Slicing-based coherence measure for refining clusters of 3D curves

We present a method for refining clusters of 3D curves using a new coherence measure. Curves are common geometric models used for representing the information derived from different types of data, in particular scientific data represented as vector and tensor fields. Our method starts with an initial set of clusters. For each cluster, we probe samples from the cluster by “slicing” it with a plane at regularly spaced locations parameterized by curve arclengths. Then we compute a stability measure based on the spatial relations between the projections of the curve points in individual slices and their change across the slices. We use this measure to decide whether to further split the cluster. We demonstrate our method to improve an agglomerative hierarchical clustering of three-dimensional Diffusion-Tensor Magnetic Resonance Imaging (DTI) integral curves that correspond to neural pathways in the brain.