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Transport of Relational Structures in Groups of Diffeomorphisms

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Abstract

This paper focuses on the issue of translating the relative variation of one shape with respect to another in a template centered representation. The context is the theory of Diffeomorphic Pattern Matching which provides a representation of the space of shapes of objects, including images and point sets, as an infinite dimensional Riemannian manifold which is acted upon by groups of diffeomorphisms. We discuss two main options for achieving our goal; the first one is the parallel translation, based on the Riemannian metric; the second one, based on the group action, is the coadjoint transport. These methods are illustrated with 3D experiments.

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Authors and Affiliations

  1. Center for Imaging Science, Johns Hopkins University, 3400 N. Charles St., Baltimore, MD, 21218, USA

    Laurent Younes, Anqi Qiu & Michael I. Miller

  2. Department of Biomedical Engineering, Johns Hopkins University, 3400 N. Charles St., Baltimore, MD, 21218, USA

    Raimond L. Winslow

Authors
  1. Laurent Younes
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  2. Anqi Qiu
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  3. Raimond L. Winslow
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  4. Michael I. Miller
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Corresponding author

Correspondence to Laurent Younes.

Additional information

This work is partially supported by NSF DMS-0456253, NIH R01-EB000975, NIH P41-RR15241, NIH R01-MH064838, NIH 1R24-HL08534301A1 and the D.W. Reynolds Foundation.

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Younes, L., Qiu, A., Winslow, R.L. et al. Transport of Relational Structures in Groups of Diffeomorphisms. J Math Imaging Vis 32, 41–56 (2008). https://doi.org/10.1007/s10851-008-0074-5

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  • DOI: https://doi.org/10.1007/s10851-008-0074-5

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