Multisensor triplet Markov fields and theory of evidence

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Hidden Markov Fields (HMF) are widely applicable to various problems of image processing. In such models, the hidden process of interest X is a Markov field, which must be estimated from its observable noisy version Y. The success of HMF is due mainly to the fact that X remains Markov conditionally on the observed process, which facilitates different processing strategies such as Bayesian segmentation. Such models have been recently generalized to ‘Pairwise’ Markov fields (PMF), which offer similar processing advantages and superior modeling capabilities. In this generalization, one directly assumes the Markovianity of the pair ( X, Y). Afterwards, ‘Triplet’ Markov fields (TMF) have been proposed, in which the distribution of ( X, Y) is the marginal distribution of a Markov field ( X, U, Y), where U is an auxiliary random field. So U can have different interpretations and, when the set of its values is not too complex, X can still be estimated from Y. The aim of this paper is to show some connections between TMF and the Dempster–Shafer theory of evidence. It is shown that TMF allow one to perform the Dempster–Shafer fusion in different general situations, possibly involving several sensors. As a consequence, Bayesian segmentation strategies remain applicable.