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Statistical Priors for Efficient Combinatorial Optimization Via Graph Cuts

  • Daniel Cremers
  • Leo Grady
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3953)

Abstract

Bayesian inference provides a powerful framework to optimally integrate statistically learned prior knowledge into numerous computer vision algorithms. While the Bayesian approach has been successfully applied in the Markov random field literature, the resulting combinatorial optimization problems have been commonly treated with rather inefficient and inexact general purpose optimization methods such as Simulated Annealing. An efficient method to compute the global optima of certain classes of cost functions defined on binary-valued variables is given by graph min-cuts. In this paper, we propose to reconsider the problem of statistical learning for Bayesian inference in the context of efficient optimization schemes. Specifically, we address the question: Which prior information may be learned while retaining the ability to apply Graph Cut optimization? We provide a framework to learn and impose prior knowledge on the distribution of pairs and triplets of labels. As an illustration, we demonstrate that one can optimally restore binary textures from very noisy images with runtimes on the order of a second while imposing hundreds of statistically learned constraints per pixel.

Keywords

Bayesian Inference Combinatorial Optimization Problem Markov Chain Monte Carlo Method Statistical Prior Stripe Pattern 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Daniel Cremers
    • 1
  • Leo Grady
    • 2
  1. 1.Department of Computer ScienceUniversity of BonnGermany
  2. 2.Department of Imaging and VisualizationSiemens Corporate ResearchPrinceton

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