In order to preserve the adaptive aspect of adaptive fusion and to find a common field of definition for all information to be fused, we propose to calculate the degree of consensus locally to each pixel. This allows to avoid the problem of the calculation of intersection for sources with different fields of definition.

At pixel level, the problem is not to calculate an intersection between distributions built on different fields, but to find an intersection between degrees of possibility of membership of a pixel to a class. These degrees are defined on the same interval: [0, 1].

With a degree of consensus calculated for each pixel, the choice of the behaviour of fusion is carried out locally to each pixel. It remains to choose between calculating a degree of consensus per class, or a degree global for all classes.

As fusion is carried out separately for each class, it is possible to calculate a degree of consensus for each one. We obtain a degree of consensus for class 1, and a fusion adapted for class 1, a degree for class 2 and one fusion adapted for class 2... The interest of this adaptive fusion completely distributed for each pixel and each class, consists in having, for a same pixel:

• a conjunctive fusion for the most plausible classes (strong degree of consensus), and
• a disjunctive fusion in for the least plausible classes (low degree of consensus or null).

The behaviour of the fusion is severe for the most plausible classes by using renormalized conjunctive fusion, and the least plausible classes are favoured with disjunctive fusion.

At last, a bad classification is reached because the most plausible classes were put at a disadvantage, compared to the least plausible classes. Moreover, using a degree of consensus per class tends to give a strong degree of membership to each class after fusion.

We thus recommend to use only one degree of consensus per pixel in order to put at the same level all the classes. As a different degree exists for each class, which degree must we choose?

• Choosing the smallest degree of consensus favours disjunctive fusion, and thus the option which assumes that the sources are not reliable. It is not the behaviour to be privileged.
  
• We thus propose to rather choose the strongest degree of consensus, and thus to favour the assumption that the sources are reliable.

Let S₁ and S₂ be two sources of information , and p be the number of classes. The sources attribute to a given pixel x the possibilities and of the membership of the pixel to each class c. The degree of consensus h of the pixel x is obtained as follows:

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