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Efficient Loopy Belief Propagation Using the Four Color Theorem

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Advanced Topics in Computer Vision

Part of the book series: Advances in Computer Vision and Pattern Recognition ((ACVPR))

Abstract

Recent work on early vision such as image segmentation, image denoising, stereo matching, and optical flow uses Markov Random Fields. Although this formulation yields an NP-hard energy minimization problem, good heuristics have been developed based on graph cuts and belief propagation. Nevertheless both approaches still require tens of seconds to solve stereo problems on recent PCs. Such running times are impractical for optical flow and many image segmentation and denoising problems and we review recent techniques for speeding them up. Moreover, we show how to reduce the computational complexity of belief propagation by applying the Four Color Theorem to limit the maximum number of labels in the underlying image segmentation to at most four. We show that this provides substantial speed improvements for large inputs, and this for a variety of vision problems, while maintaining competitive result quality.

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Acknowledgements

This work was supported by the Flemish Hercules Foundation project RICH and the Flemish iMinds project on Future Health.

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Authors and Affiliations

  1. VISICS, ESAT-PSI/iMinds, KU Leuven, Leuven, Belgium

    Radu Timofte & Luc Van Gool

  2. Computer Vision Lab, D-ITET, ETH Zurich, Zurich, Switzerland

    Luc Van Gool

Authors
  1. Radu Timofte
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  2. Luc Van Gool
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Corresponding author

Correspondence to Radu Timofte .

Editor information

Editors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università di Catania, Catania, Italy

    Giovanni Maria Farinella

  2. Dipartimento di Matematica e Informatica, Università di Catania, Catania, Italy

    Sebastiano Battiato

  3. Department of Engineering, University of Cambridge, Cambridge, United Kingdom

    Roberto Cipolla

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Timofte, R., Van Gool, L. (2013). Efficient Loopy Belief Propagation Using the Four Color Theorem. In: Farinella, G., Battiato, S., Cipolla, R. (eds) Advanced Topics in Computer Vision. Advances in Computer Vision and Pattern Recognition. Springer, London. https://doi.org/10.1007/978-1-4471-5520-1_11

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  • DOI: https://doi.org/10.1007/978-1-4471-5520-1_11

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-5519-5

  • Online ISBN: 978-1-4471-5520-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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