On a Geodesic Equation for Planar Conformal Template Matching

Stephen Marsland 1 Robert Mclachlan 2 Klas Modin 1 Matthew Perlmutter 2
1 SEAT - School of Engineering and Advanced Technology [Palmerston]
2 Institute of Fundamental Sciences [Palmerston]
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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Pennec, Xavier and Joshi, Sarang and Nielsen, Mads. 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, 2011
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Contributeur : Xavier Pennec <>
Soumis le : jeudi 15 septembre 2011 - 13:18:32
Dernière modification le : vendredi 16 septembre 2011 - 10:22:37
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Stephen Marsland, Robert Mclachlan, Klas Modin, Matthew Perlmutter. On a Geodesic Equation for Planar Conformal Template Matching. Pennec, Xavier and Joshi, Sarang and Nielsen, Mads. 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, 2011. 〈inria-00623918〉

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