Figure 1.

The construction of the PDF for the direction of tractography is shown. Broad fiber ODFs, shown in box (A), may be due to either fanning or curvature, and curve inference distinguishes between these cases. In the case of fanning, fanning of the streamlines propagated in tractography will occur in only one direction [+, as indicated by the polarity vector in box (C)], while in the other direction, there is a merge [− in box (C)]. In the merge direction, and in the case of curvature, tractography follows non-zero directions in the PDF for the fiber ODF maximum [box (B)]. The PDF for the direction of propagation for curvature is then equal to the PDF for the fiber ODF maximum (B), and the PDF for the direction of propagation for fanning/merging (C) is the combination of the average fiber ODF (A) and the PDF for its maximum (B). Box (D) illustrates how the streamlines will propagate using FACT integration in the cases of fanning (left) and merging (right). Box (E) illustrates how the streamlines will propagate in the case of curvature. The fiber ODF maximum is assumed to represent the intermediate tangent to the curve, which is used as a discretized approximation to the curve segment in the voxel, entering and exiting the voxel where the curve would have done.