Non-Euclidean Analysis for Covariance Matrix Data with Application to Diffusion tensor Images

Covariance matrix data has gained significant importance in many applications, e.g. diffusion tensor imaging, principal component analysis, structure tensor analysis, etc. Our work mainly focuses on developing statistical methodologies for analysing covariance matrix data, taking into account the non-Euclidean nature of the covariance matrix. Non-Euclidean metrics including the log-Euclidean, Riemannian, power Euclidean and, in particular, Procrustes size-and-shape distance have been used for defining the mean of covariance matrices. The proposed methods have been applied to process diffusion tensor images from human brain