Parameter Estimation in Hidden Fuzzy Markov Random Fields and Image Segmentation

Abstract

This paper proposes a new unsupervised fuzzy Bayesian image segmentation method using a recent model using hidden fuzzy Markov fields. The originality of this model is to use Dirac and Lebesgue measures simultaneously at the class field level, which allows the coexistence of hard and fuzzy pixels in a same picture. We propose to solve the main problem of parameter estimation by using of a recent general method of estimation in the case of hidden data, called iterative conditional estimation (ICE), which has been successfully applied in classical segmentation based on hidden Markov fields. The first part of our work involves estimating the parameters defining the Markovian distribution of the noise-free fuzzy picture. We then combine this algorithm with the ICE method in order to estimate all the parameters of the fuzzy picture corrupted with noise. Last, we combine the parameter estimation step with two segmentation methods, resulting in two unsupervised statistical fuzzy segmentation methods. The efficiency of the proposed methods is tested numerically on synthetic images and a fuzzy segmentation of a real image of clouds is studied.