New algorithms for convex cost tension problem with application to computer vision Journal Article


Author(s): Kolmogorov, Vladimir; Shioura, Akiyoshi
Article Title: New algorithms for convex cost tension problem with application to computer vision
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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 {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.
Keywords: Discrete convex function; Minimum cost flow; Minimum cost tension; Submodular function
Journal Title: Discrete Optimization
Volume: 6
Issue 4
ISSN: 1572-5286
Publisher: Elsevier  
Date Published: 2009-11-01
Start Page: 378
End Page: 393
DOI: 10.1016/j.disopt.2009.04.006
Open access: no
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