Higher-order clique reduction without auxiliary variables

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

    9 Citations (Scopus)

    Abstract

    We introduce a method to reduce most higher-order terms of Markov Random Fields with binary labels into lower-order ones without introducing any new variables, while keeping the minimizer of the energy unchanged. While the method does not reduce all terms, it can be used with existing techniques that transformsarbitrary terms (by introducing auxiliary variables) and improve the speed. The method eliminates a higher-order term in the polynomial representation of the energy by finding the value assignment to the variables involved that cannot be part of a global minimizer and increasing the potential value only when that particular combination occurs by the exact amount that makes the potential of lower order. We also introduce a faster approximation that forego the guarantee of exact equivalence of minimizer in favor of speed. With experiments on the same field of experts dataset used in previous work, we show that the roof-dual algorithm after the reduction labels significantly more variables and the energy converges more rapidly.

    Original languageEnglish
    Title of host publicationProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
    PublisherIEEE Computer Society
    Pages1362-1369
    Number of pages8
    ISBN (Print)9781479951178, 9781479951178
    DOIs
    Publication statusPublished - 2014 Sep 24
    Event27th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2014 - Columbus
    Duration: 2014 Jun 232014 Jun 28

    Other

    Other27th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2014
    CityColumbus
    Period14/6/2314/6/28

    Fingerprint

    Labels
    Roofs
    Polynomials
    Experiments

    Keywords

    • Graph cuts
    • Higher order
    • Order reduction
    • Pseudo-Boolean functions

    ASJC Scopus subject areas

    • Software
    • Computer Vision and Pattern Recognition

    Cite this

    Ishikawa, H. (2014). Higher-order clique reduction without auxiliary variables. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (pp. 1362-1369). [6909573] IEEE Computer Society. https://doi.org/10.1109/CVPR.2014.177

    Higher-order clique reduction without auxiliary variables. / Ishikawa, Hiroshi.

    Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. IEEE Computer Society, 2014. p. 1362-1369 6909573.

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

    Ishikawa, H 2014, Higher-order clique reduction without auxiliary variables. in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition., 6909573, IEEE Computer Society, pp. 1362-1369, 27th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2014, Columbus, 14/6/23. https://doi.org/10.1109/CVPR.2014.177
    Ishikawa H. Higher-order clique reduction without auxiliary variables. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. IEEE Computer Society. 2014. p. 1362-1369. 6909573 https://doi.org/10.1109/CVPR.2014.177
    Ishikawa, Hiroshi. / Higher-order clique reduction without auxiliary variables. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. IEEE Computer Society, 2014. pp. 1362-1369
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