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

Vladimir Kolmogorov, Akiyoshi Shioura

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)378-393
Number of pages16
JournalDiscrete Optimization
Issue number4
Publication statusPublished - 2009 Nov
Externally publishedYes


  • Discrete convex function
  • Minimum cost flow
  • Minimum cost tension
  • Submodular function

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Applied Mathematics


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