backscatterers distributed over the cell. The amount 
of energy backscattered by these individual 
scatterers can be equal or can vary and the 
positional distribution of them is regular or 
irregular. In a non-homogeneous cell the dominant 
scatterers will have the highest influence on the 
phase, therefore variation in the position of 
dominance will vary the phase significantly. These 
points with a relatively high response (figure 1) 
will also have a too large influence on the 
computation of the coherence map (figure 2). This 
influence can be reduced by means of a filter 
combination as described in this paper. 
Apart from temporal changes, decorrelation can 
also be a consequence of an improper (too large) 
distance (base) between the two sensors during the 
data acquisition. In case of the extraction of 
thematic information, the decorrelation related to 
the base line should be minimized such that 
  
Figure 2 Coherence map of The ERS-1/2 pair 
differences that appear can be considered to come 
mainly from temporal decorrelation. 
1.1 Coherence 
The complex coherence between two SAR images 
is defined by (Touzi et al., 1996): 
E\S, - 55) 
E IS E IS, 
  
and the estimator of the coherence is defined by 
M 
: . 5146 
RS a; a, -¢€ 
^ izl 
SC i y : T (a5; y 
izl izl 
  
  
For each map element, the coherence is computed 
in a window surrounding that point. The value 
between 0 and 1 is related to the equality of the bi- 
directional signal of the two sub-images (from 
master and slave). A constant phase shift between 
the corresponding elements of the images does not 
modify that value. In the computation of the 
coherence, by the above given formula, is the 
contribution of such a constant phase shift 
eliminated. 
However, the influence of a strong backscatterer 
(e.g. a corner reflection) is dominant in its 
surrounding in the computation of the coherency. 
This dominance results in a high coherence over a 
larger area than in reality the case. For example, an 
element in a sub-image of the same size as the 
kernel of the (filter) operator (40 * 7 elements) 
represent a very strong scatterer (e.g. thousand 
times the scatterers in its surrounding in both the 
ERS-1 and the ERS-2. This strong scatterer will 
overrule the other elements at a distance smaller 
than the kernel size. That means that a large kernel 
(e.g. 150*150meter in ground size) shows a very 
high coherence over that area without being 
realistic. 
If the coherence map is used for thematic 
information extraction, then important information 
can be hidden by this way of coherence 
computation. The images in figure 3 visualize this 
Intemational Archives of Photogrammetry and Remote Sensing. Vol. XXXII, Part 7, Budapest, 1998 
539