A New Riemannian Setting for Surface Registration

Abstract : We present a new approach for matching regular surfaces in a Riemannian setting. We use a Sobolev type metric on deformation vector fields which form the tangent bundle to the space of surfaces. In this article we compare our approach with the diffeomorphic matching framework. In the latter approach a deformation is prescribed on the ambient space, which then drags along an embedded surface. In contrast our metric is defined directly on the deformation vector field and can therefore be called an \it inner metric. We also show how to discretize the corresponding geodesic equation and compute the gradient of the cost functional using finite elements.
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Submitted on : Friday, September 16, 2011 - 10:11:47 AM
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Martin Bauer, Martins Bruveris. A New Riemannian Setting for Surface Registration. 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.182-193. ⟨inria-00624210⟩

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