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Fusion by Dempster-Schafer's Rule of the Four Spectral
Bands MSS4 to MSS7 of LANDSAT Image
and Out-Image Data


It is interesting to notice that Dempster-Schafer's rule manages correctly a great amount of sources, and therefore the conflict generated by these numerous sources.

While having a conjunctive behaviour, Dempster-Schafer's rule does not fail when a conflict occurs, unlike the simple conjunctive fusion. The classification rate of 81.36% (see table 47) is comparable to the rate obtained by quantified adaptive fusion (84.76%).

This good performance is due to the modeling of uncertainty ($\theta$) of each source to clearly determine a single class for a pixel to classify. This uncertainty represents the degree of confusion of the source. $\theta$ corresponds to the union of all the classes, and this choice makes it possible, in the event of conflict, to defer part of the mass of evidence on each class. There thus remains a possibility so that the class of membership of the pixel is any of all the classes.

In the event of conflict between some sources which judge impossible that the pixel belongs to a class c, and all the other sources (majority) which selected this same class c as most plausible for the pixel, uncertainty $\theta$ makes it possible to avoid the failure of fusion by assigning, for classes rejecting the option of class c, a small part of the mass of evidence to this class c (at the same time as for all the other classes). This mechanism makes it possible to avoid that the mass assigned to class c is brutally reset by only one source which considers impossible this class.



  

Table 47: Fusion by Dempster-Shafer's rule of the spectral bands MSS4 to MSS7 and out-image data: distance to roads, plateaux, vales, slope orientation, slope steepness, edges, irrigation, MNT and distance to urban areas.

Rates of classification obtained
$\mbox{\ }$Class Number of pixels  

correctly classified

(A)             

Number of pixels

in samples     

(B)            

Rate of pixels    

correctly classified

(A/B)         

       1 400 459 87.15%
       2 398 459 86.71%
       3 234 306 76.47%
       4 313 391 80.05%
       5 409 459 89.11%
       6 418 459 91.07%
       7 260 459 56.64%
       8 265 459 57.73%
       9 443 459 96.51%
TOTAL 3140 3910 80.31%



  

Table 48: Inter-classes confusion matrix, in percentages, relating to classification after fusion by Dempster-Shafer's rule of the spectral bands MSS4 to MSS7 and out-image data: distance to roads, plateaux, vales, slope orientation, slope steepness, edges, irrigation, MNT and distance to urban areas.

  Class Observed  
 Class Expected 1 2 3 4 5 6 7 8 9 Unclassified 
1 87.15 2.61 - 8.06 1.74 0.44 - - - -
2 1.09 86.71 0.44 6.32 5.45 - - - - -
3 3.59 - 76.47 2.61 16.67 0.33 0.33 - - -
4 0.77 - 10.23 80.05 8.18 0.77 - - - -
5 0.22 - 0.22 10.46 89.11 - - - - -
6 2.40 0.22 0.22 1.53 4.58 91.07 - - - -
7 1.09 - - - 2.40 1.74 56.64 0.44 37.69 -
8 - - - - - - 3.49 57.73 38.78 -
9 - - - - 0.65 1.31 1.53 - 96.51 -




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