#### Technical Report USC-SIPI-132

“Stochastic and Deterministic Networks for Texture Segmentation”

by B. S. Manjunath, Tal Simchony, and Rama Chellappa

September 1988

This paper describes several texture segmentation algorithms based on deterministic and stochastic relaxation principles. We are mainly interested in developing algorithms which can be implemented on highly parallel networks. the segmentation process is posed as an optimization problem and two different optimality criteria are considered. The first criterion involves maximizing the posterior distribution of the intensity array given the label array (Maximum a posteriori (MAP) estimate). The posterior distribution of the texture labels is derived by modeling the textures as Gauss Markov Random Fields (GMRF) and characterizing the distribution of different texture labels by an Ising model. Fast approximate solutions for MAP are obtained using deterministic relaxation techniques implemented on a standard Hopfield type neural network. For comparison purposes simulated annealing is used to obtain the global optimum of the MAP estimate. A stochastic algorithm is then proposed which introduces learning into the iterations of the Hopfield network. This iterated hill climbing algorithm combines the fast convergence of deterministic relaxation with the sustained exploration of the stochastic algorithms. However unlike simulated annealing, this is guaranteed to find only a local minimum. The second optimally criterion requires minimizing the expected percentage of missclassification per pixel by maximizing the posterior marginal distribution. We use the Maximum Posterior Marginal (MPM) algorithm to obtain the corresponding solution. All these methods implemented on parallel networks can be easily extended for hierarchical segmentation and we present results of the various schemes in classifying real textured images.

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