Minimizing non-submodular functions with graph cuts - a review

Vladimir Kolmogorov and Cartsen Rother.

In IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), 29(7):1274-1279, July 2007.


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, non-submodular 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.