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Local bilinear computation of Jacobi sets
Univ Stuttgart VISUS, Germany.
Univ Stuttgart VISUS, Germany.
Univ Utah SCI, UT USA.
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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2022 (English)In: The Visual Computer, ISSN 0178-2789, E-ISSN 1432-2315, Vol. 38, p. 3435-3448Article in journal (Refereed) Published
Abstract [en]

We propose a novel method for the computation of Jacobi sets in 2D domains. The Jacobi set is a topological descriptor based on Morse theory that captures gradient alignments among multiple scalar fields, which is useful for multi-field visualization. Previous Jacobi set computations use piecewise linear approximations on triangulations that result in discretization artifacts like zig-zag patterns. In this paper, we utilize a local bilinear method to obtain a more precise approximation of Jacobi sets by preserving the topology and improving the geometry. Consequently, zig-zag patterns on edges are avoided, resulting in a smoother Jacobi set representation. Our experiments show a better convergence with increasing resolution compared to the piecewise linear method. We utilize this advantage with an efficient local subdivision scheme. Finally, our approach is evaluated qualitatively and quantitatively in comparison with previous methods for different mesh resolutions and across a number of synthetic and real-world examples.

Place, publisher, year, edition, pages
Springer , 2022. Vol. 38, p. 3435-3448
Keywords [en]
Jacobi set; Topological data analysis; Multi-fields; Visualization techniques
National Category
Media Engineering
Identifiers
URN: urn:nbn:se:liu:diva-187499DOI: 10.1007/s00371-022-02557-4ISI: 000819263900001OAI: oai:DiVA.org:liu-187499DiVA, id: diva2:1690130
Note

Funding Agencies|Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) [DFG 270852890-GRK 2160/2, DFG 251654672-TRR 161]; Swedish Research Council (VR) [2019-05487]; U.S. Department of Energy (DOE) [DOE DE-SC0021015]; National Science Foundation (NSF) [NSF IIS-1910733]

Available from: 2022-08-25 Created: 2022-08-25 Last updated: 2023-02-28Bibliographically approved

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Hotz, Ingrid

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