Image segmentation using GMRF models: parameters estimation and applications

Stochastic models of images are commonly represented in terms of three random processes (random fields) defined on the region of support of the image. The observed image process G is considered as a composite of two random process: a high level process G^h, which represents the regions (or classes) that form the observed image; and a low level process G^l, which describes the statistical characteristics of each region (or class). The representation G = (G^h, G^l) has been widely used in the image processing literature in the past two decades. In this paper, we consider the low level process G^l as mixture of normal distributions, and we use the expectation-maximization (EM) algorithm to estimate the mean, the variance, and proportion for each distribution. A popular model for the high level process G^h has been the Gibbs-Markov random field (GMRF) model. We introduce a novel unsupervised approach to estimate the parameters of a GMRF model. In this approach, we estimate the model parameters that maximize the posteriori probability of each pixel in a given image. The MAP estimate is obtained using a combination of genetic search and deterministic optimization using the iterated conditional mode (ICM) approach of Besag. The desired estimate of the GMRF parameters is the one corresponding to the MAP estimate. The approach has been applied on real images (Spiral CT slices) and provides satisfactory results.