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 publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Pages400-413
    Number of pages14
    Volume7577 LNCS
    EditionPART 6
    DOIs
    Publication statusPublished - 2012
    Event12th European Conference on Computer Vision, ECCV 2012 - Florence
    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)03029743
    ISSN (Electronic)16113349

    Other

    Other12th European Conference on Computer Vision, ECCV 2012
    CityFlorence
    Period12/10/712/10/13

    Fingerprint

    Pseudo-Boolean Functions
    Roofs
    Labels
    Duality
    Linearly
    Lower bound
    First-order
    Analogue
    Boolean functions
    Optimization
    Energy
    Concepts

    Keywords

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

    ASJC Scopus subject areas

    • Computer Science(all)
    • Theoretical Computer Science

    Cite this

    Windheuser, T., Ishikawa, H., & Cremers, D. (2012). Generalized roof duality for multi-label optimization: Optimal lower bounds and persistency. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (PART 6 ed., Vol. 7577 LNCS, 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

    Generalized roof duality for multi-label optimization : Optimal lower bounds and persistency. / Windheuser, Thomas; Ishikawa, Hiroshi; Cremers, Daniel.

    Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7577 LNCS PART 6. ed. 2012. p. 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).

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

    Windheuser, T, Ishikawa, H & Cremers, D 2012, Generalized roof duality for multi-label optimization: Optimal lower bounds and persistency. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). PART 6 edn, vol. 7577 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 6, vol. 7577 LNCS, pp. 400-413, 12th European Conference on Computer Vision, ECCV 2012, Florence, 12/10/7. https://doi.org/10.1007/978-3-642-33783-3_29
    Windheuser T, Ishikawa H, Cremers D. Generalized roof duality for multi-label optimization: Optimal lower bounds and persistency. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). PART 6 ed. Vol. 7577 LNCS. 2012. p. 400-413. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 6). https://doi.org/10.1007/978-3-642-33783-3_29
    Windheuser, Thomas ; Ishikawa, Hiroshi ; Cremers, Daniel. / Generalized roof duality for multi-label optimization : Optimal lower bounds and persistency. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7577 LNCS PART 6. ed. 2012. pp. 400-413 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 6).
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