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Geometry Aware Merge Tree Comparisons for Time-Varying Data with Interleaving Distances
University of Utah, Salt Lake City, Utah, United States.
Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0001-5352-1086
Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0003-0632-1545
Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0001-7285-0483
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2023 (English)In: IEEE Transactions on Visualization and Computer Graphics, ISSN 1077-2626, E-ISSN 1941-0506, Vol. 29, no 8, p. 3489-3506Article in journal (Refereed) Published
Abstract [en]

Merge trees, a type of topological descriptor, serve to identify and summarize the topological characteristics associated with scalar fields. They present a great potential for the analysis and visualization of time-varying data. First, they give compressed and topology-preserving representations of data instances. Second, their comparisons provide a basis for studying the relations among data instances, such as their distributions, clusters, outliers, and periodicities. A number of comparative measures have been developed for merge trees. However, these measures are often computationally expensive since they implicitly consider all possible correspondences between critical points of the merge trees. In this paper, we perform geometry-aware comparisons of merge trees. The main idea is to decouple the computation of a comparative measure into two steps: a labeling step that generates a correspondence between the critical points of two merge trees, and a comparison step that computes distances between a pair of labeled merge trees by encoding them as matrices. We show that our approach is general, computationally efficient, and practically useful. Our general framework makes it possible to integrate geometric information of the data domain in the labeling process. At the same time, it reduces the computational complexity since not all possible correspondences have to be considered. We demonstrate via experiments that such geometry-aware merge tree comparisons help to detect transitions, clusters, and periodicities of a time-varying dataset, as well as to diagnose and highlight the topological changes between adjacent data instances.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2023. Vol. 29, no 8, p. 3489-3506
Keywords [en]
Merge trees, merge tree metrics, topological data analysis, topology in visualization
National Category
Computer Sciences Human Computer Interaction Geometry
Identifiers
URN: urn:nbn:se:liu:diva-194719DOI: 10.1109/tvcg.2022.3163349ISI: 001022080200004PubMedID: 35349444Scopus ID: 2-s2.0-85127499657OAI: oai:DiVA.org:liu-194719DiVA, id: diva2:1764769
Note

Funding: DOE [DE-SC0021015]; NSF [IIS 1910733]; Swedish e-Science Research Center (SeRC); Excellence Center at Linkoping - Lund in Information Technology (ELLIIT); Swedish Research Council [2019-05487]; Wallenberg AI, Autonomous Systems and Software Program (WASP)

Available from: 2023-06-09 Created: 2023-06-09 Last updated: 2023-08-30Bibliographically approved

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Masood, Talha BinRasheed, FarhanHotz, Ingrid

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