Roof duality for polynomial 0-1 optimization
Mathematical Programming: Series A and B
Recognition problems for special classes of polynomials in 0-1 variables
Mathematical Programming: Series A and B
Fast Approximate Energy Minimization via Graph Cuts
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computing Geodesics and Minimal Surfaces via Graph Cuts
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Energy Minimization via Graph Cuts: Settling What is Possible
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Minimizing Nonsubmodular Functions with Graph Cuts-A Review
IEEE Transactions on Pattern Analysis and Machine Intelligence
P³ & Beyond: Move Making Algorithms for Solving Higher Order Functions
IEEE Transactions on Pattern Analysis and Machine Intelligence
Note: The expressive power of binary submodular functions
Discrete Applied Mathematics
Global Stereo Reconstruction under Second-Order Smoothness Priors
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fusion Moves for Markov Random Field Optimization
IEEE Transactions on Pattern Analysis and Machine Intelligence
Transformation of General Binary MRF Minimization to the First-Order Case
IEEE Transactions on Pattern Analysis and Machine Intelligence
Curvature regularization for curves and surfaces in a global optimization framework
EMMCVPR'11 Proceedings of the 8th international conference on Energy minimization methods in computer vision and pattern recognition
Global Interactions in Random Field Models: A Potential Function Ensuring Connectedness
SIAM Journal on Imaging Sciences
Statistical priors for efficient combinatorial optimization via graph cuts
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part III
Efficient belief propagation with learned higher-order markov random fields
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part II
Discrete Applied Mathematics
Generalized roof duality for pseudo-boolean optimization
ICCV '11 Proceedings of the 2011 International Conference on Computer Vision
A graph cut algorithm for higher-order Markov Random Fields
ICCV '11 Proceedings of the 2011 International Conference on Computer Vision
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Many problems in computer vision can be turned into a large-scale boolean optimization problem, which is in general NP-hard. In this paper, we further develop one of the most successful approaches, namely roof duality, for approximately solving such problems for higher-order models. Two new methods that can be applied independently or in combination are investigated. The first one is based on constructing relaxations using generators of the submodular function cone. In the second method, it is shown that the roof dual bound can be applied in an iterated way in order to obtain a tighter relaxation. We also provide experimental results that demonstrate better performance with respect to the state-of-the-art, both in terms of improved bounds and the number of optimally assigned variables.