Belief Function Theory - Information Fusion in Signal and Image Processing - page 114

any C i ∈ Bel( A ), a certain number of precautions have

to be taken in order to decide in favor of a composite hypothesis. We can, for exam-
ple, imagine making a decision in favor of a composite hypothesis if the arguments
involving the simple hypotheses are not strong enough.

A and because Bel( D ) ≥

Thus, in Figure 7.2, the decision was made according to the maximum belief over
all of the hypotheses except D . Let us note that, in this simple case, the maximum
credibility is equivalent to the maximum plausibility, since m 1 ⊕

m 2 is a Bayesian
mass function. With this rule, the decision is made in favor of a simple hypothesis in
the points where other masses are equal to zero and in favor of a composite hypothesis
otherwise. This way, we obtain interesting results since the partial volume points are
detected as a composite hypothesis, whereas the areas without ambiguity are well
segmented. Figure 7.3 shows the results obtained by making a decision in favor of a
simple hypothesis with the maximum belief.

C3

C2

C2 U C3

C1 U C3

C1 U C2

C1

C1 (brain)

C2 (ventricles + CSF)

C3 (ALD)
C1 U C2
C1 U C3

C2 U C3

Figure 7.2. The different decision areas depending on the values of m 2 ( C 3 )

and the decision image, by taking the maximum belief over all of the hypotheses except

m 1 ( C 2 ) and

D