Generalized Flows for Optimal Inference in Higher Order MRF-MAP

IEEE Transactions on Pattern Analysis and Machine Intelligence
Chetan AroraS N Maheshwari

Abstract

Use of higher order clique potentials in MRF-MAP problems has been limited primarily because of the inefficiencies of the existing algorithmic schemes. We propose a new combinatorial algorithm for computing optimal solutions to 2 label MRF-MAP problems with higher order clique potentials. The algorithm runs in time O(2(k)n(3)) in the worst case (k is size of clique and n is the number of pixels). A special gadget is introduced to model flows in a higher 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 the capacity of an edge and a cut are generalized to define a flow problem. We show that in this flow graph, when the clique potentials are submodular, the max flow is equal to the min cut, which also is the optimal solution to the problem. We show experimentally that our algorithm provides significantly better solutions in practice and is hundreds of times faster than solution schemes like Dual Decomposition [1], TRWS [2] and Reduction [3], [4], [5]. The framework represents a significant advance in handling higher order problems making optimal inference practical for medium sized cliques.

References

Sep 22, 2006·IEEE Transactions on Pattern Analysis and Machine Intelligence·Vladimir Kolmogorov
May 15, 2007·IEEE Transactions on Pattern Analysis and Machine Intelligence·Vladimir Kolmogorov, Carsten Rother
Jun 15, 2007·IEEE Transactions on Pattern Analysis and Machine Intelligence·Nikos Komodakis, Georgios Tziritas
Apr 28, 2010·IEEE Transactions on Pattern Analysis and Machine Intelligence·Hiroshi Ishikawa
May 19, 2010·IEEE Transactions on Pattern Analysis and Machine Intelligence·Nikos KomodakisGeorgios Tziritas
Aug 25, 2010·IEEE Transactions on Pattern Analysis and Machine Intelligence·Uma MudenagudiPrem Kumar Kalra
Jun 1, 1984·IEEE Transactions on Pattern Analysis and Machine Intelligence·S Geman, D Geman

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Citations

Jul 6, 2016·Medical Image Analysis·Nikos ParagiosEvangelia I Zacharaki

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