Fuzzy Random Fields and Unsupervised Image Segmentation

This paper deals with the statistical unsupervised image segmentation using fuzzy random fields. We introduce a new fuzzy model containing two components: a “hard” component, which describes “pure” pixels and a “fuzzy” component, which describes “mixed” pixels. First, we introduce a procedure to simulate this fuzzy field based on a Gibbs sampler step followed by a second step involving white or correlated Gaussian noises. Then we study the different steps of unsupervised image segmentation. Four different blind segmentation methods are performed: the conditional expectation, two variants of the maximum likelihood, and the least squares approach. As our methods are unsupervised, the parameters required are estimated by the stochastic estimation maximization (SEM) algorithm, which is a stochastic variant of the expectation maximization (EM) algorithm, adapted to our model. These “fuzzy segmentation” methods are compared with a classical “hard segmentation” one, without taking the fuzzy class into account. Our study shows that our “fuzzy” SEM algorithm provides reliables estimators, especially regarding the good robustness properties of the segmentation methods. Furthermore, we point out that this “fuzzy segmentation” always improves upon the “hard segmentation” results.