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The probability mass functions are parametrized either as mixtures or exponential distributions, for which a natural gradient method is applied.

Once the mass functions are calculated for all the used factors, the Dempster's rules of the combination is used to obtain the four integrated mass functions (Dempster 1968).

Once the mass functions are estimated for each image to be fused, the DS combination rule and decision are applied to obtain the final segmentation.

Once the mass functions are estimated by the assumption of GD, the DS combination rule is applied to obtain the final segmented image.

This equation includes the means and standard deviations of the pmfs of the genuine and imposter distributions, combined into a measure of how well separated the two probability mass functions are separated from each other [9].

Considering two mass functions (m_1) and (m_2), the conjunctive combination rule is defined as: (2 To make a decision, we try to select the most likely hypothesis which may be difficult to realize directly with the basics of the belief functions theory where mass functions are given not only to singletons but also to subsets of hypothesis.

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A combination of any two mass functions is another mass function.

In this study, the method of generating the mass functions is based on the assumption of a GD [24].

For one hand, we know that the DS fusion result of all these mass functions is a TMC, and on the other hand, the result of this fusion is the posterior probability p ( x | y ).

Let us bring up the following intuitive result: when one of the mass functions is Bayesian (probabilistic), the DS fusion result given by Equation (10) is also Bayesian [14].

According to the intersection table (see Figure 2) obtained by the Dempster rule, the combination of two mass functions is given as follows: Figure 2 The intersection table obtained by the Dempster rule.

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