Minimizing nonsubmodular functions with graph cuts - A review

V. Kolmogorov, C. Rother, IEEE Transactions on Pattern Analysis and Machine Intelligence 29 (2007) 1274–1279.

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Abstract
Optimization techniques based on graph cuts have become a standard tool for many vision applications. These techniques allow to minimize efficiently certain energy functions corresponding to pairwise Markov Random Fields (MRFs). Currently, there is an accepted view within the computer vision community that graph cuts can only be used for optimizing a limited class of MRF energies (e.g., submodular functions). In this survey, we review some results that show that graph cuts can be applied to a much larger class of energy functions (in particular, nonsubmodular functions). While these results are well-known in the optimization community, to our knowledge they were not used in the context of computer vision and MRF optimization. We demonstrate the relevance of these results to vision on the problem of binary texture restoration.
Publishing Year
Date Published
2007-07-01
Journal Title
IEEE Transactions on Pattern Analysis and Machine Intelligence
Volume
29
Issue
7
Page
1274 - 1279
IST-REx-ID

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Kolmogorov V, Rother C. Minimizing nonsubmodular functions with graph cuts - A review. IEEE Transactions on Pattern Analysis and Machine Intelligence. 2007;29(7):1274-1279. doi:10.1109/TPAMI.2007.1031
Kolmogorov, V., & Rother, C. (2007). Minimizing nonsubmodular functions with graph cuts - A review. IEEE Transactions on Pattern Analysis and Machine Intelligence, 29(7), 1274–1279. https://doi.org/10.1109/TPAMI.2007.1031
Kolmogorov, Vladimir, and Carsten Rother. “Minimizing Nonsubmodular Functions with Graph Cuts - A Review.” IEEE Transactions on Pattern Analysis and Machine Intelligence 29, no. 7 (2007): 1274–79. https://doi.org/10.1109/TPAMI.2007.1031.
V. Kolmogorov and C. Rother, “Minimizing nonsubmodular functions with graph cuts - A review,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 29, no. 7, pp. 1274–1279, 2007.
Kolmogorov V, Rother C. 2007. Minimizing nonsubmodular functions with graph cuts - A review. IEEE Transactions on Pattern Analysis and Machine Intelligence. 29(7), 1274–1279.
Kolmogorov, Vladimir, and Carsten Rother. “Minimizing Nonsubmodular Functions with Graph Cuts - A Review.” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 29, no. 7, IEEE, 2007, pp. 1274–79, doi:10.1109/TPAMI.2007.1031.

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