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

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A Correction to this article was published on 27 July 2024

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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.

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Acknowledgements

This work is partially supported by a grant from SERB, Govt. of India (CRG/2021/005278). VN acknowledges support from the Alexander von Humboldt Foundation, and Berlin MATH+ under the Visiting Scholar program. Part of this work was completed when VN was a guest Professor at the Zuse Institute Berlin.

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Authors and Affiliations

  1. University of Utah, Salt Lake City, USA

    Dhruv Meduri

  2. Indian Institute of Science, Bangalore, India

    Mohit Sharma & Vijay Natarajan

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D.M. Methodology,Theoretical Analysis, Visualization, Software, Experiments, Writing—Original Draft, Review and Editing. M.S. Experiments, Visualization, Writing—All Illustrations, Review and Editing. V.N. Conceptualization of this study, Methodology, Writing—Review and Editing.

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Meduri, D., Sharma, M. & Natarajan, V. Jacobi set simplification for tracking topological features in time-varying scalar fields. Vis Comput 40, 4843–4855 (2024). https://doi.org/10.1007/s00371-024-03484-2

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