: This document presents two deterministic algorithms for the maximum a posteriori estimation of a one dimensional, binary Markov random field from noisy observations. Extensions to other related problems, such as one dimensional signal matching, and estimation of continuous valued Markov random fields are also discussed. Finally, the author presents an experimental comparison of the performance of optimal algorithms with a stochastic approximation scheme (simulated annealing). Additional keywords: Mathematical models, Dynamic programming, Gaussian noise, White noise, Army research. (Author)

A very fruitful approach to the solution of image segmentation and surface reconstruction tasks is their formulation as estimation problems via the use of Markov random field models and Bayes theory. However, the Maximuma Posteriori (MAP) estimate, which is the one most frequently used, is suboptimal in these cases. We show that for segmentation problems the optimal Bayesian estimator is the maximizer of the posterior marginals, while for reconstruction tasks, the threshold posterior mean has the best possible performance. We present efficient distributed algorithms for approximating these estimates in the general case. Based on these results, we develop a maximum likelihood that leads to a parameter-free distributed algorithm for restoring piecewise constant images. To illustrate these ideas, the reconstruction of binary patterns is discussed in detail.

Bayesian Estimation of One Dimensional Discrete Markov Random Fields.

Citations

Optimal Bayesian Estimators For Image Segmentation and Surface Reconstruction

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