Reduced Connectivity for Local Bilinear Jacobi Sets

Klötzl, Daniel; Krake, Tim; Zhou, Youjia; Stober, Jonathan M.; Schulte, Kathrin; Hotz, Ingrid; Wang, Bei; Weiskopf, Daniel

doi:10.1109/topoinvis57755.2022.00011

Cited by 2 publications

(1 citation statement)

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“…The method identifies less significant portions of the Jacobi set and removes them by modifying the individual scalar fields locally. Recently developed methods [29,30] compute a clutter-free visual representation of the Jacobi set by considering a bilinear interpolant. The method removes zig-zag artifacts while maintaining the topological structure.…”

Section: Related Workmentioning

confidence: 99%

Jacobi Set Simplification for Tracking Topological Features in Time-Varying Scalar Fields

Meduri,

Sharma,

Natarajan

2024

Preprint

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The Jacobi set of a bivariate scalar field is the set of points where the gradients of the two constituent scalar fields align with each other. It captures the regions of topological changes in the bivariate field. The Jacobi set is a bivariate analog of critical points, and may correspond to features of interest. In the specific case of time-varying fields and when one of the scalar fields is time, the Jacobi set corresponds to temporal tracks of critical points, and serves as a feature-tracking graph. The Jacobi set of a bivariate field or a time-varying scalar field is complex, resulting in cluttered visualizations that are difficult to analyze. This paper addresses the problem of Jacobi set simplification. Specifically, we use the time-varying scalar field scenario to introduce a method that computes a reduced Jacobi set. The method is based on a stability measure called robustness that was originally developed for vector fields and helps capture the structural stability of critical points. We also present a mathematical analysis for the method, and describe an implementation for 2D time-varying scalar fields. Applications to both synthetic and real-world datasets demonstrate the effectiveness of the method for tracking features.

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Section: Related Workmentioning

confidence: 99%