On a Geodesic Equation for Planar Conformal Template Matching

Stephen Marsland; Robert Mclachlan; Klas Modin; Matthew Perlmutter

inria-00623918, version 1

On a Geodesic Equation for Planar Conformal Template Matching

Stephen Marsland ¹, Robert Mclachlan ², Klas Modin ¹, Matthew Perlmutter ²

Proceedings of the Third International Workshop on Mathematical Foundations of Computational Anatomy - Geometrical and Statistical Methods for Modelling Biological Shape Variability (2011) 52-63

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.

1: School of Engineering and Advanced Technology [Palmerston] (SEAT)
Massey University
2: Institute of Fundamental Sciences [Palmerston]
Massey University

Collaboration : Session 02: Beyond Riemannian geometry

inria-00623918, version 1
http://hal.inria.fr/inria-00623918
oai:hal.inria.fr:inria-00623918
From: Xavier Pennec <>
Submitted on: Thursday, 15 September 2011 13:18:32
Updated on: Friday, 16 September 2011 10:22:37

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