Weighted Procrustes Analysis for Diffusion Tensor Imaging

There has been substantial interest in the development of methods for processing diffusion tensor fields, taking into account the non-Euclidean nature of the tensor space. In this paper, we generalise Procrustes analysis to weighted Procrustes analysis for diffusion tensor smoothing, interpolation, regularisation and segmentation in which an arbitrary number of tensors can be processed efficiently with the additional flexibility of controlling their individual contributions. An algorithm has been developed for calculating the weighted Procrustes mean tensor. A weighted regularisation model with Procrustes size-and shape metric is proposed which incorporates the smoothness of the neighbourhood and the regularisation with the diffusion behaviour of interest. Our methods and a study of Procrustes anisotropy measure are illustrated on both synthetic and real diffusion tensor data.