A new approach to the maximum-flow problem
Journal of the ACM (JACM)
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Examples of max-flow and min-cut problems with duality gaps in continuous networks
Mathematical Programming: Series A and B
International Journal of Computer Vision
Fast Approximate Energy Minimization via Graph Cuts
IEEE Transactions on Pattern Analysis and Machine Intelligence
Linear algebra operators for GPU implementation of numerical algorithms
ACM SIGGRAPH 2003 Papers
Sparse matrix solvers on the GPU: conjugate gradients and multigrid
ACM SIGGRAPH 2003 Papers
Computing Geodesics and Minimal Surfaces via Graph Cuts
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Discrete exterior calculus
What Energy Functions Can Be Minimizedvia Graph Cuts?
IEEE Transactions on Pattern Analysis and Machine Intelligence
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Convex Optimization
"GrabCut": interactive foreground extraction using iterated graph cuts
ACM SIGGRAPH 2004 Papers
A Non-Local Algorithm for Image Denoising
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Second-order Cone Programming Methods for Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
Globally Minimal Surfaces by Continuous Maximal Flows
IEEE Transactions on Pattern Analysis and Machine Intelligence
Journal of Mathematical Imaging and Vision
Graph Cuts via $\ell_1$ Norm Minimization
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Convex Formulation of Continuous Multi-label Problems
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part III
The Split Bregman Method for L1-Regularized Problems
SIAM Journal on Imaging Sciences
The piecewise smooth Mumford-Shah functional on an arbitrary graph
IEEE Transactions on Image Processing
Maximum flows and minimum cuts in the plane
Journal of Global Optimization
Discrete Calculus: Applied Analysis on Graphs for Computational Science
Discrete Calculus: Applied Analysis on Graphs for Computational Science
Faster graph-theoretic image processing via small-world and quadtree topologies
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction
SIAM Journal on Imaging Sciences
A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging
Journal of Mathematical Imaging and Vision
MICCAI'05 Proceedings of the 8th international conference on Medical image computing and computer-assisted intervention - Volume Part II
Exact optimization for Markov random fields with convex priors
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonlocal Discrete Regularization on Weighted Graphs: A Framework for Image and Manifold Processing
IEEE Transactions on Image Processing
Supervised feature selection in graphs with path coding penalties and network flows
The Journal of Machine Learning Research
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Maximum flow (and minimum cut) algorithms have had a strong impact on computer vision. In particular, graph cut 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 artifacts 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 artifacts 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.