  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.
