Efficient MAP approximation for dense energy functions
ICML '06 Proceedings of the 23rd international conference on Machine learning
Convergent Tree-Reweighted Message Passing for Energy Minimization
IEEE Transactions on Pattern Analysis and Machine Intelligence
Robust message-passing for statistical inference in sensor networks
Proceedings of the 6th international conference on Information processing in sensor networks
Linear Programming Relaxations and Belief Propagation -- An Empirical Study
The Journal of Machine Learning Research
A Linear Programming Approach to Max-Sum Problem: A Review
IEEE Transactions on Pattern Analysis and Machine Intelligence
Approximate Labeling via Graph Cuts Based on Linear Programming
IEEE Transactions on Pattern Analysis and Machine Intelligence
Efficiently solving convex relaxations for MAP estimation
Proceedings of the 25th international conference on Machine learning
Computer Vision and Image Understanding
Graphical Models, Exponential Families, and Variational Inference
Foundations and Trends® in Machine Learning
Upper bound for variational free energy of Bayesian networks
Machine Learning
Cortical circuitry implementing graphical models
Neural Computation
Training an active random field for real-time image denoising
IEEE Transactions on Image Processing
Minimizing and learning energy functions for side-chain prediction
RECOMB'07 Proceedings of the 11th annual international conference on Research in computational molecular biology
Total absolute Gaussian curvature for stereo prior
ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part II
Towards more efficient and effective LP-based algorithms for MRF optimization
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part II
Norm-product belief propagation: primal-dual message-passing for approximate inference
IEEE Transactions on Information Theory
Improved Moves for Truncated Convex Models
The Journal of Machine Learning Research
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
Comparison of energy minimization algorithms for highly connected graphs
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part II
A comparative study of energy minimization methods for markov random fields
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part II
High-level synthesis: productivity, performance, and software constraints
Journal of Electrical and Computer Engineering - Special issue on ESL Design Methodology
Segmentation of objects in a detection window by Nonparametric Inhomogeneous CRFs
Computer Vision and Image Understanding
Diverse M-best solutions in markov random fields
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part V
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A wide range of low level vision problems have been formulated in terms of finding the most probable assignment of a Markov Random Field (or equivalently the lowest energy configuration). Perhaps the most successful example is stereo vision. For the stereo problem, it has been shown that finding the global optimum is NP hard but good results have been obtained using a number of approximate optimization algorithms. In this paper we show that for standard benchmark stereo pairs, the global optimum can be found in about 30 minutes using a variant of the belief propagation (BP) algorithm. We extend previous theoretical results on reweighted belief propagation to account for possible ties in the beliefs and using these results we obtain easily checkable conditions that guarantee that the BP disparities are the global optima. We verify experimentally that these conditions are typically met for the standard benchmark stereo pairs and discuss the implications of our results for further progress in stereo.