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Chaînes et arbres de Markov évidentiels avec applications à la segmentation des processus non stationnaires

Abstract : The triplet Markov chains (TMC) generalize the pairwise Markov chains (PMC), and the latter generalize the hidden Markov chains (HMC). Otherwise, in an HMC the posterior distribution of the hidden process can be viewed as a particular case of the so called "Dempster's combination rule" of its prior Markov distribution p with a probability q defined from the observations. When we place ourselves in the theory of evidence context by replacing p by a mass function m, the result of the Dempster's combination of m with q generalizes the conventional posterior distribution of the hidden process. Although this result is not necessarily a Markov distribution, it has been recently shown that it is a TMC, which renders traditional restoration methods applicable. Further, these results remain valid when replacing the Markov chains with Markov trees. We propose to extend these results to Pairwise Markov trees. Further, we show the practical interest of such combination in the unsupervised segmentation of non stationary hidden Markov chains, with application to unsupervised image segmentation.
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https://hal.archives-ouvertes.fr/hal-01347969
Contributor : Médiathèque Télécom Sudparis & Institut Mines-Télécom Business School <>
Submitted on : Friday, July 22, 2016 - 9:37:10 AM
Last modification on : Wednesday, November 25, 2020 - 3:26:56 AM

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  • HAL Id : hal-01347969, version 1

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Pierre Lanchantin, Wojciech Pieczynski. Chaînes et arbres de Markov évidentiels avec applications à la segmentation des processus non stationnaires. Traitement du Signal, Lavoisier, 2005, 22 (1), pp.15 - 26. ⟨hal-01347969⟩

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