Directional functions for orientation distribution estimation

We propose a novel method to obtain the orientation distribution function (ODF) from diffusion weighted signals measured using the Q-ball imaging methodology. Past work has involved using the spherical harmonics or radial basis functions to represent the ODF. In this work, we propose a novel function that has the ability to compactly represent signals measured using high angular resolution diffusion imaging (HARDI). Further, the closed form solution for computing the corresponding ODF turns out to be the Watson distribution used in directional statistics. As a special case, we formulate a directional function for which the ODF is the von Mises-Fisher (vMF) distribution. Experiments on some synthetic data show the robustness of the proposed method to represent ODF´s in the presence of noise. We also compare the method with ODF estimation using spherical harmonics and show some of its advantages.