Image Registration by Geodesic Warps Using Conformal Mappings

Details Image Registration by Geodesic Warps Using Conformal Mappings Image Registration by Geodesic Warps Using Conformal Mappings

2012-03-18

arxiv.org/abs/1203.3982v1

Mathematics

Dynamical Systems

Scientific paper

In this paper we study planar conformal deformations, motivated by the warps that evolutionary biologist D'Arcy Wentworth Thompson used to deform images of one species into another. The approach is to equip the infinite dimensional manifold of conformal embeddings with a Riemannian metric, and then use the corresponding geodesic equation in order to obtain diffeomorphic warps. After deriving the geodesic equation, a numerical discretisation method is developed. Several examples of geodesic warps are then given.

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