A Riemannian approach to anisotropic filtering of tensor fields

Authors:
C. A. Castaño-Moraga;C. Lenglet;R. Deriche;J. Ruiz-Alzola
Affiliations:
I.N.R.I.A., Projet Odyssée, 2004 route des lucioles, 06902 Sophia-Antipolis, France and Center for Technology in Medicine, Signals and Communications Department, Building B, University of Las ...;I.N.R.I.A., Projet Odyssée, 2004 route des lucioles, 06902 Sophia-Antipolis, France;I.N.R.I.A., Projet Odyssée, 2004 route des lucioles, 06902 Sophia-Antipolis, France;Center for Technology in Medicine, Signals and Communications Department, Building B, University of Las Palmas de Gran Canaria, Campus de Tafira s/n, 35017 Tafira, Spain and Canary Islands Institu ...
Venue:
Signal Processing
Year:
2007

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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.