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Fast and simple calculus on tensors in the log-Euclidean framework.

Vincent Arsigny 1 Pierre Fillard 1 Xavier Pennec 1 Nicholas Ayache 1 
1 ASCLEPIOS - Analysis and Simulation of Biomedical Images
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : Computations on tensors have become common with the use of DT-MRI. But the classical Euclidean framework has many defects, and affine-invariant Riemannian metrics have been proposed to correct them. These metrics have excellent theoretical properties but lead to complex and slow algorithms. To remedy this limitation, we propose new metrics called Log-Euclidean. They also have excellent theoretical properties and yield similar results in practice, but with much simpler and faster computations. Indeed, Log-Euclidean computations are Euclidean computations in the domain of matrix logarithms. Theoretical aspects are presented and experimental results for multilinear interpolation and regularization of tensor fields are shown on synthetic and real DTI data.
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Submitted on : Thursday, July 15, 2010 - 2:30:29 PM
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Vincent Arsigny, Pierre Fillard, Xavier Pennec, Nicholas Ayache. Fast and simple calculus on tensors in the log-Euclidean framework.. International Conference on Medical Image computing and Computer-Assisted Intervention, Oct 2005, Palm Springs, CA, United States. pp.115-22, ⟨10.1007/11566465_15⟩. ⟨inria-00502669⟩



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