Hidden evidential Markov trees and image segmentation

The problem addressed in this paper is that of statistical segmentation of images using hidden Markov models. The problem is to introduce a prior evidential knowledge, defined by a mass function, or equivalently, by a belief function. We notice that the result of the Dempster-Shafer fusion of an evidential Markov field with a probability provided by the observations is not necessarily a Markov field. Thus using classical Bayesian segmentation as MPM or MAP is not tractable. In order to solve this problem, we show that the use of Markov trees, which is an another way of modelling the spatial dependence of the class random process, leads to tractable segmentation methods. In fact, the Dempster-Shafer fusion does not destroy the Markovianity in the a posteriori distribution and thus the classical Bayesian segmentation methods like as MPM or MAP may used. Furthermore, some ways of the model parameter estimation are indicated.