Optimization Algorithms for Discrete Markov Random Fields, with Applications to Computer Vision

A large variety of important tasks in low?-level vision, image analysis and pat?tern recognition can be formulated as discrete labeling problems where one seeks to optimize some measure of the quality of the labeling. For example such is the case in optical flow estimation, stereo matching, image restoration to men?tion only a few of them. Discrete Markov Random Fields are ideal candidates for modeling these labeling problems and, for this reason, they are ubiquitous in computer vision. Therefore, an issue of paramount importance, that has at?tracted a significant amount of computer vision research over the past years, is how to optimize discrete Markov Random Fields efficiently and accurately. The main theme of this thesis is concerned exactly with this issue. Two novel MRF op?timization schemes are thus presented, both of which manage to extend current state-?of?-the?-art techniques in significant ways. On one hand, a novel framework is proposed that is based on the duality theory of Linear Programming (LP) and provides an alternative as well as more general view of existing graph ?cut methods such as the ?expansion technique, which is included merely as a special case. Moreover, unlike ?expansion which is valid only for MRFs with metric potentials, the derived algorithms provably generate almost optimal solutions for a much wider class of MRFs that are frequently encountered in computer vision, which is an important advance. Results on a variety of low level vision tasks demonstrate the efficacy of our approach. On the other hand, a novel optimization scheme, called Priority? Belief Propagation, is proposed which carries two very important extensions over standard Belief Propagation (BP): priority?-based message scheduling and dynamic label pruning. For the first time, these two extensions work in cooperation in order to deal with one of the major limitations of BP: its inefficiency in handling MRFs with very large discrete state?-spaces. Moreover, both extensions are generic and do not make any use of domain? specific knowledge. They are therefore applicable to any discrete Markov Random Field, i.e. a very wide class of problems in computer vision.