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Limited-Memory Belief Propagation via Nested Optimization

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Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR 2017)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10746))

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Abstract

In this work we express resource-efficient MAP inference as joint optimization problem w.r.t. (i) messages (i.e. reparametrizations) and (ii) surrogate potentials that are upper bounds for the problem of interest and allow efficient inference. We show that resulting nested optimization task can be solved on trees by a convergent and efficient algorithm, and that its loopy extension also returns convincing MAP solutions in practice. We demonstrate the utility of the method on dense correspondence and image completion problems.

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Notes

  1. 1.

    Stricly speaking we do not use a majorizer, but only (less constrained) upper bounds.

  2. 2.

    We focus on problems with at most pairwise cliques, which are most relevant in practice, but everything can be generalized to higher order cliques straightforwardly.

  3. 3.

    The expression \({\mathbf x}_\alpha \setminus x_s\) is shorthand for \(\{ {\mathbf x}'_\alpha : x'_s = x_s \}\). We will also write compactly \(\alpha \ni s\) instead of \(\{ \alpha : s \in \alpha \}\).

  4. 4.

    We prefer the term “resident set” over “particles”, since—in contrast to particle message passing—our method maintains messages also for non-resident states.

  5. 5.

    One can make the algorithm (trivially) convergent e.g. by conditionally updating the primal solution, such that the solution with minimal primal objective so far is always reported.

  6. 6.

    And \(4.7\%\) when using the weaker product label space relaxation [20] with unary potentials being computed on the fly.

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Authors and Affiliations

  1. Toshiba Research Europe, Cambridge, UK

    Christopher Zach

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  1. Christopher Zach
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Correspondence to Christopher Zach .

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Editors and Affiliations

  1. Ca’ Foscari University of Venice, Venice, Italy

    Marcello Pelillo

  2. University of York, York, United Kingdom

    Edwin Hancock

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Zach, C. (2018). Limited-Memory Belief Propagation via Nested Optimization. In: Pelillo, M., Hancock, E. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 2017. Lecture Notes in Computer Science(), vol 10746. Springer, Cham. https://doi.org/10.1007/978-3-319-78199-0_34

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  • DOI: https://doi.org/10.1007/978-3-319-78199-0_34

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