540 
  
unwanted effect. 
The data used for these pictures is artificial. One 
image is created using a randomizer (figure 3a) and 
the second one is derived from the first by a 
“controlled” phase shift (figure 3b). One element of 
the first and the corresponding one of the second 
improvement since the kernel size of the coherence 
filter can not be too large. If the kernel is too large, 
a smoothing of the coherence will be the result and 
this will reduce the effective resolution of the 
coherence map. The lower the resolution the less 
thematic information remains. But a small kernel 
  
Figure 3 a) Master image, b) Slave image and c) Coherence 
got a relatively very high value. From these two 
data sets in complex format the coherence is 
computed by means of the formula given above. In 
figure 3c the result is shown. The images contain 
25 * 25 elements. An average filter (kernel size is 
5*5 elements) is applied for the filtering of the 
components of the formula. 
1.2 Filters 
As can be seen in figure 3, the central pixel in the 
master and slave have a big influence on its 
surrounding at the coherence computation. To 
avoid this, an adapted filter can be used for 
example a gaussian weighted mean or a sinc 
function. However this will hardly give an 
Figure 4 Coherence map of normalized 
images 
size will not be effective in case of a corner 
reflection since a too strong fall off in the 
contribution of the sub_ image elements will lead 
to a coherence map that consists of the coherency 
which is computed from almost only individual 
points. Such a coherence map will show up a high 
variation in coherency, leading to noisy result. 
To give each element the same “strength” in the 
computation of the coherence in a window, the 
complex vector must be normalized, which means 
that the coherence computation is only based on the 
phase information. In the case that an average filter 
is used for the computation, the phase of each 
element gives the same contribution to that 
computation. In figure 4 the coherence of the 
normalized images is given. 
The disadvantage of the coherence computation 
from normalized images is that those points with a 
high backscatter and a high coherence get a 
significant lower coherence value assigned because 
of the strong influence of their surrounding. 
It can be concluded that a filter process should be 
developed that avoids the reduction of the 
coherence value in case of strong coherent 
scatterers and on the other hand these strong 
scatterers should not increase the coherence value 
if that is not valid. For that purpose, a modified 
average filter is used. The function of this filter is 
the computation of the coherency of a sub-image 
without taking the central element in account. The 
center of the filter kernel is equal to zero. In figure 
5 and 6, the coherence maps that are created by the 
two types of average filters are shown. The 
different functionality is clearly demonstrated in 
the center of the image. 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXII, Part 7, Budapest, 1998