%0 Conference Paper %A Zhou, Diwei %A Dryden, Ian L. %A Koloydenko, Alexey %A Bai, Li %D 2015 %T Procrustes analysis of diffusion tensor data %U https://repository.lboro.ac.uk/articles/conference_contribution/Procrustes_analysis_of_diffusion_tensor_data/9376478 %K untagged %K Mathematical Sciences not elsewhere classified %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. %I Loughborough University