Tensorlines: advection-diffusion based propagation through diffusion tensor fields

Tracking linear features through tensor field datasets is an open research problem with widespread utility in medical and engineering disciplines. Existing tracking methods, which consider only the preferred local diffusion direction as they propagate, fail to accurately follow features as they enter regions of local complexity. This shortcoming is a result of partial voluming; that is, voxels in these regions often contain contributions from multiple features. These combined contributions result in ambiguities when deciding local primary feature orientation based solely on the preferred diffusion direction. We introduce a novel feature extraction method which we term tensorline propagation. Our method resolves the above ambiguity by incorporating information about the nearby orientation of the feature, as well as the anisotropic classification of the local tensor. The nearby orientation information is added in the spirit of an advection term in a standard diffusion based propagation technique, and has the effect of stabilizing the tracking. To demonstrate the efficacy of tensorlines, we apply this method to the neuroscience problem of tracking white-matter bundles within the brain.