On What Manifold Do Diffusion Tensors Live?

Diffusion tensor imaging has become an important research and clinical tool, owing to its unique ability to infer microstructural properties of living tissue. Increased use has led to a demand for statistical tools to analyze diffusion tensor data and perform, for example, confidence estimates, ROI analysis, and group comparisons. A first step towards developing a statistical framework is establishing the basic notion of distance between tensors. We investigate the properties of two previously proposed metrics that define a Riemannian manifold: the affine-invariant and Euclidean metrics. We find that the Euclidean metric is more appropriate for intra-voxel comparisons, and suggest that a context-dependent metric may be required for inter-voxel comparisons.