Combinatorial Continuous Maximal Flows

Abstract : 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.
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Article dans une revue
SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2011, 4, pp.905-930. <10.1137/100799186>
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Soumis le : mardi 27 décembre 2011 - 20:34:22
Dernière modification le : lundi 21 mars 2016 - 11:28:55
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Camille Couprie, Leo Grady, Hugues Talbot, Laurent Najman. Combinatorial Continuous Maximal Flows. SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2011, 4, pp.905-930. <10.1137/100799186>. <hal-00525822v2>



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