High angular resolution diffusion imaging (HARDI) permits the computation of water molecule displacement probabilities over a sphere of possible displacement directions. This probability is often referred to as the orientation distribution function (ODF). In this paper we present a novel model for the diffusion ODF namely, a mixture of von Mises-Fisher (vMF) distributions. Our model is compact in that it requires very few variables to model complicated ODF geometries which occur specifically in the presence of heterogeneous nerve fiber orientation. We also present a Riemannian geometric framework for computing intrinsic distances, in closed-form, and performing interpolation between ODFs represented by vMF mixtures. As an example, we apply the intrinsic distance within a hidden Markov measure field segmentation scheme. We present results of this segmentation for HARDI images of rat spinal cords ? which show distinct regions within both the white and gray matter. It should be noted that...
Tim McGraw, Baba C. Vemuri, Robert Yezierski, Thom