Unsupervised segmentation of noisy and textured images using Markov random fields

Abstract

This paper proposes a general unsupervised segmentation algorithm which estimates all model parameters, including the number of regions, as part of the segmentation. The general image model is a hierarchical one, consisting of Markov random fields as components of the model. The MAP criterion is adopted, in principle, for the simultaneous image segmentation and parameter estimation procedures. Due to the difficulty of implementing the MAP segmentation with a large number of unknown parameters, a novel modification of the MAP criterion is proposed. For the model parameters having closed-form ML estimates, these estimates are substituted back into the objective function to reduce the difficulty of the maximization. The remaining maximization is implemented by a recursive segmentation-parameter estimation algorithm, which yields a partial optimal solution (POS) to the maximization problem. In the special case where all model parameters have closed-form ML estimates, the proposed algorithm is equivalent to implementing the MAP criterion. The number of regions in the image is determined through a model fitting criterion tagged on to the segmentation algorithm. Special forms of the general unsupervised segmentation algorithm are developed for the segmentation of noisy and textured images. For noisy images, the image is assumed to consist of uniform graylevel regions modeled by a class of Gibbs random fields and corrupted by additive, white, region-dependent, Gaussian noise. For textured images, the image is assumed to consist of regions, modeled by a class of Gibbs random fields, which are filled with textures, modeled by Gaussian Markov random fields. The algorithms for both classes of images are applied to a wide range of images—generated according to the model, hand-drawn, natural and Brodatz textures, their combinations, and outdoor images—with notable success. Despite the large number of unknown parameters (as many as 14 for some noisy images and 36 for some textured images), the algorithms yield good segmentations, accurate estimates for the parameters, and the correct number of regions.