Jacobi set simplification for tracking topological features in time-varying scalar fields

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 featur...

Full description

Saved in:
Bibliographic Details
Published in:The Visual computer 2024-07, Vol.40 (7), p.4843-4855
Main Authors: Meduri, Dhruv, Sharma, Mohit, Natarajan, Vijay
Format: Article
Language:English
Subjects:
Algorithms
Artificial Intelligence
Bivariate analysis
Computer Graphics
Computer Science
Critical point
Effectiveness
Fields (mathematics)
Image Processing and Computer Vision
Mathematical analysis
Methods
Scalars
Simplification
Structural stability
Topology
Tracking
Visualization
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0178-2789
1432-2315
DOI:10.1007/s00371-024-03484-2