International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
The two fuzzy change detectors used independent training data 
but they were evaluated on the same data set comparatively to 
the combiner. The derived FA and FOA measures from the 
different approaches are reported in table 2. As can be seen, the 
fuzzy integral outperformed the individual change detectors 
although the category water — soil has performed somewhat 
better with the simultaneous analysis based change detector. 
This empirical finding is due to the fact that the difference of 
performance between the two change detectors is important. In 
such a case the fuzzy integral produces an accuracy lower than 
that of the most precise change detector. In other classes the 
fuzzy integral gives the best fuzzy accuracy rates yielding to a 
significant improvement of the FOA rate. In fact, this 
combination rule tends to increase the overall fuzzy accuracy by 
equalizing the fuzzy accuracies in individual classes. 
  
  
  
Class CA (94) SA (94) FI (96) 
1 98.38 89.06 100 
2 67.54 73.00 87.30 
3 78.52 75.52 90.74 
4 83.91 75.94 97.20 
5 61.84 82.61 86.76 
6 77.21 80.90 88.84 
7 17.65 49.69 46.08 
8 75.90 66.78 87.39 
FOA 70.56 74.43 86.56 
  
Table 2. Fuzzy accuracy values obtained for the individual 
change detectors against the combination process 
3.2. Visual inspection 
The visual inspection of the resulting change detection map 
indicates how the considered system generalizes. Since we are 
using fuzzy systems, the output is hardened by affecting each 
pixel to the land cover class which corresponds to the maximum 
fuzzy membership value. Thus, in the final change detection 
map, each land cover class takes a particular color. Figure 3 
shows the resulting maps obtained for the two change detectors 
as well as the combined system. In this figure only the three 
change classes (Classes whose labels are 5, 6, 7) are depicted. 
As can be seen, the two change detectors produce considerable 
misclassification rates. According to figure 3.(a), the 
comparative analysis neglects an important change surface in 
the river and so detects badly the class water — soil. Moreover, 
it presents a considerable amount of omission in the class 
construction — soil. Instead, the simultaneous analysis based 
change detector presents important overestimation rates in the 
classes construction — soil and water — soil. In fact, errors in 
the class 5 are related to the clouds which were not selected as 
belonging to the class X — clouds, while errors in the class 7 
are due to changes in vegetal areas which have not been 
considered in the training set. As shown in figure 3.(c), the 
fuzzy integral performs better, and can increase the detection 
accuracy in the different change classes while reducing the false 
alarm rate. This means that the fuzzy integral combines the two 
change detectors by extracting the correct decision from both so 
that it derives the best final decision. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
   
  
  
   
  
  
  
   
   
  
  
  
   
  
  
  
  
  
  
  
   
   
  
  
  
   
  
  
  
  
  
  
  
  
   
  
  
  
   
   
  
  
Figure 3. Change detection maps (a : Comparative analysis, 
b : Simultaneous analysis, c : Fuzzy integral) 
  
  
BI Construction = soil E Water © soil 
= Vegetation = soil 
  
  
  
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