Multiscale Comparison And Clustering Of Three-Dimensional Trajectories Based On Curvature Maxima

This paper presents a multiscale comparison method for three-dimensional trajectories. In order to deal with the problem that zero-crossings of curvature cannot be determined for space curve, we utilize the maxima of curvature. The method first traces the positions of curvature maxima across scales for recognizing the hierarchy of partial trajectories. Then it performs cross-scale matching of partial trajectories derived from two input trajectories, and obtains the structurally best matches. Finally, it calculates the value-based dissimilarity for each pair of the matched partial trajectories and output as the final dissimilarity between trajectories that can be further used for clustering or classification tasks. In experiments on the UCI character trajectory dataset we demonstrate that reasonable correspondences were captured successfully and the derived dissimilarity yielded good clustering results comparable to DTW. We also demonstrate using real medical data that the method could generate interesting clusters that might reflect distribution of fibrotic stages.