Abstruct- A class of multiscale stochastic models based on scale-recursive dynamics on trees has recently been introduced. Theoretical and experimental results have shown that these models provide an extremely rich framework for representing both processes which are intrinsically multiscale, e.g., llf processes, as well as 1-D Markov processes and 2-D Markov random fields. Moreover, efficient optimal estimation algorithms have been developed for these models by exploiting their scale-recursive structure. In this paper, we exploit this structure in order to develop a computationally efficient and parallelizable algorithm for likelihood calculation. We illustrate one possible application to texture discrimination and demonstrate that likelihood-based methods using our algorithm achieve performance comparable to that of Gaussian Markov random field based techniques, which in general are prohibitively complex computationally. I.

We introduce in this work the notion of a generalised mixture and propose some methods for estimating it, along with applications to unsupervised statistical image segmentation. A distribution mixture is said to be "generalised" when the exact nature of components is not known, but each belongs to a finite known set of families of distributions. For instance, we can consider a mixture of three distributions, each being exponential or Gaussian. The problem of estimating such a mixture contains thus a new difficulty : we have to label each of three components (there are eight possibilities). We show that the classical mixture estimation algorithms Expectation-Maximization (EM), Stochastic EM (SEM), and Iterative Conditional Estimation (ICE) can be adapted to such situations once as we dispose of a method of recognition of each component separately. That is, when we know that a sample proceeds from one family of the set considered, we have a decision rule for what family it belongs to. considering the Pearson system, which is a set of eight families, the decision rule above is defined by the use of "skewness" and "kurtosis". The different algorithms so obtained are then applied to the problem of unsupervised Bayesian image segmentation. We propose the adaptive versions of SEM, EM and ICE in the case of "blind", i.e., "pixel by pixel", segmentation. "Global" segmentation methods require modelling by Hidden Random Markov Fields and we propose adaptations of two traditional parameter estimation algorithms: Gibbsian EM (GEM) and ICE allowing the estimation of generalized mixtures corresponding to Pearson's system. The efficiency of different methods is compared via numerical studies and the results of unsupervised segmentation of three real radar images by different methods a...

We present a new algorithm for segmentation of textured images using a multiresolution Bayesian approach. The new algorithm uses a multiresolution Gaussian autoregressive (MGAR) model for the pyramid representation of the observed image, and assumes a multiscale Markov random field model for the class label pyramid. Unlike previously proposed Bayesian multiresolution segmentation approaches, which have either used a single-resolution representation of the observed image or implicitly assumed independence between different levels of a multiresolution representation of the observed image, the models used in this paper incorporate correlations between different levels of both the observed image pyramid and the class label pyramid. The criterion used for segmentation is the minimization of the expected value of the number of misclassified nodes in the multiresolution lattice. The estimate which satisfies this criterion is referred to as the "multiresolution maximization of the posterior ma...

. The use of random fields, which allows one to take into account the spatial interaction among random variables in complex systems, becomes a frequent tool in numerous problems of statistical mechanics, spatial statistics, neural network modelling, and others. In particular, Markov random field based techniques can be of exceptional efficiency in some image processing problems, like segmentation or edge detection. In statistical image segmentation, that we address in this work, the model is generally defined by the probability distribution of the class field, which is assumed to be a Markov field, and the probability distributions of the observations field conditional to the class field. Under some hypotheses, the a posteriori distribution of the class field, i.e. conditional to the observations field, is still a Markov distribution and the latter property allows one to apply different bayesian methods of segmentation like Maximum a Posteriori (MAP) or Maximum of Posterior Mode (MPM). However, in such models the segmentation of textured images is difficult to perform and one has to resort to some model approximations. The originality of our contribution is to consider the markovianity of the couple (class field, observations field). We obtain a different model; in particular, the class field is not necessarily a Markov field. However, the posterior distribution of the class field is a Markov distribution, which makes possible bayesian MAP and MPM segmentations. Furthermore, the model proposed makes possible textured image segmentation with no approximations. Key words: hidden Markov fields, pairwise Markov fields, bayesian image segmentation, textured images. 1.

The aim of this paper is to apply the recent pairwise Markov chain model, which generalizes the hidden Markov chain one, to the unsupervised restoration of hidden data. The main novelty is an original parameter estimation method, valid in a general setting where the form of the possibly correlated noise is not known. Several experimental results are presented in both Gaussian and generalized mixture contexts. They show the advantages of the pairwise Markov chain model with respect to classical hidden Markov chain one for supervised and unsupervised restorations.

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 expectationmaximization (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.

The use of random fields, which allows one to take into account the spatial interaction among random variables in complex systems, is a frequent tool in numerous problems of statistical image processing, like segmentation or edge detection.

This work deals with unsupervised sonar image segmentation. We present a new estimation segmentation procedure using the recent iterative method of estimation called Iterative Conditional Estimation (ICE) [1]. This method takes into account the variety of the laws in the distribution mixture of a sonar image and the estimation of the parameters of the label field (modeled by a Markov Random Field (MRF)). For the estimation step, we use a maximum likelihood technique to estimate the noise model parameters, and the least squares method proposed by Derin et al. [2] to estimate the MRF prior model. Then, in order to obtain an accurate segmentation map and to speed up the convergence rate, we use a multigrid strategy exploiting the previously estimated parameters. This technique has been successfully applied to real sonar images 1 , and is compatible with an automatic processing of massive amounts of data. 1

this paper we present new results relative to the "expectation-maximization/maximization of the posterior marginals" (EM/MPM) algorithm for simultaneous parameter estimation and segmentation of textured images. The EM/MPM algorithm uses a Markov random field model for the pixel class labels and alternately approximates the MPM estimate of the pixel class labels and estimates parameters of the observed image model. The goal of the EM/MPM algorithm is to minimize the expected value of the number of misclassified pixels. We present new theoretical results in this paper which show that the algorithm can be expected to achieve this goal, to the extent that the EM estimates of the model parameters are close to the true values of the model parameters. We also present new experimental results demonstrating the performance of the EM/MPM algorithm. EDICS: IP 1.5

In this paper we present a new algorithm for segmentation of noisy or textured images using the expectation -maximization (EM) algorithm for estimating parameters of the probability mass function of the pixel class labels and the maximization of the posterior marginals (MPM) criterion for the segmentation operation. A Markov random field (MRF) model is used for the pixel class labels. We present experimental results demonstrating the use of the new algorithm on synthetic images and medical imagery. 1. INTRODUCTION This paper addresses the problem of segmenting a noisy or textured grayscale image using statistical models. Each pixel in the observed image must be assigned membership to one of a finite number of classes depending on statistical properties of the pixel and its neighbors. The individual pixel classifications, or labels, form a matrix or two-dimensional field, with the same dimensions as the observed image, in which the value at a given spatial location reflects the class t...