Higher-order clique reduction without auxiliary variables

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

11 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 (Electronic)9781479951178, 9781479951178
DOIs
Publication statusPublished - 2014 Sep 24
Event27th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2014 - Columbus, United States
Duration: 2014 Jun 232014 Jun 28

Publication series

NameProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
ISSN (Print)1063-6919

Conference

Conference27th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2014
CountryUnited States
CityColumbus
Period14/6/2314/6/28

Keywords

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

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition

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  • 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] (Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition). IEEE Computer Society. https://doi.org/10.1109/CVPR.2014.177