Procrustes Analysis of Diffusion Tensor Data

¹School of Mathematical Sciences, University of Nottingham, Nottingham, UK; ²CMIAG Research Group, University of Nottingham, Nottingham, UK; ³Mathematics Department, Royal Holloway University of London, London, UK; ⁴School of Computer Science and IT, University of Nottingham, Nottingham, UK

Since the diffusion tensor (DT) is a symmetric, positive-definite matrix, we consider an alternative non-Euclidean metric for statistical analysis based on the weighted Procrustes mean. By computing the full Procrustes metric from a diffusion tensor to isotropy, we find an alternative measure of anisotropy called Procrustes anisotropy. For comparison, we plot geodesic paths between two DT’s with Euclidean, Log-Euclidean, Cholesky, Procrustes, Riemannian and root-Euclidean metrics. We find that FA and PA maps from smoothed and interpolated tensor fields with Procrustes analysis provide an improved method to investigate the diffusion anisotropy in human brain compared to using the raw DT images.