Metamorphoses Through Lie Group Action

We formally analyze a computational problem which has important applications in image understanding and shape analysis. The problem can be summarized as follows. Starting from a group action on a Riemannian manifold M, we introduce a modification of the metric by partly expressing displacements on M as an effect of the action of some group element. The study of this new structure relates to evolutions on M under the combined effect of the action and of residual displacements, called metamorphoses. This can and has been applied to image processing problems, providing in particular diffeomorphic matching algorithms for pattern recognition.

Authors and Affiliations

1. CMLA, ENS de Cachan, 61, avenue du President Wilson, 94235 Cachan CEDEX , France

   Alain Trouvé

2. Department of Applied Mathematics and Statistics and Center for Imaging Science, The Johns Hopkins University, 3400 N-Charles Street, Baltimore, MD 21218-2686, USA

   Laurent Younes

Corresponding authors

Correspondence to Alain Trouvé or Laurent Younes.

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