Generalized Roof Duality for Pseudo-Boolean Optimization

Fredrik Kahl, Petter Strandmark

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceedingpeer-review

22 Citations (SciVal)


The number of applications in computer vision that model higher-order interactions has exploded over the last few years. The standard technique for solving such problems is to reduce the higher-order objective function to a quadratic pseudo-boolean function, and then use roof duality for obtaining a lower bound. Roof duality works by constructing the tightest possible lower-bounding submodular function, and instead of optimizing the original objective function, the relaxation is minimized.
We generalize this idea to polynomials of higher degree, where quadratic roof duality appears as a special case. Optimal relaxations are defined to be the ones that give the maximum lower bound. We demonstrate that important properties such as persistency still hold and how the relaxations can be efficiently constructed for general cubic and quartic pseudo-boolean functions. From a practical point of view, we show that our relaxations perform better than state-of-the-art for a wide range of problems, both in terms of lower bounds and in the number of assigned variables.
Original languageEnglish
Title of host publicationIEEE International Conference on Computer Vision (ICCV)
PublisherIEEE - Institute of Electrical and Electronics Engineers Inc.
Number of pages8
Publication statusPublished - 2011
EventIEEE International Conference on Computer Vision (ICCV), 2011 - Barcelona, Spain
Duration: 2011 Nov 62011 Nov 13


ConferenceIEEE International Conference on Computer Vision (ICCV), 2011

Subject classification (UKÄ)

  • Computer Vision and Robotics (Autonomous Systems)
  • Mathematics


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