Anisotropic Fanning Aware Low-Rank Tensor Approximation Based Tractography

Low-rank higher-order tensor approximation has been used successfully to extract discrete directions for tractography from continuous fiber orientation density functions (fODFs). However, while it accounts for fiber crossings, it has so far ignored fanning, which has led to incomplete reconstructions. In this work, we integrate an anisotropic model of fanning based on the Bingham distribution into a recently proposed tractography method that performs low-rank approximation with an Unscented Kalman Filter. Our technical contributions include an initialization scheme for the new parameters, which is based on the Hessian of the low-rank approximation, pre-integration of the required convolution integrals to reduce the computational effort, and representation of the required 3D rotations with quaternions. Results on 12 subjects from the Human Connectome Project confirm that, in almost all considered tracts, our extended model significantly increases completeness of the reconstruction, while reducing excess, at acceptable additional computational cost. Its results are also more accurate than those from a simpler, isotropic fanning model that is based on Watson distributions.