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Statistics and Analysis of Shapes pp 335–361Cite as

Modeling Planar Shape Variation via Hamiltonian Flows of Curves

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Abstract

The application of the theory of deformable templates to the study of the action of a group of diffeomorphisms on deformable objects provides a powerful framework to compute dense one-to-one matchings on d-dimensional domains. In this paper, we derive the geodesic equations that govern the time evolution of an optimal matching in the case of the action on 2D curves with various driving matching terms, and provide a Hamiltonian formulation in which the initial momentum is represented by an L 2 vector field on the boundary of the template.

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Author information

Authors and Affiliations

  1. LAGA (CNRS, UMR 7539) and L2TI, Université Paris, 13, Av. Jean-baptiste Clément, F-93430, Villetaneuse

    Joan Glaunès

  2. Ecole Normale Supérieure de Cachan, CMLA (CNRS, UMR 1611), 61 avenue du Président Wilson, F-94235, Cachan, CEDEX

    Alain Trouvé

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

    Laurent Younes

Authors
  1. Joan Glaunès
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  2. Alain Trouvé
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  3. Laurent Younes
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, NC, 27606-7914, USA

    Hamid Krim

  2. School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-0250, USA

    Anthony Yezzi Jr.

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© 2006 Birkhäuser Boston

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Glaunès, J., Trouvé, A., Younes, L. (2006). Modeling Planar Shape Variation via Hamiltonian Flows of Curves. In: Krim, H., Yezzi, A. (eds) Statistics and Analysis of Shapes. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4481-4_14

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