Generalized roof duality for multi-label optimization: Optimal lower bounds and persistency

Thomas Windheuser, Hiroshi Ishikawa, Daniel Cremers

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Citations (Scopus)

Abstract

We extend the concept of generalized roof duality from pseudo-boolean functions to real-valued functions over multi-label variables. In particular, we prove that an analogue of the persistency property holds for energies of any order with any number of linearly ordered labels. Moreover, we show how the optimal submodular relaxation can be constructed in the first-order case.

Original languageEnglish
Title of host publicationComputer Vision, ECCV 2012 - 12th European Conference on Computer Vision, Proceedings
Pages400-413
Number of pages14
EditionPART 6
DOIs
Publication statusPublished - 2012 Oct 30
Event12th European Conference on Computer Vision, ECCV 2012 - Florence, Italy
Duration: 2012 Oct 72012 Oct 13

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 6
Volume7577 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference12th European Conference on Computer Vision, ECCV 2012
CountryItaly
CityFlorence
Period12/10/712/10/13

Keywords

  • MRF
  • computer vision
  • higher-order
  • multi-label
  • roof duality

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Windheuser, T., Ishikawa, H., & Cremers, D. (2012). Generalized roof duality for multi-label optimization: Optimal lower bounds and persistency. In Computer Vision, ECCV 2012 - 12th European Conference on Computer Vision, Proceedings (PART 6 ed., pp. 400-413). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7577 LNCS, No. PART 6). https://doi.org/10.1007/978-3-642-33783-3_29