Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging

Details Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging

2009-10-09

arxiv.org/abs/0910.1656v1

Annals of Applied Statistics 2009, Vol. 3, No. 3, 1102-1123

Statistics

Applications

Published in at http://dx.doi.org/10.1214/09-AOAS249 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Ins

Scientific paper

10.1214/09-AOAS249

The statistical analysis of covariance matrix data is considered and, in particular, methodology is discussed which takes into account the non-Euclidean nature of the space of positive semi-definite symmetric matrices. The main motivation for the work is the analysis of diffusion tensors in medical image analysis. The primary focus is on estimation of a mean covariance matrix and, in particular, on the use of Procrustes size-and-shape space. Comparisons are made with other estimation techniques, including using the matrix logarithm, matrix square root and Cholesky decomposition. Applications to diffusion tensor imaging are considered and, in particular, a new measure of fractional anisotropy called Procrustes Anisotropy is discussed.

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