Anisotropy preserving interpolation of diffusion tensors

The growing importance of statistical studies of Diffusion Tensor Images (DTI) requires the development of a processing framework that accounts for the non-scalar and nonlinear nature of diffusion tensors. This motivation led a number of authors to consider a Riemannian framework for DTI processing because a Riemannian structure on the data space is sufficient to redefine most processing operations. As a prominent example, the Log-Euclidean metric proposed in [1] has emerged as a popular tool because it accounts for the tensor nature of DTI data at a computational cost that remains competitive with respect to standard tools. A limitation of the Log-Euclidean metric is its tendency to degrade the anisotropy of tensors through the standard operations of processing. Because anisotropy is the core information that motivates tensor imaging, the present paper proposes a novel metric that is anisotropy preserving while retaining the desirable properties of the Log-Euclidean metric. The properties of the proposed metric are illustrated on the basic operation of interpolating between diffusion tensors.