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A Riemannian approach to anisotropic filtering of tensor fields

Carlos Alberto Castaño Moraga 1, 2 Christophe Lenglet 1 Rachid Deriche 1 Juan Ruiz-Alzola 3
1 ODYSSEE - Computer and biological vision
DI-ENS - Département d'informatique de l'École normale supérieure, CRISAM - Inria Sophia Antipolis - Méditerranée , ENS Paris - École normale supérieure - Paris, Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech
Abstract : Tensors are nowadays an increasing research domain in different areas, especially in image processing, motivated for example by diffusion tensor magnetic resonance imaging (DT-MRI). Up to now, algorithms and tools developed to deal with tensors were founded on the assumption of a matrix vector space with the constraint of remaining symmetric positive definite matrices. On the contrary, our approach is grounded on the theoretically well-founded differential geometrical properties of the space of multivariate normal distributions, where it is possible to define an affine-invariant Riemannian metric and express statistics on the manifold of symmetric positive definite matrices. In this paper, we focus on the contribution of these tools to the anisotropic filtering and regularization of tensor fields. To validate our approach we present promising results on both synthetic and real DT-MRI data.
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https://hal.inria.fr/inria-00426951
Contributor : Service Ist Inria Sophia Antipolis-Méditerranée / I3s <>
Submitted on : Wednesday, October 28, 2009 - 4:11:25 PM
Last modification on : Thursday, July 1, 2021 - 5:58:02 PM

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  • HAL Id : inria-00426951, version 1

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Carlos Alberto Castaño Moraga, Christophe Lenglet, Rachid Deriche, Juan Ruiz-Alzola. A Riemannian approach to anisotropic filtering of tensor fields. Signal Processing, Elsevier, 2007, 87, pp.263-276. ⟨inria-00426951⟩

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