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A rigorous framework for diffusion tensor calculus

Batchelor, PG; Moakher, M; Atkinson, D; Calamante, F; Connelly, A; (2005) A rigorous framework for diffusion tensor calculus. MAGN RESON MED , 53 (1) 221 - 225. 10.1002/mrm.20334.

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Abstract

In biological tissue, all eigenvalues of the diffusion tensor are assumed to be positive. Calculations in diffusion tensor MRI generally do not take into account this positive definiteness property of the tensor. Here, the space of positive definite tensors is used to construct a framework for diffusion tensor analysis. The method defines a distance function between a pair of tensors and the associated shortest path (geodesic) joining them. From this distance a method for computing tensor means, a new measure of anisotropy, and a method for tensor interpolation are derived. The method is illustrated using simulated and in vivo data. (C) 2004 Wiley-Liss, Inc.

Type:Article
Title:A rigorous framework for diffusion tensor calculus
DOI:10.1002/mrm.20334
Keywords:positive definite, mean of tensors, tensor interpolation, anisotropy, SPATIAL NORMALIZATION, MRI, ANISOTROPY
UCL classification:UCL > School of Life and Medical Sciences > Faculty of Medical Sciences > Medicine (Division of)
UCL > School of BEAMS > Faculty of Engineering Science > Medical Physics and Bioengineering

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