Diffusion-tensor data from medical MR imaging consists of a 3 × 3 symmetric positive semi-definite matrix at each voxel. The issue of how to understand, and how to meaningfully display this type of data has been gaining interest since its development as a noninvasive investigative tool [1]. Several schemes have been developed, usually aimed at the display of the spatial geometric structure of each voxel characterized by its eigenvectors. However these efforts have used colour merely as a visualization device, without regard to an underlying metric structure between voxels. At the same time, some work has been developed on analyzing whole-brain structure using independent component analysis, making use of similarity between tensors to identify separated overall structures, e.g. for de-noising of spatial features. In this paper we consider using colour to understand these separated structures, mapping a true metric giving a similarity measure between tensors into a perceptually uniform colour space, so that colour difference corresponds to true difference. We show that such a colour map can better discriminate regions of distinct diffusion properties in the brain than previous methods.