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Optimal Transport for Manifold-Valued Images

  • Jan Henrik Fitschen
  • Friederike LausEmail author
  • Bernhard Schmitzer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10302)

Abstract

We introduce optimal transport-type distances for manifold-valued images. To do so we lift the initial data to measures on the product space of image domain and signal space, where they can then be compared by optimal transport with a transport cost that combines spatial distance and signal discrepancy. Applying recently introduced ‘unbalanced’ optimal transport models leads to more natural results. We illustrate the benefit of the lifting with numerical examples for interpolation of color images and classification of handwritten digits.

Keywords

Color Space Image Domain Signal Space Back Projection Optimal Transport 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

Funding by the German Research Foundation (DFG) within the Research Training Group 1932 “Stochastic Models for Innovations in the Engineering Sciences”, project area P3, is gratefully acknowledged.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Jan Henrik Fitschen
    • 1
  • Friederike Laus
    • 1
    Email author
  • Bernhard Schmitzer
    • 2
  1. 1.Department of MathematicsUniversity of KaiserslauternKaiserslauternGermany
  2. 2.Institute for Computational and Applied MathematicsUniversity of MünsterMünsterGermany

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