) = 0; g(x) 
n * 
0; x = 1,2,...,M 
0; x M+1,M+2,...,N 
As this property is identical in the two images, we obtain y « O. The 
same result is obtained if f and g are augmented with their mean 
values instead of zeroes. This method can apparently not be used to 
avoid wrap-around effects on matching. 
Another method to repress wrap-around effects is to multiply the 
images with a window function w(x) which tends to zero at the 
boundaries of the image. Suitable choices for w(x) are for instance 
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