Unsupervised segmentation of noisy and textured images modelled with Gibbs random fields

We view a given image as a realization of a doubly stochastic image model, which is made up of an observable noise (or texture) process(es) and a hidden region process. Specifically, a Gaussian-Markov random field model is used for the noise (or texture) process(es) and a Gibbs random field model is used for the region process. Adopting these stochastic models for representing images, our objective is to use an estimation-theoretic method for segmenting images into regions with similar features. We assume no prior knowledge about the model parameter values and the number of regions in the image. To achieve this objective, it is necessary to estimate the model parameters from the given noisy (or textured) image. Thus, we study the existence and the uniqueness of the maximum likelihood (ML) and the maximum pseudo-likelihood (MPL) estimates for a class of Gibbsian/Exponential distributions. This study allows us to devise new implementations for some known parameter estimation techniques. These new implementations developed for the parameter estimation problem are then used to devise an unsupervised image segmentation algorithm. We adopt the maximum a posteriori (MAP) estimation criterion for the simultaneous parameter estimation and segmentation problem. Since the direct maximization of the MAP criterion is infeasible, we modify the MAP criterion to make it implementable. Specifically, part of the model parameters is eliminated from the maximization by substituting their ML estimates into the probability distributions. The rest of the parameters are estimated iteratively with the segmentation, which is implemented through a relaxation procedure. Due to the deviation from the optimal maximization, the resulting criterion is a modified MAP, and the resulting segmentation is a partial optimal solution (POS) of the overall maximization. Obtaining POS\u27s under different assumptions for the \u27number of regions\u27 in the image, we choose the optimal value for the \u27number of regions\u27 by maximizing a new model-fitting criterion. This general unsupervised segmentation is then adopted to two classes of images, namely, noisy images and textured images. Versions of the algorithm are developed for each of these classes. The performance of the algorithm is tested on a wide range of noisy (and textured) images. Despite the difficulty of the problem, the algorithm yields good segmentations, accurate estimates for the parameters and the correct number of regions