Estimation of generalized multisensor hidden Markov chains and unsupervised image segmentation

Abstract

This paper attacks the problem of generalized multisensor mixture estimation. A distribution mixture is said to be generalized when the exact nature of components is not known, but each of them belongs to a finite known set of families of distributions. Estimating such a mixture entails a supplementary difficulty: One must label, for each class and each sensor, the exact nature of the corresponding distribution. Such generalized mixtures have been studied assuming that the components lie in the Pearson system. Adaptations of classical algorithms, such as Expectation-Maximization, Stochastic Expectation-Maximization, or Iterative Conditional Estimation, can then be used to estimate such mixtures in the context of independent identically distributed data and hidden Markov random fields. We propose a more general procedure with applications to estimating generalized multisensor hidden Markov chains. Our proposed method is applied to the problem of unsupervised image segmentation. The method proposed allows one to: (i) identify the conditional distribution for each class and each sensor, (ii) estimate the unknown parameters in this distribution, (iii) estimate priors, and (iv) estimate the "true" class image.