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

Meduri, D and Sharma, M and Natarajan, V (2024) Jacobi set simplification for tracking topological features in time-varying scalar fields. In: Visual Computer, 40 (7).

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Abstract

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. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.

Item Type:	Journal Article
Publication:	Visual Computer
Publisher:	Springer Science and Business Media Deutschland GmbH
Additional Information:	The copyright for this article belongs to Springer Science and Business Media Deutschland GmbH.
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	20 Aug 2024 13:20
Last Modified:	20 Aug 2024 13:20
URI:	http://eprints.iisc.ac.in/id/eprint/85484

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