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International Conference on Geometric Science of Information

GSI 2015: Geometric Science of Information pp 159–167Cite as

The Abstract Setting for Shape Deformation Analysis and LDDMM Methods

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9389))

Abstract

This paper aims to define a unified setting for shape registration and LDDMM methods for shape analysis. This setting turns out to be sub-Riemannian, and not Riemannian. An abstract definition of a space of shapes in \(\mathbb {R}^d\) is given, and the geodesic flow associated to any reproducing kernel Hilbert space of sufficiently regular vector fields is showed to exist for all time.

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Author information

Authors and Affiliations

  1. Johns Hopkins University, Baltimore, MD, USA

    Sylvain Arguillère

Authors
  1. Sylvain Arguillère
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Correspondence to Sylvain Arguillère .

Editor information

Editors and Affiliations

  1. Bâtiment Alan Turing, CS35003, École Polytechnique, Palaiseau, France

    Frank Nielsen

  2. Thales Land\& Air Systems, Limours, France

    Frédéric Barbaresco

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Arguillère, S. (2015). The Abstract Setting for Shape Deformation Analysis and LDDMM Methods. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2015. Lecture Notes in Computer Science(), vol 9389. Springer, Cham. https://doi.org/10.1007/978-3-319-25040-3_18

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  • DOI: https://doi.org/10.1007/978-3-319-25040-3_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25039-7

  • Online ISBN: 978-3-319-25040-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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