TY - JOUR

T1 - New algorithms for convex cost tension problem with application to computer vision

AU - Kolmogorov, Vladimir

AU - Shioura, Akiyoshi

N1 - Funding Information:
The authors thank Kazuo Murota for valuable comments on the manuscript. The first author is supported by EPSRC. The second author is partially supported by Grant-in-Aid of the Ministry of Education, Culture, Sports, Science and Technology of Japan.

PY - 2009/11

Y1 - 2009/11

N2 - 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 {dot operator} 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.

AB - 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 {dot operator} 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.

KW - Discrete convex function

KW - Minimum cost flow

KW - Minimum cost tension

KW - Submodular function

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U2 - 10.1016/j.disopt.2009.04.006

DO - 10.1016/j.disopt.2009.04.006

M3 - Article

AN - SCOPUS:68449099927

VL - 6

SP - 378

EP - 393

JO - Discrete Optimization

JF - Discrete Optimization

SN - 1572-5286

IS - 4

ER -