Transformation of general binary mrf minimization to the first-order case

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    70 Citations (Scopus)


    We introduce a transformation of general higher-order Markov random field with binary labels into a first-order one that has the same minima as the original. Moreover, we formalize a framework for approximately minimizing higher-order multilabel MRF energies that combines the new reduction with the fusion-move and QPBO algorithms. While many computer vision problems today are formulated as energy minimization problems, they have mostly been limited to using first-order energies, which consist of unary and pairwise clique potentials, with a few exceptions that consider triples. This is because of the lack of efficient algorithms to optimize energies with higher-order interactions. Our algorithm challenges this restriction that limits the representational power of the models so that higher-order energies can be used to capture the rich statistics of natural scenes. We also show that some minimization methods can be considered special cases of the present framework, as well as comparing the new method experimentally with other such techniques.

    Original languageEnglish
    Article number5444874
    Pages (from-to)1234-1249
    Number of pages16
    JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
    Issue number6
    Publication statusPublished - 2011



    • Energy minimization
    • graph cuts
    • higher-order MRFs
    • pseudo-Boolean function

    ASJC Scopus subject areas

    • Artificial Intelligence
    • Computer Vision and Pattern Recognition
    • Software
    • Computational Theory and Mathematics
    • Applied Mathematics

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