Importance Sampling Spherical Harmonics to Improve Probabilistic Tractography

We consider the problem of improving the accuracy and reliability of probabilistic white matter tractography methods by improving the built-in sampling scheme, which randomly draws, from a diffusion model such as the orientation distribution function (ODF), a direction of propagation. Existing methods employing inverse transform sampling require an ad hoc thresholding step to prevent the less likely directions from being sampled. We herein propose to perform importance sampling of spherical harmonics, which redistributes an input point set on the sphere to match the ODF using hierarchical sample warping. This produces a point set that is more concentrated around the modes, allowing the subsequent inverse transform sampling to generate orientations that are in better accordance with the local fiber configuration. Integrated into a Kalman filter-based framework, our approach is evaluated through experiments on synthetic, phantom, and real datasets.