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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
A-Fuzzy Measure: Let Z = Ei Zube the set of available 
change detectors. 
For each change detector z;to be combined, we associate a 
fuzzy measure g, (z ;) indicating its performance in the class À. 
For a given pixel, let h, (z;) be the objective evidence of the 
change detector z;for the class &. The set of change detectors is 
then rearranged such that the following relation holds: 
h, (zı )= iE (z,)2 0. 
We obtain an change 
detectors A = iz. so that A,= z, and A; = A4; ( Uz;. 
ascending — sequence of 
The fuzzy measures of the obtained change detectors are 
constructed as 
- g (4) e.) Ag, (4,4) (es) 
For each class, A is determined by solving an n-1 degree 
equation (Cho and Kim, 1995; Cho, 1995): 
n 
[[b+2g,(e;)]=1+2 (6) 
i=l 
Fuzzy Integral: for a given class k the Sugeno fuzzy integral is 
computed as 
n : 
Is(k)- [hog= Max|Min(^, (z; ). 2, (4))] (7) 
In the present case 7 is equal to 2. Also, the computation of the 
fuzzy integral would only require the knowledge of the 
importance of each source expressed by the fuzzy measure (Cho 
and Kim, 1995). These quantities can be computed by several 
ways. In this study, for each change detector the fuzzy measure 
is defined as being the fuzzy accuracy per land cover class 
computed on a validation set. 
3. EXPERIMENTAL RESULTS 
The study area is a portion of a coastal region located in the 
north of Algeria (Algiers), for which two SPOT images were 
selected to test the validity of change detector combination. The 
first image has been captured in May 1989, while the second 
image was captured in June 1991 (Figure 2). Due to the weak 
rainfall in this period, the study site has undergone important 
changes. Therefore, we were interested in those changes from 
water, construction, and vegetation to nakedly soil. However, 
the satellite data depict other changes caused by the presence of 
clouds in the second image. To avoid all surprising effect of this 
factor, an additional class ‘X = Clouds’ was taken into account. 
X denotes whatever land cover class. Hence, the selected land 
cover categories are listed in table 1. 
711 
3.1. Quantitative evaluation 
Unlike the hard classification techniques, the fuzzy set theory 
provides several measures for accuracy assessment beyond the 
standard error matrix. A number of approaches are available as 
the fuzzy distance measure and the fuzzy entropy. In this paper, 
we use the fuzzy accuracy (FA) per land cover class as well as 
the fuzzy overall accuracy (FOA), for performance evaluation 
(Bärdossy and Samaniego, 2002). 
  
(b) 
Figure 2. Coastal region of Algiers 
(a : image of 1989, b : image of 1991) 
  
Class labels Description (1989 c» 1991) 
  
1 Water = water 
2 Vegetation = vegetation 
3 Construction = construction 
4 Soil = soil 
5 Construction = soil 
6 Vegetation = soil 
7 Water = soil 
8 X = clouds 
  
Table 1. Classes of interest