New algorithms for convex cost tension problem with application to computer vision |
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Authors: | Vladimir Kolmogorov Akiyoshi Shioura |
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Affiliation: | aAdastral Park Campus, University College London, Adastral Park, Martlesham Heath, IP5 3RE, UK;bGraduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan |
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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 , where is the range of primal variables and is the time needed to compute a minimum cut in a graph with nodes and 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. |
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Keywords: | Minimum cost tension Minimum cost flow Discrete convex function Submodular function |
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