Unsupervised segmentation of nonstationary data using triplet Markov chains

An important issue in statistical image and signal segmentation consists in estimating the hidden variables of interest. For this purpose, various Bayesian estimation algorithms have been developed, particularly in the framework of hidden Markov chains, thanks to their efficient theory that allows one to recover the hidden variables from the observed ones even for large data. However, such models fail to handle nonstationary data in the unsupervised context. In this paper, we show how the recent triplet Markov chains, which are strictly more general models with comparable computational complexity, can be used to overcome this limit through two different ways: (i) in a Bayesian context by considering the switches of the hidden variables regime depending on an additional Markov process; and, (ii) by introducing Dempster-Shafer theory to model the lack of precision of the hidden process prior distributions, which is the origin of data nonstationarity. Furthermore, this study analyzes both approaches in order to determine which one is better-suited for nonstationary data. Experimental results are shown for sampled data and noised images.