Kolmogorov, V; Shioura, A; (2009) New algorithms for convex cost tension problem with application to computer vision. **DISCRETE OPTIM** , 6 (4) 378 - 393. 10.1016/j.disopt.2009.04.006.

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## Abstract

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. (C) 2009 Elsevier B.V. All rights reserved.

Type: | Article |
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Title: | New algorithms for convex cost tension problem with application to computer vision |

DOI: | 10.1016/j.disopt.2009.04.006 |

Keywords: | Minimum cost tension, Minimum cost flow, Discrete convex function, Submodular function, TOTAL VARIATION MINIMIZATION, NETWORK FLOW PROBLEM, MARKOV RANDOM-FIELDS, ENERGY MINIMIZATION, GRAPH CUTS, OPTIMIZATION |

UCL classification: | UCL > School of BEAMS > Faculty of Engineering Science > Computer Science |

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