Please use this identifier to cite or link to this item: http://hdl.handle.net/10553/49714
Title: A Riemannian approach to anisotropic filtering of tensor fields
Authors: Castaño-Moraga, C. A.
Lenglet, C.
Deriche, R.
Ruiz-Alzola, J. 
UNESCO Clasification: 3325 Tecnología de las telecomunicaciones
Keywords: Signal processing
Tensors
Issue Date: 2007
Publisher: 0165-1684
Journal: Signal Processing 
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.
URI: http://hdl.handle.net/10553/49714
ISSN: 0165-1684
DOI: 10.1016/j.sigpro.2006.02.049
Source: Signal Processing[ISSN 0165-1684],v. 87, p. 263-276
Appears in Collections:Artículos
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