  Statistical analysis of Diffusion Tensor Imaging (DTI) data requires a
computational framework that is both numerically tractable (to account for the
high dimensional nature of the data) and geometric (to account for the
nonlinear nature of diffusion tensors). Building upon earlier studies that have
shown that a Riemannian framework is appropriate to address these challenges,
the present paper proposes a novel metric and an accompanying computational
framework for DTI data processing. The proposed metric retains the geometry and
the computational tractability of earlier methods grounded in the affine
invariant metric. In addition, and in contrast to earlier methods, it provides
an interpolation method which preserves anisotropy, a central information
carried by diffusion tensor data.
