Lifted Wasserstein Matcher for Fast and Robust Topology Tracking

摘要: This paper presents a robust and efficient method for tracking topological features in time-varying scalar data. Structures are tracked based on the optimal matching between persistence diagrams with respect to Wasserstein metric. fundamentally relies solving assignment problem, special case of transport, all consecutive timesteps. Our approach two main contributions. First, we revisit seminal algorithm by Kuhn Munkres which specifically adapt problem an way. Second, propose extension metric that significantly improves geometrical stability domain-embedded pairs. We show this lifting has additional positive side-effect improving matrix sparsity therefore computing time. The global framework computes finds matchings parallel every timestep. Critical trajectories constructed associating successively matched pairs over Merging splitting events detected threshold post-processing stage. Extensive experiments real-life datasets our is up orders magnitude faster than algorithm. Moreover, compared modern approximation method, provides competitive runtimes while guaranteeing exact results. demonstrate utility extracting critical point from various compare it existing methods associated overlaps volumes. Robustness noise temporal resolution downsampling empirically demonstrated.