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On a Geodesic Equation for Planar Conformal Template Matching

Abstract : In this paper we consider planar conformal deformations, motivated by the warps that Wentworth Thompson used to deform images of one species into another. We study an equation for geodesic motion on the infinite dimensional Fréchet manifold $Con(D,R^2)$ of conformal embeddings of the disk into the plane. We demonstrate that solutions may be represented as sheets, and use the sheet ansatz to derive a numerical discretization scheme. We also show that the equation admits totally geodesic solutions corresponding to scaling and translation, but not to affine transformations.
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https://hal.inria.fr/inria-00623918
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Submitted on : Thursday, September 15, 2011 - 1:18:32 PM
Last modification on : Thursday, February 7, 2019 - 4:45:38 PM
Long-term archiving on: : Friday, December 16, 2011 - 2:22:48 AM

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Stephen Marsland, Robert Mclachlan, Klas Modin, Matthew Perlmutter. On a Geodesic Equation for Planar Conformal Template Matching. Proceedings of the Third International Workshop on Mathematical Foundations of Computational Anatomy - Geometrical and Statistical Methods for Modelling Biological Shape Variability, Sep 2011, Toronto, Canada. pp.52-63. ⟨inria-00623918⟩

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