File(s) under permanent embargo

Reason: This item is currently closed access.

Procrustes analysis of diffusion tensor data

conference contribution
posted on 25.03.2015, 10:18 authored by Diwei ZhouDiwei Zhou, Ian L. Dryden, Alexey Koloydenko, Li Bai
Diffusion tensor imaging (DTI) is becoming increasingly important in clinical studies of diseases such as multiple sclerosis and schizophrenia, and also in investigating brain connectivity. Hence, there is a growing need to process diffusion tensor (DT) images within a statistical framework based on appropriate mathematical metrics. However, the usual Euclidean operations are often unsatisfactory for diffusion tensors due to the symmetric, positive-definiteness property. A DT is a type of covariance matrix and non-Euclidean metrics have been adapted naturally for DTI processing [1]. In this paper, Procrustes analysis has been used to define a weighted mean of diffusion tensors that provides a suitable average of a sample of tensors. For comparison, six geodesic paths between a pair of diffusion tensors are plotted using the Euclidean as well as various non-Euclidean distances. We also propose a new measure of anisotropy -Procrustes anisotropy (PA). Fractional anisotropy (FA) and PA maps from an interpolated and smoothed diffusion tensor field from a healthy human brain are shown as an application of the Procrustes method.


European Commission FP6 Marie Curie programme through the CMIAG Research Training Network



  • Science


  • Mathematical Sciences

Published in

17th Annual Conference of International Society for Magnetic Resonance in Medicine


3583 - 3583


ZHOU, D. ... et al., 2009. Procrustes analysis of diffusion tensor data. IN: Proceedings of the 17th Annual Conference of International Society for Magnetic Resonance in Medicine, USA, p.3583.


Curran Associates, Inc.


AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at:

Publication date



This is a conference paper.