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International Conference on Scale Space and Variational Methods in Computer Vision

SSVM 2015: Scale Space and Variational Methods in Computer Vision pp 629–641Cite as

A sparse algorithm for dense optimal transport

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9087))

Abstract

Discrete optimal transport solvers do not scale well on dense large problems since they do not explicitly exploit the geometric structure of the cost function. In analogy to continuous optimal transport we provide a framework to verify global optimality of a discrete transport plan locally. This allows construction of a new sparse algorithm to solve large dense problems by considering a sequence of sparse problems instead. Any existing discrete solver can be used as internal black-box. The case of noisy squared Euclidean distance is explicitly detailed. We observe a significant reduction of run-time and memory requirements.

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Author information

Authors and Affiliations

  1. CEREMADE, Université Paris-Dauphine, Paris, France

    Bernhard Schmitzer

Authors
  1. Bernhard Schmitzer
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Correspondence to Bernhard Schmitzer .

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Editors and Affiliations

  1. University of Bordeaux, Talence, France

    Jean-François Aujol

  2. ENS Cachan, Cachan, France

    Mila Nikolova

  3. University of Bordeaux, Talence, France

    Nicolas Papadakis

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© 2015 Springer International Publishing Switzerland

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Schmitzer, B. (2015). A sparse algorithm for dense optimal transport. In: Aujol, JF., Nikolova, M., Papadakis, N. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2015. Lecture Notes in Computer Science(), vol 9087. Springer, Cham. https://doi.org/10.1007/978-3-319-18461-6_50

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  • DOI: https://doi.org/10.1007/978-3-319-18461-6_50

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-18460-9

  • Online ISBN: 978-3-319-18461-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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