Dempster-Shafer fusion of evidential pairwise Markov fields

Hidden Markov fields (HMFs) have been successfully used in many areas to take spatial information into account. In such models, the hidden process of interest X is a Markov field, that is to be estimated from an observable process Y. The possibility of such estimation is due to the fact that the conditional distribution of the hidden process with respect to the observed one remains Markovian. The latter property remains valid when the pairwise process (X,Y) is Markov and such models, called pairwise Markov fields (PMFs), have been shown to offer larger modeling capabilities while exhibiting similar processing cost. Further extensions lead to a family of more general models called triplet Markov fields (TMFs) in which the triplet (U,X,Y) is Markov where U is an underlying process that may have different meanings according to the application. A link has also been established between these models and the theory of evidence, opening new possibilities of achieving Dempster-Shafer fusion in Markov fields context. The aim of this paper is to propose a unifying general formalism allowing all conventional modeling and processing possibilities regarding information imprecision, sensor unreliability and data fusion in Markov fields context. The generality of the proposed formalism is shown theoretically through some illustrative examples dealing with image segmentation, and experimentally on hand-drawn and SAR images.