Simplifying Jacobi Sets Topology and Geometry by Selective Smoothing of Bivariate 2D Scalar Fields
| dc.contributor.author | Raith, Felix | |
| dc.contributor.author | Scheuermann, Gerik | |
| dc.contributor.author | Heine, Christian | |
| dc.date.accessioned | 2025-07-30T08:06:29Z | |
| dc.date.available | 2025-07-30T08:06:29Z | |
| dc.date.issued | 2025 | |
| dc.description.abstract-translated | The topological analysis of multivariate fields is vital when investigating the relationship between functions. Jacobi sets, the set of all points at which the gradients of the functions are linearly dependent, are an essential tool for such analyses, as they extend the notion of critical points from scalar fields to multivariate fields. However, the Jacobi sets can become very complex, in particular, due to numerical errors and noise. These problems occur in practice, such as in eddy detection on sea surfaces. Although several methods for simplifying Jacobi sets exist in the literature, they mainly reduce Jacobi sets visually without adjusting the function values, which is essential for further data processing. This paper introduces a novel algorithm that changes the values of functions in a 2D bivariate scalar field, resulting in simplified Jacobi sets. For this, we use a neighborhood graph to identify the Jacobi sets to simplify, visualize the complexity of the Jacobi set for real-world examples, and compare the results with prior work. The new approach preserves features better and simplifies the geometry of the Jacobi sets by reducing zigzag patterns. | en |
| dc.description.sponsorship | This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - SCHE 663/17-1. The authors thank Markus Stommel of the Leibniz Institute of Polymer Research Dresden, Germany for providing the tensile bar data sets and Bill Kuo, Wei Wang, Cindy Bruyere, Tim Scheitlin, and Don Middleton of the U.S. National Center for Atmospheric Research (NCAR), and the U.S. National Science Foundation (NSF) for providing the Weather Research and Forecasting (WRF) Model simulation data of Hurricane Isabel. The authors acknowledge the financial support by the Federal Ministry of Education and Research of Germany and by Sächsische Staatsministerium für Wissenschaft, Kultur und Tourismus in the program Center of Excellence for AI-research “Center for Scalable Data Analytics and Artificial Intelligence Dresden/Leipzig”, project identification number: SCADS24B. | |
| dc.description.sponsorship | This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - SCHE 663/17-1. The authors thank Markus Stommel of the Leibniz Institute of Polymer Research Dresden, Germany for providing the tensile bar data sets and Bill Kuo, Wei Wang, Cindy Bruyere, Tim Scheitlin, and Don Middleton of the U.S. National Center for Atmospheric Research (NCAR), and the U.S. National Science Foundation (NSF) for providing the Weather Research and Forecasting (WRF) Model simulation data of Hurricane Isabel. The authors acknowledge the financial support by the Federal Ministry of Education and Research of Germany and by Sächsische Staatsministerium für Wissenschaft, Kultur und Tourismus in the program Center of Excellence for AI-research “Center for Scalable Data Analytics and Artificial Intelligence Dresden/Leipzig”, project identification number: SCADS24B. | en |
| dc.format | 10 s. | cs |
| dc.format.mimetype | application/pdf | |
| dc.identifier.doi | http://www.doi.org/10.24132/JWSCG.2025-7 | |
| dc.identifier.issn | 1213-6972 (print) | |
| dc.identifier.issn | 1213-6964 (online) | |
| dc.identifier.uri | http://hdl.handle.net/11025/62201 | |
| dc.language.iso | en | en |
| dc.publisher | Václav Skala - UNION Agency | cs |
| dc.rights | © Václav Skala - UNION Agency | en |
| dc.rights.access | openAccess | en |
| dc.subject | Jacobiho množina | cs |
| dc.subject | topologická analýza dat | cs |
| dc.subject | bivariační data | cs |
| dc.subject | topologické zjednodušení | cs |
| dc.subject.translated | Jacobi set | en |
| dc.subject.translated | topological data analysis | en |
| dc.subject.translated | bivariate data | en |
| dc.subject.translated | topological simplification | en |
| dc.title | Simplifying Jacobi Sets Topology and Geometry by Selective Smoothing of Bivariate 2D Scalar Fields | en |
| dc.type | článek | cs |
| dc.type | article | en |
| dc.type.status | Peer-reviewed | en |
| dc.type.version | publishedVersion | en |
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