Minimizing count-based high order terms in markov random fields
EMMCVPR'11 Proceedings of the 8th international conference on Energy minimization methods in computer vision and pattern recognition
Discrete Applied Mathematics
Generic cuts: an efficient algorithm for optimal inference in higher order MRF-MAP
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part V
Generalized roof duality for multi-label optimization: optimal lower bounds and persistency
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part VI
Tighter relaxations for higher-order models based on generalized roof duality
ECCV'12 Proceedings of the 12th international conference on Computer Vision - Volume Part III
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
Computer Vision and Image Understanding
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We introduce a transformation of general higher-order Markov random field with binary labels into a first-order one that has the same minima as the original. Moreover, we formalize a framework for approximately minimizing higher-order multilabel MRF energies that combines the new reduction with the fusion-move and QPBO algorithms. While many computer vision problems today are formulated as energy minimization problems, they have mostly been limited to using first-order energies, which consist of unary and pairwise clique potentials, with a few exceptions that consider triples. This is because of the lack of efficient algorithms to optimize energies with higher-order interactions. Our algorithm challenges this restriction that limits the representational power of the models so that higher-order energies can be used to capture the rich statistics of natural scenes. We also show that some minimization methods can be considered special cases of the present framework, as well as comparing the new method experimentally with other such techniques.