Browsing by Author "Yan, Lin"

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    Multilevel Robustness for 2D Vector Field Feature Tracking, Selection and Comparison
    (© 2023 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd., 2023) Yan, Lin; Ullrich, Paul Aaron; Van Roekel, Luke P.; Wang, Bei; Guo, Hanqi; Hauser, Helwig and Alliez, Pierre
    Critical point tracking is a core topic in scientific visualization for understanding the dynamic behaviour of time‐varying vector field data. The topological notion of robustness has been introduced recently to quantify the structural stability of critical points, that is, the robustness of a critical point is the minimum amount of perturbation to the vector field necessary to cancel it. A theoretical basis has been established previously that relates critical point tracking with the notion of robustness, in particular, critical points could be tracked based on their closeness in stability, measured by robustness, instead of just distance proximity within the domain. However, in practice, the computation of classic robustness may produce artifacts when a critical point is close to the boundary of the domain; thus, we do not have a complete picture of the vector field behaviour within its local neighbourhood. To alleviate these issues, we introduce a multilevel robustness framework for the study of 2D time‐varying vector fields. We compute the robustness of critical points across varying neighbourhoods to capture the multiscale nature of the data and to mitigate the boundary effect suffered by the classic robustness computation. We demonstrate via experiments that such a new notion of robustness can be combined seamlessly with existing feature tracking algorithms to improve the visual interpretability of vector fields in terms of feature tracking, selection and comparison for large‐scale scientific simulations. We observe, for the first time, that the minimum multilevel robustness is highly correlated with physical quantities used by domain scientists in studying a real‐world tropical cyclone dataset. Such an observation helps to increase the physical interpretability of robustness.
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    Scalar Field Comparison with Topological Descriptors: Properties and Applications for Scientific Visualization
    (The Eurographics Association and John Wiley & Sons Ltd., 2021) Yan, Lin; Masood, Talha Bin; Sridharamurthy, Raghavendra; Rasheed, Farhan; Natarajan, Vijay; Hotz, Ingrid; Wang, Bei; Smit, Noeska and Vrotsou, Katerina and Wang, Bei
    In topological data analysis and visualization, topological descriptors such as persistence diagrams, merge trees, contour trees, Reeb graphs, and Morse-Smale complexes play an essential role in capturing the shape of scalar field data. We present a state-of-the-art report on scalar field comparison using topological descriptors. We provide a taxonomy of existing approaches based on visualization tasks associated with three categories of data: single fields, time-varying fields, and ensembles. These tasks include symmetry detection, periodicity detection, key event/feature detection, feature tracking, clustering, and structure statistics. Our main contributions include the formulation of a set of desirable mathematical and computational properties of comparative measures, and the classification of visualization tasks and applications that are enabled by these measures.