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Abstract-This paper describes several texture segmentation algorithms based on deterministic and stochastic relaxation principles, and their implementation on parallel networks. The segmentation problem is posed as an optimization problem and two different optimality criteria a r e considered. The first criterion involves maximizing the posterior distribution of the intensity field given the label field (maximum a posteriori (MAP) estimate). The posterior distribution of the texture labels is derived by modeling the textures as Gauss Markov random field (GMRF) and characterizing the distribution of different texture labels by a discrete multilevel Markov model. Fast approximate solutions for MAP a r e obtained using deterministic relaxation techniques implemented on a Hopfield neural network and are compared with those of simulated annealing in obtaining the MAP estimate. A stochastic algorithm which introduces learning into the iterations of the Hopfield network is proposed. This iterated hill-climbing algorithm combines fast convergence of deterministic relaxation with the sustained exploration of the stochastic algorithms, but is guaranteed to find only a local minimum. The second optimality criterion requires minimizing the expected percentage of misclassification per pixel by maximizing the posterior marginal distribution, and the maximum posterior marginal (MPM) algorithm is used to obtain the corresponding solution. All these methods implemented on parallel networks can he easily extended for hierarchical segmentation and we present rewlts of the various schemes in classifying some real textured images.

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