Merge Tree Geodesics and Barycenters with Path Mappings

  • 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.

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Author:Florian WetzelsORCiD, Mathieu PontORCiD, Julien TiernyORCiD, Christoph GarthORCiD
Document Type:Article
Language of publication:English
Date of Publication (online):2023/10/25
Year of first Publication:2023
Publishing Institution:Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau
Date of the Publication (Server):2024/05/07
Page Number:11
First Page:1095
Last Page:1105
Faculties / Organisational entities:Kaiserslautern - Fachbereich Informatik
DDC-Cassification:0 Allgemeines, Informatik, Informationswissenschaft / 004 Informatik
Licence (German):Zweitveröffentlichung