%0 DATA
%A Diwei, Zhou
%A Ian L., Dryden
%A Alexey, Koloydenko
%A Li, Bai
%D 2015
%T Procrustes analysis of diffusion tensor data
%U https://repository.lboro.ac.uk/articles/Procrustes_analysis_of_diffusion_tensor_data/9376478
%K untagged
%X 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.