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Optimal Transport for Diffeomorphic Registration

  • Jean Feydy
  • Benjamin Charlier
  • François-Xavier VialardEmail author
  • Gabriel Peyré
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10433)

Abstract

This paper introduces the use of unbalanced optimal transport methods as a similarity measure for diffeomorphic matching of imaging data. The similarity measure is a key object in diffeomorphic registration methods that, together with the regularization on the deformation, defines the optimal deformation. Most often, these similarity measures are local or non local but simple enough to be computationally fast. We build on recent theoretical and numerical advances in optimal transport to propose fast and global similarity measures that can be used on surfaces or volumetric imaging data. This new similarity measure is computed using a fast generalized Sinkhorn algorithm. We apply this new metric in the LDDMM framework on synthetic and real data, fibres bundles and surfaces and show that better matching results are obtained.

Supplementary material

455905_1_En_34_MOESM1_ESM.zip (5.4 mb)
Supplementary material 1 (zip 5513 KB)

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Jean Feydy
    • 1
    • 2
  • Benjamin Charlier
    • 3
    • 5
  • François-Xavier Vialard
    • 4
    • 6
    Email author
  • Gabriel Peyré
    • 1
    • 5
  1. 1.DMA – École Normale SupérieureParisFrance
  2. 2.CMLA – ENS CachanCachanFrance
  3. 3.Institut Montpelliérain Alexander Grothendieck, Univ. MontpellierMontpellierFrance
  4. 4.Univ. Paris-Dauphine - PSL ResearchParisFrance
  5. 5.CNRSParisFrance
  6. 6.INRIA MokaplanParisFrance

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