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Fast and Simple Computations on Tensors with Log-Euclidean Metrics.
Abstract : Computations on tensors, i.e. symmetric positive definite real matrices in medical imaging, appear in many contexts. In medical imaging, these computations have become common with the use of DT-MRI. The classical Euclidean framework for tensor computing has many defects, which has recently led to the use of Riemannian metrics as an alternative. So far, only affine-invariant metrics had been proposed, which have excellent theoretical properites but lead to complex algorithms with a high computational cost. In this article, we present a new familly of metrics, called Log-Euclidean. These metrics have the same excellent theoretical properties as affine-invariant metrics and yield very similar results in practice. But they lead to much more simple computations, with a much lighter computational cost, very close to the cost of the classical Euclidean framework. Indeed, Riemannian computations become Euclidean computations in the logarithmic domain with Log-Euclidean metrics. We present in this article the complete theory for these metrics, and show experimental results for multilinear interpolation, dense extrapolation of tensors and anisotropic diffusion of tensor fields.
Cited literature [1 references]
https://hal.inria.fr/inria-00070423
Contributor : Rapport de Recherche Inria Connect in order to contact the contributor
Submitted on : Friday, May 19, 2006 - 8:27:00 PM
Last modification on : Friday, February 4, 2022 - 3:14:37 AM
Long-term archiving on: : Sunday, April 4, 2010 - 9:11:01 PM
Contributor : Rapport de Recherche Inria Connect in order to contact the contributor
Submitted on : Friday, May 19, 2006 - 8:27:00 PM
Last modification on : Friday, February 4, 2022 - 3:14:37 AM
Long-term archiving on: : Sunday, April 4, 2010 - 9:11:01 PM