Gibbs Random Fields, Fuzzy Clustering, and the Unsupervised Segmentation of Textured Images

In this paper we present an unsupervised segmentation strategy for textured images, based on a hierarchical model in terms of discrete Markov Random Fields. The textures are modeled as Gaussian Gibbs Fields, while the image partition is modeled as a Markov Mesh Random Field. The segmentation is achieved in two phases: the first one consists of evaluating, from disjoint blocks which are classified as homogeneous, the model parameters for each texture present in the image. This unsupervised learning phase uses a fuzzy clustering procedure, applied to the features extracted from every pixel block, to determine the number of textures in the image and to roughly locate the corresponding regions. The second phase consists of the fine segmentation of the image, using Bayesian local decisions based on the previously obtained model parameters. The originality of the proposed approach lies in the three following aspects: (1) the Gibbs distribution corresponding to each texture type is expressed in terms of its canonical potential. This formulation leads to a compact formulation of the global field energy, in terms of the marginal probabilities over pixel cliques. A similar expression is also introduced in the partition model. Such formulations lead to the decomposition of the segmentation problem into a set of local statistical decisions; (2) the segmentation strategy consists of an unsupervised estimation, in which the model parameters are evaluated directly from the observation, by means of a fuzzy clustering technique; (3) no arbitrary assumption is made concerning the number of textures present. Rather, the fuzzy clustering procedure used to estimate the model parameters is applied in a hierarchical manner, searching for a cluster configuration of maximum plausibility.