On Relaxation Algorithms Based on Markov Random Fields

Abstract : Many computer vision problems can be formulated as computing the minimum energy states of thermal dynamic systems. However, due to the complexity of the energy functions, the solutions to the minimization problem are very difficult to acquire in practice. Stochastic and deterministic methods exist to approximate the solutions, but they fail to be both efficient and robust. This paper describes a new deterministic method--the Highest Confidence First algorithm--to approximate the minimum energy solution to the image labeling problem under the Maximum A Posteriori (MAP) criterion. This method uses Markov Random Fields to model spatial prior knowledge of images and likelihood probabilities to represent external observations regarding hypotheses of image entities. Following an order decided by a dynamic stability measure, the image entities make make local estimates based on the combined knowledge of priors and observations. The solutions so constructed compare favorably to the ones produced by existing methods and that the computation is more predictable and less expensive. Keywords: Image segmentation; Bayesian approach.

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