Estimation of fuzzy Gaussian mixture and unsupervised statistical image segmentation.pdf

IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 6, NO. 3, MARCH 1997 425 Estimation of Fuzzy Gaussian Mixture and Unsupervised Statistical Image Segmentation He?le?ne Caillol, Wojciech Pieczynski, and Alain Hillion, Associate Member, IEEE Abstract—This paper addresses the estimation of fuzzy Gauss- ian distribution mixture with applications to unsupervised sta- tistical fuzzy image segmentation. In a general way, the fuzzy approach enriches the current statistical models by adding a fuzzy class, which has several interpretations in signal pro- cessing. One such interpretation in image segmentation is the simultaneous appearance of several thematic classes on the same site. We introduce a new procedure for estimating of fuzzy mixtures, which is an adaptation of the iterative conditional estimation (ICE) algorithm to the fuzzy framework. We first describe the blind estimation, i.e., without taking into account any spatial information, valid in any context of independent noisy observations. Then we introduce, in a manner analogous to classical hard segmentation, the spatial information by two different approaches: contextual segmentation and adaptive blind segmentation. In the first case, the spatial information is taken into account at the segmentation step level, and in the second case it is taken into account at the parameter estimation step level. The results obtained with the iterative conditional estimation algorithm are compared to those obtained with expectation- maximization (EM) and the stochastic EM (SEM) algorithms, on both parameter estimation and unsupervised segmentation levels, via simulations. The methods proposed appear as complementary to the fuzzy C-means algorithms. I. INTRODUCTION T HE statistical approach to the image segmentation prob- lem requires modeling two random fields. For the set of pixels, is the unobservable random field whose realizations are the true nature of the observed scene, and is the observed random field, which is seen as a corru