Fuzzy Sets and Possibility Theory - Information Fusion in Signal and Image Processing - page 173

- they have a compromise behavior in the case of partial conflict: these cases are
the most problematic and the operators are then “cautious”.
The difficulty is then to find a good conflict measure. That suggested as the maxi-
mum of the intersection between two possibility distributions [DUB 92a] is not always
well suited to image processing problems, particularly for the classification of multi-
source data. Fuzzy distances (see, for example, [BLO 99]) can provide solutions to
this problem.
The advantage of DC operators for image processing is undeniable, since they
allow us to take into consideration a wider variety of situations, several of which occur
simultaneously in image processing. Here are a few examples:
- sources can be in conflict when they provide information regarding one type of
event (a class, for example) and consonant for another class;
- sources can have different overall reliabilities;
- a source can be reliable for one class and poorly reliable for another, etc.
Unfortunately, these operators still have not, in our opinion, been developed far
enough in image processing and would deserve specific research.
This classification, which includes all of the commonly used operators, constitutes
a first criterion for choosing an operator for a specific application.
A second criterion is given by the properties of operators and their interpretations
in terms of uncertain, imprecise, incomplete or ambiguous data fusion.
The commutativity and associativity properties reflect the fact that the result of the
combination does not depend on what order the elements of information are arranged
in when they are combined. Whereas commutativity is satisfied by all of the commonly
used operators, this is not systematic with associativity (means and symmetric sums
usually are not associative). These two properties are often laid out as the minimum
properties that fusion operators have to satisfy. However, human reasoning does not
always comply with them. For example, a photo interpreter often starts by constructing
a primary interpretation of the scene based on a single image, then improves this in-
terpretation by using the other images, according to a process that clearly is not com-
mutative.
The existence of an identity element means that a source yielding this value will
have no influence on the result of the combination and represents some sort of indif-
ference on the part of the source towards the information sought, or even a complete
absence of knowledge regarding it. Such an element exists for t-norms and t-conorms.