Repository landing page
research
Combinatorial Continuous Maximal Flows
Abstract
26 pagesInternational audienceMaximum 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- info:eu-repo/semantics/article
- Journal articles
- Image Segmentation
- Convex optimization
- Discrete Calculus
- Total Variation minimization
- AMS 35J05, 35L05, 35Q90, 35Q93, 65K10, 65K15, 68U10, 90C25, 90C35, 90C51
- [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV]
- [INFO.INFO-CV]Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV]
- [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]