A Hypergraph-Based Reduction for Higher-Order Binary Markov Random Fields

IEEE Transactions on Pattern Analysis and Machine Intelligence
Alexander FixRamin Zabih

Abstract

Higher-order Markov Random Fields, which can capture important properties of natural images, have become increasingly important in computer vision. While graph cuts work well for first-order MRF's, until recently they have rarely been effective for higher-order MRF's. Ishikawa's graph cut technique [1], [2] shows great promise for many higher-order MRF's. His method transforms an arbitrary higher-order MRF with binary labels into a first-order one with the same minima. If all the terms are submodular the exact solution can be easily found; otherwise, pseudoboolean optimization techniques can produce an optimal labeling for a subset of the variables. We present a new transformation with better performance than [1], [2], both theoretically and experimentally. While [1], [2] transforms each higher-order term independently, we use the underlying hypergraph structure of the MRF to transform a group of terms at once. For n binary variables, each of which appears in terms with k other variables, at worst we produce n non-submodular terms, while [1], [2] produces O(nk). We identify a local completeness property under which our method perform even better, and show that under certain assumptions several important vision problems (includi...Continue Reading

References

Sep 21, 2004·IEEE Transactions on Pattern Analysis and Machine Intelligence·Vladimir Kolmogorov, Ramin Zabih
May 15, 2007·IEEE Transactions on Pattern Analysis and Machine Intelligence·Vladimir Kolmogorov, Carsten Rother
Apr 19, 2008·IEEE Transactions on Pattern Analysis and Machine Intelligence·Richard SzeliskiCarsten Rother
Jul 4, 2009·IEEE Transactions on Pattern Analysis and Machine Intelligence·Pushmeet KohliPhilip H S Torr
Oct 17, 2009·IEEE Transactions on Pattern Analysis and Machine Intelligence·Oliver WoodfordAndrew Fitzgibbon
Apr 28, 2010·IEEE Transactions on Pattern Analysis and Machine Intelligence·Hiroshi Ishikawa
Jun 19, 2010·IEEE Transactions on Pattern Analysis and Machine Intelligence·Victor LempitskyAndrew Blake

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Citations

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

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