Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems
Journal of the ACM (JACM)
Fast Approximate Energy Minimization via Graph Cuts
IEEE Transactions on Pattern Analysis and Machine Intelligence
What Energy Functions Can Be Minimizedvia Graph Cuts?
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Convergent Tree-Reweighted Message Passing for Energy Minimization
IEEE Transactions on Pattern Analysis and Machine Intelligence
Minimizing Nonsubmodular Functions with Graph Cuts-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
A simple combinatorial algorithm for submodular function minimization
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
International Journal of Computer Vision
Robust Higher Order Potentials for Enforcing Label Consistency
International Journal of Computer Vision
Probabilistic Graphical Models: Principles and Techniques - Adaptive Computation and Machine Learning
Transformation of General Binary MRF Minimization to the First-Order Case
IEEE Transactions on Pattern Analysis and Machine Intelligence
Generalized roof duality and bisubmodular functions
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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We propose a new algorithm called Generic Cuts for computing optimal solutions to 2 label MRF-MAP problems with higher order clique potentials satisfying submodularity. The algorithm runs in time O(2kn3) in the worst case (k is clique order and n is the number of pixels). A special gadget is introduced to model flows in a high order clique and a technique for building a flow graph is specified. Based on the primal dual structure of the optimization problem the notions of capacity of an edge and cut are generalized to define a flow problem. We show that in this flow graph max flow is equal to min cut which also is the optimal solution to the problem when potentials are submodular. This is in contrast to all prevalent techniques of optimizing Boolean energy functions involving higher order potentials including those based on reductions to quadratic potential functions which provide only approximate solutions even for submodular functions. We show experimentally that our implementation of the Generic Cuts algorithm is more than an order of magnitude faster than all algorithms including reduction based whose outputs on submodular potentials are near optimal.