Honorable Mention

Merge Tree Geodesics and Barycenters with Path Mappings

Florian Wetzels, Mathieu Pont, Julien Tierny, Christoph Garth

Room: 106

2023-10-26T04:00:00ZGMT-0600Change your timezone on the schedule page
Exemplar figure, described by caption below
A comparison of the Wasserstein interpolation of merge trees with the novel path mapping interpolation, together with the corresponding mappings embedded in the scalar field. The path mapping distance clearly yields a more meaningful interpolated merge tree.
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Topological data analysis, merge trees, scalar data, ensemble data


Comparative visualization of scalar fields is often facilitated using similarity measures such as edit distances. In this paper, we describe a novel approach for similarity analysis of scalar fields that combines two recently introduced techniques: Wasserstein geodesics/barycenters as well as path mappings, a branch decomposition-independent edit distance. Effectively, we are able to leverage the reduced susceptibility of path mappings to small perturbations in the data when compared with the original Wasserstein distance. Our approach therefore exhibits superior performance and quality in typical tasks such as ensemble summarization, ensemble clustering, and temporal reduction of time series, while retaining practically feasible runtimes. Beyond studying theoretical properties of our approach and discussing implementation aspects, we describe a number of case studies that provide empirical insights into its utility for comparative visualization, and demonstrate the advantages of our method in both synthetic and real-world scenarios. We supply a C++ implementation that can be used to reproduce our results.