Our skeletonization algorithm is based on the anisotropic vector diffusion. We first compute and diffuse the gradient vector field, and then calculate a map, called skeleton magnitude map, by summing up all the outgoing vectors minus all the incoming vectors, at each voxel. The obtained map gives a magnitude (or, possibility) for each voxel being on the skeletons. From the skeleton magnitude map, we then trace the skeletons by, for example, Canny¡¯s edge tracing algorithm or other ridge tracing methods. The problem to be solved is the proof of the connectivity, the thickness, and the topology-preservation of the obtained skeletons.

Fig. 5 Top: original density map; gradient vector fields (iso- & aniso-)
Bottom: skeleton magnitude maps (iso- & aniso-); skeleton tracing

Fig. 6 The skeletons of the bullfrog hair bundle tip link.
Left: overall dataset. Right: skeletons of a sub-volume