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Foundations of Computational Mathematics

, Volume 5, Issue 2, pp 173–198 | Cite as

Metamorphoses Through Lie Group Action

  • Alain Trouvé
  • Laurent Younes
Article

Abstract

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.

Groups of diffeomorphisms Infinite-dimensional shape spaces Geodesics Shape recognition Image registration 

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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.CMLA, ENS de Cachan, 61, avenue du President Wilson, 94235 Cachan CEDEX France
  2. 2.Department of Applied Mathematics and Statistics and Center for Imaging Science, The Johns Hopkins University, 3400 N-Charles Street, Baltimore, MD 21218-2686USA

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