# 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.
Type de document :
Communication dans un congrès
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
Domaine :

Littérature citée [12 références]

https://hal.inria.fr/inria-00623918
Contributeur : Xavier Pennec <>
Soumis le : jeudi 15 septembre 2011 - 13:18:32
Dernière modification le : vendredi 16 septembre 2011 - 10:22:37
Document(s) archivé(s) le : vendredi 16 décembre 2011 - 02:22:48

### Fichier

MFCA11_2_2.pdf
Fichiers produits par l'(les) auteur(s)

### Identifiants

• HAL Id : inria-00623918, version 1

### Citation

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〉

### Métriques

Consultations de la notice

## 171

Téléchargements de fichiers