Total variation on a tree

Vladimir Kolmogorov, Thomas Pock, Michal Rolinek

Research output: Contribution to journalArticlepeer-review


We consider the problem of minimizing the continuous valued total variation subject to different unary terms on trees and propose fast direct algorithms based on dynamic programming to solve these problems. We treat both the convex and the nonconvex case and derive worst-case complexities that are equal to or better than existing methods. We show applications to total variation based two dimensional image processing and computer vision problems based on a Lagrangian decomposition approach. The resulting algorithms are very effcient, offer a high degree of parallelism, and come along with memory requirements which are only in the order of the number of image pixels.

Original languageEnglish
Pages (from-to)605-636
Number of pages32
JournalSIAM Journal on Imaging Sciences
Issue number2
Publication statusPublished - 3 May 2016


  • Dynamic programming
  • Primal-dual optimization
  • Total variation

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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