Optimal Bayesian Estimators for Image Segmentation and Surface Reconstruction

摘要

A very fruitful approach to the solution of image segmentation and surface reconstruction tasks in their formulation as estimation problems via the use of Markov random field models and Bayes theory. However, the Maximum a Posteriori estimate, which is the one most frequently used, is suboptimal in these cases. This document shows that for segmentation problems, the optimal Bayesian estimator is the maximizer of the posterior marginals, while for reconstruction tasks, the thresholded posterior mean has the best possible performance. Presented are efficient distributed algorithms for approximating these estimates in the general case. Based on these results, the author develops a maximum likelihood procedure 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.