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Norm-product belief propagation: primal-dual message-passing for approximate inference
IEEE Transactions on Information Theory
Dual decomposition for natural language processing
HLT '11 Proceedings of the 49th Annual Meeting of the Association for Computational Linguistics: Tutorial Abstracts of ACL 2011
An alternating direction method for dual MAP LP relaxation
ECML PKDD'11 Proceedings of the 2011 European conference on Machine learning and knowledge discovery in databases - Volume Part II
Filter-Based mean-field inference for random fields with higher-order terms and product label-spaces
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part V
The lazy flipper: efficient depth-limited exhaustive search in discrete graphical models
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part VII
Approximate envelope minimization for curvature regularity
ECCV'12 Proceedings of the 12th international conference on Computer Vision - Volume Part III
Submodular relaxation for MRFs with high-order potentials
ECCV'12 Proceedings of the 12th international conference on Computer Vision - Volume Part III
Journal of Artificial Intelligence Research
Computer Vision and Image Understanding
Energy distribution view for monotonic dual decomposition
International Journal of Approximate Reasoning
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This paper introduces a new rigorous theoretical framework to address discrete MRF-based optimization in computer vision. Such a framework exploits the powerful technique of Dual Decomposition. It is based on a projected subgradient scheme that attempts to solve an MRF optimization problem by first decomposing it into a set of appropriately chosen subproblems, and then combining their solutions in a principled way. In order to determine the limits of this method, we analyze the conditions that these subproblems have to satisfy and demonstrate the extreme generality and flexibility of such an approach. We thus show that by appropriately choosing what subproblems to use, one can design novel and very powerful MRF optimization algorithms. For instance, in this manner we are able to derive algorithms that: 1) generalize and extend state-of-the-art message-passing methods, 2) optimize very tight LP-relaxations to MRF optimization, and 3) take full advantage of the special structure that may exist in particular MRFs, allowing the use of efficient inference techniques such as, e.g., graph-cut-based methods. Theoretical analysis on the bounds related with the different algorithms derived from our framework and experimental results/comparisons using synthetic and real data for a variety of tasks in computer vision demonstrate the extreme potentials of our approach.