Fuzzy random fields and unsupervised image segmentation

Statistical unsupervised image segmentation using fuzzy random fields is treated. A fuzzy model containing a hard component, which describes pure pixels, and a fuzzy component which describes mixed pixels, is introduced. A procedure for simulating, a fuzzy field based on a Gibbs sampler step followed by a second step involving white or correlated Gaussian noises is given. Then the different steps of unsupervised image segmentation are studied. Four different blind segmentation methods are performed: the conditional expectation, two variants of the maximum likelihood, and the least squares approach. The parameters required are estimated by the stochastic estimation maximization (SEM) algorithm, a stochastic variant of the expectation maximization (EM) algorithm. These fuzzy segmentation methods are compared with a classical hard segmentation method, without taking the fuzzy class into account. The study shows that the fuzzy SEM algorithm provides reliables estimators. Furthermore, fuzzy segmentation always improves upon the hard segmentation results