Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
An efficient implementation of a scaling minimum-cost flow algorithm
Journal of Algorithms
Polynomial Methods for Separable Convex Optimization in Unimodular Linear Spaces with Applications
SIAM Journal on Computing
Mathematical Programming: Series A and B
An efficient algorithm for image segmentation, Markov random fields and related problems
Journal of the ACM (JACM)
Fast Approximate Energy Minimization via Graph Cuts
IEEE Transactions on Pattern Analysis and Machine Intelligence
Discrete Applied Mathematics
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Efficient graph-based energy minimization methods in computer vision
Efficient graph-based energy minimization methods in computer vision
Discrete Convex Analysis: Monographs on Discrete Mathematics and Applications 10
Discrete Convex Analysis: Monographs on Discrete Mathematics and Applications 10
On Steepest Descent Algorithms for Discrete Convex Functions
SIAM Journal on Optimization
Solving the Convex Cost Integer Dual Network Flow Problem
Management Science
An Experimental Comparison of Min-Cut/Max-Flow Algorithms for Energy Minimization in Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
A New Framework for Approximate Labeling via Graph Cuts
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
A faster strongly polynomial time algorithm for submodular function minimization
Mathematical Programming: Series A and B
Total variation minimization and a class of binary MRF models
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
A fast and exact algorithm for total variation minimization
IbPRIA'05 Proceedings of the Second Iberian conference on Pattern Recognition and Image Analysis - Volume Part I
Phase unwrapping via graph cuts
IbPRIA'05 Proceedings of the Second Iberian conference on Pattern Recognition and Image Analysis - Volume Part I
Exact optimization for Markov random fields with convex priors
IEEE Transactions on Pattern Analysis and Machine Intelligence
Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Seamless image stitching by minimizing false edges
IEEE Transactions on Image Processing
Phase Unwrapping via Graph Cuts
IEEE Transactions on Image Processing
A fast solver for truncated-convex priors: quantized-convex split moves
EMMCVPR'11 Proceedings of the 8th international conference on Energy minimization methods in computer vision and pattern recognition
Submodularity on a tree: unifying L-convex and bisubmodular functions
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
A Spatial Regularization Approach for Vector Quantization
Journal of Mathematical Imaging and Vision
Global Solutions of Variational Models with Convex Regularization
SIAM Journal on Imaging Sciences
Multi-label Moves for MRFs with Truncated Convex Priors
International Journal of Computer Vision
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Motivated by various applications to computer vision, we consider the convex cost tension problem, which is the dual of the convex cost flow problem. In this paper, we first propose a primal algorithm for computing an optimal solution of the problem. Our primal algorithm iteratively updates primal variables by solving associated minimum cut problems. We show that the time complexity of the primal algorithm is O(K@?T(n,m)), where K is the range of primal variables and T(n,m) is the time needed to compute a minimum cut in a graph with n nodes and m edges. We then develop an improved version of the primal algorithm, called the primal-dual algorithm, by making good use of dual variables in addition to primal variables. Although its time complexity is the same as that of the primal algorithm, we can expect a better performance in practice. We finally consider an application to a computer vision problem called the panoramic image stitching.