Publication Details |
| Category | Text Publication |
| Reference Category | Journals |
| DOI | 10.24132/JWSCG.2025-7 |
| Title (Primary) | Simplifying Jacobi sets’ topology and geometry by selective smoothing of bivariate 2D scalar fields |
| Author | Raith, F.
; Scheuermann, G.; Heine, C. |
| Source Titel | Journal of WSCG |
| Year | 2025 |
| Department | ENVINF |
| Volume | 33 |
| Issue | 1-2 |
| Page From | 63 |
| Page To | 72 |
| Language | englisch |
| Topic | T8 Georesources |
| Keywords | Jacobi set; topological data analysis; bivariate data; topological simplification |
| Abstract | 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. |
| Persistent UFZ Identifier | https://www.ufz.de/index.php?en=20939&ufzPublicationIdentifier=31864 |
| Raith, F., Scheuermann, G., Heine, C. (2025): Simplifying Jacobi sets’ topology and geometry by selective smoothing of bivariate 2D scalar fields Journal of WSCG 33 (1-2), 63 - 72 10.24132/JWSCG.2025-7 |
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