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Procrustes analysis of diffusion tensor data
conference contribution
posted on 2015-03-25, 10:18 authored by Diwei ZhouDiwei Zhou, Ian L. Dryden, Alexey Koloydenko, Li BaiDiffusion 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.
Funding
European Commission FP6 Marie Curie programme through the CMIAG Research Training Network
History
School
- Science
Department
- Mathematical Sciences