This paper addresses the estimation of fuzzy Gaussian distribution mixture with applications to unsupervised statistical 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 processing. 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 algorithms, on both parameter estimation and unsupervised segmentation levels, via simulations. The methods proposed appear as complementary to the fuzzy C-means algorithms.

The paper considers the statistical modelling of fully developed backscattering in the case of SAR images of the ocean surface. According to the random-walk theory, the SAR image grey level is modelled as the product of a speckle noise and a variable which is dependent on the reflectivity of the illuminated surface and the radar-point-spread fonction. The purpose of the study is the statistical modelling of the latter variable. As nothing is known about these statistics, the authors propose the use of an estimation method based on a system of distributions. The set contains known density probability fonctions with very flexible shapes that are supposed to fit its distribution. The associated image intensity distributions are processed and form a new system called KUBW, referring to the special fonctions used to generate the distributions. The classical K law belongs to the new system of distributions. By using a statistical test on the intensity distribution, the authors assess the relevance of the system of distributions in comparison with the classical model. The paper concludes with a discussion of the merits of the method and its extension to the case of ocean SAR image applications.

No abstract

No abstract

No abstract