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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 ()
of each source to clearly determine a single class for a pixel to classify.
This uncertainty represents the degree of confusion of the source.
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
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.
Rates of classification obtained | |||
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Number of pixels correctly classified (A) |
Number of pixels in samples (B) |
Rate of pixels
correctly classified |
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% |
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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 | - |