Unsupervised segmentation of nonstationary pairwise Markov Chains using evidential priors

Abstract

Hidden Markov models have been widely used to solve some inverse problems occurring in image and signal processing. These models have been recently generalized to pairwise Markov chains, which present higher modeling capabilities with comparable computational complexity. To be applicable in the unsupervised context, both models assume the data of interest stationary. When these latter are actually stationary, the models yield satisfactory results thanks to some Bayesian techniques such as MPM and MAP. However, when the data are nonstationary, they fail to establish an appropriate link with the data and the obtained results are quite poor. One interesting way to overcome this drawback is to use the Dempster-Shafer theory of evidence by introducing a mass function to model the lack of knowledge of the a priori distributions of the hidden data to be recovered. It has been shown that the use of such theory in the hidden Markov chains context yields significantly better results than those provided by the standard models. The aim of this paper is to apply the same theory in the pairwise Markov chains context to deal with nonstationary data hidden with correlated noise. We show that MPM restoration of data remains workable thanks to the triplet Markov models formalism. We also provide the corresponding parameters estimation in the unsupervised context. The new evidential model is then assessed through experiments conducted on synthetic and real images.