Combinatorial Continuous Maximal Flows
| Autor: | Couprie, Camille, Grady, Leo, Talbot, Hugues, Najman, Laurent |
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| Rok vydání: | 2010 |
| Předmět: | |
| Zdroj: | SIAM Journal on Imaging Sciences 4 (2011) 905-930 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1137/100799186 |
| Popis: | Maximum flow (and minimum cut) algorithms have had a strong impact on computer vision. In particular, graph cuts algorithms provide a mechanism for the discrete optimization of an energy functional which has been used in a variety of applications such as image segmentation, stereo, image stitching and texture synthesis. Algorithms based on the classical formulation of max-flow defined on a graph are known to exhibit metrication artefacts in the solution. Therefore, a recent trend has been to instead employ a spatially continuous maximum flow (or the dual min-cut problem) in these same applications to produce solutions with no metrication errors. However, known fast continuous max-flow algorithms have no stopping criteria or have not been proved to converge. In this work, we revisit the continuous max-flow problem and show that the analogous discrete formulation is different from the classical max-flow problem. We then apply an appropriate combinatorial optimization technique to this combinatorial continuous max-flow CCMF problem to find a null-divergence solution that exhibits no metrication artefacts and may be solved exactly by a fast, efficient algorithm with provable convergence. Finally, by exhibiting the dual problem of our CCMF formulation, we clarify the fact, already proved by Nozawa in the continuous setting, that the max-flow and the total variation problems are not always equivalent. Comment: 26 pages |
| Databáze: | arXiv |
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