Probabilistic Gradient-Based Extrema Tracking

Emma Nilsson, Jonas Lukasczyk, Talha Bin Masood, Christoph Garth, Ingrid Hotz

Room: 106

2023-10-22T03:00:00ZGMT-0600Change your timezone on the schedule page
Exemplar figure, described by caption below
The image shows our result using gradient-based tracking on maxima of a valence electronic density distribution in a molecular dynamics simulation. The graph in (e) shows feature changes between time steps, while the top row (a-d) shows volume renderings of the density and the maxima. Each interesting feature is colored and highlighted based on the index of the maximum. In (f), we show closeups of a split event using the graph. On top, the line thickness encodes a binary matching and below, the line thickness encodes four probability categories based on our proposed maximum descending manifold overlap.
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Feature tracking is a common task in visualization applications, where methods based on topological data analysis (TDA) have successfully been applied in the past for feature definition as well as tracking. In this work, we focus on tracking extrema of temporal scalar fields. A family of TDA approaches address this task by establishing one-to-one correspondences between extrema based on discrete gradient vector fields. More specifically, two extrema of subsequent time steps are matched if they fall into their respective ascending and descending manifolds. However, due to this one-to-one assignment, these approaches are prone to fail where, e.g., extrema are located in regions with low gradient magnitude, or are located close to boundaries of the manifolds. Therefore, we propose a probabilistic matching that captures a larger set of possible correspondences via neighborhood sampling, or by computing the overlap of the manifolds. We illustrate the usefulness of the approach with two application cases.