Geodesic-loxodromes for diffusion tensor interpolation and difference measurement.


Gordon Kindlmann, Raúl San José Estépar, Marc Niethammer, Steven Haker, and Carl-Fredrik Westin. 2007. “Geodesic-loxodromes for diffusion tensor interpolation and difference measurement.” Med Image Comput Comput Assist Interv, 10, Pt 1, Pp. 1-9. Copy at


In algorithms for processing diffusion tensor images, two common ingredients are interpolating tensors, and measuring the distance between them. We propose a new class of interpolation paths for tensors, termed geodesic-loxodromes, which explicitly preserve clinically important tensor attributes, such as mean diffusivity or fractional anisotropy, while using basic differential geometry to interpolate tensor orientation. This contrasts with previous Riemannian and Log-Euclidean methods that preserve the determinant. Path integrals of tangents of geodesic-loxodromes generate novel measures of over-all difference between two tensors, and of difference in shape and in orientation.