Fig. 2.

Asymmetric fod estimation procedure. A) General principle to obtain an A-fod in the current voxel v along orientation u_i. When considering only one neighbouring voxel at a time, the algorithm tries to match the amplitude of fod_v along u_i with the one of fod_x along –u_i. Voxel x and its fod_x are selected amongst the other neighbours of v, because the vector w_x (connecting the centre of voxel v to the one of voxel x, dashed line) is the closest to vector u_i. B) Toy example of complex fibre pattern, i.e., fibre fanning. The first column shows the resulting voxel-wise S-fods overlaid on top of the simulated ground truth simulated patterns. The middle column shows the conjunction fod weighting the contribution of multiple neighbouring voxels (vector z in Eqs. (3), (4))) for the first iteration of the A-fod estimation algorithm (top right voxel in the bending case, leftmost voxel for the fibre fanning configuration). The last column shows that, after 3 iterations, the resulting A-fod captures the right fanning polarity (i.e., increased dispersion along the left-right orientation).