When a conflict occurs between sources, the quantified adaptive fusion assumes that a part only of the sources available are reliable. These sources supposed reliable are those which agree each other at least a little. The other sources, which create the conflict, are supposed to be the unreliable sources.

To determine which are the reliable sources, the criterion used is the height of the intersection of the distributions of possibility, or degree of consensus. The problems arising from the use of this fusion, within the satellite framework of the images, are the same ones as those met during the application of a simple adaptive fusion:

• How shall we calculate the height of the intersection between the distributions of possibility?
• Globally on the whole distributions built starting from the samples, or
• locally in each pixel?

As previously, the solution of local calculation in each pixel is retained in order to preserve the adaptive feature of the method and to work on data defined on a same field.

• At pixel level, shall we calculate a height of intersection for each class or a global height for all the classes?
• A height calculated for each class has the quality to be best suited for all the particular cases of each class.

However, the essential objective, after fusion, is to classify the pixel in one of the classes. Thus, the comparison of the degrees of membership of the pixel to each class must make it possible to reveal a class more plausible than the others. However quantified adaptive fusion aims to select the most reliable sources in order to get rid of the constraint of the conflict between sources and to use conjunctive fusion. A degree of consensus calculated for each class will erase the conflict met for each one, and thus each class becomes a plausible class for this pixel. Instead of improving the distinction between the classes plausible for a pixel, this system increases confusion between the classes and decreases the performances of classification.

• At the opposite, a degree of total consensus for all the classes, but local to each pixel, avoids this problem. We will select n reliable sources, where n is the greatest number of reliable sources for each class. The classes supported by a maximum of sources are favoured, the others are eliminated as considered to be less plausible for the pixel since they are supported by a lower number of sources. Thus is satisfied the intuitive condition which assesses that the more there are sources which support a class, the more this class is plausible.

As we did for adaptive fusion, we use a degree of consensus local to each pixel, but global for all the classes:

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