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Optimal Bayesian Estimators for Image Segmentation and Surface Reconstruction

Author(s)
Marroquin, Jose L.
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Abstract
sA very fruitful approach to the solution of image segmentation andssurface reconstruction tasks is their formulation as estimationsproblems via the use of Markov random field models and Bayes theory.sHowever, the Maximuma Posteriori (MAP) estimate, which is the one mostsfrequently used, is suboptimal in these cases. We show that forssegmentation problems the optimal Bayesian estimator is the maximizersof the posterior marginals, while for reconstruction tasks, thesthreshold posterior mean has the best possible performance. We presentsefficient distributed algorithms for approximating these estimates insthe general case. Based on these results, we develop a maximumslikelihood that leads to a parameter-free distributed algorithm forsrestoring piecewise constant images. To illustrate these ideas, thesreconstruction of binary patterns is discussed in detail.
Date issued
1985-04-01
URI
http://hdl.handle.net/1721.1/5614
Other identifiers
AIM-839
Series/Report no.
AIM-839
Keywords
Bayesian estimation, Markov random fields, image segmentation, ssurface reconstruction, image restoration

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