Multi-Scale Topological Analysis of Asymmetric Tensor Fields on Surfaces

Khan, Fariba; Roy, Lawrence; Zhang, Eugene; Qu, Botong; Hung, Shih-Hsuan; Yeh, Harry; Laramee, Robert S.; Zhang, Yue

Abstract

Asymmetric tensor fields have found applications in many science and engineering domains, such as fluid dynamics. Recent advances in the visualization and analysis of 2D asymmetric tensor fields focus on pointwise analysis of the tensor field and effective visualization metaphors such as colors, glyphs, and hyperstreamlines. In this paper, we provide a novel multi-scale topological analysis framework for asymmetric tensor fields on surfaces. Our multi-scale framework is based on the notions of eigenvalue and eigenvector graphs. At the core of our framework are the identification of atomic operations that modify the graphs and the scale definition that guides the order in which the graphs are simplified to enable clarity and focus for the visualization of topological analysis on data of different sizes. We also provide efficient algorithms to realize these operations. Furthermore, we provide physical interpretation of these graphs. To demonstrate the utility of our system, we apply our multi-scale analysis to data in computational fluid dynamics.

Citation

Khan, F., Roy, L., Zhang, E., Qu, B., Hung, S., Yeh, H., …Zhang, Y. (2020). Multi-Scale Topological Analysis of Asymmetric Tensor Fields on Surfaces. IEEE Transactions on Visualization and Computer Graphics, 26(1), 270 - 279. https://doi.org/10.1109/tvcg.2019.2934314

• Journal Article Type: Article
• Acceptance Date: Jun 1, 2019
• Online Publication Date: Aug 19, 2019
• Publication Date: Jan 1, 2020
• Deposit Date: Jan 15, 2021
• Publicly Available Date: Mar 17, 2021
• Journal: IEEE Transactions on Visualization and Computer Graphics
• Print ISSN: 1077-2626
• Electronic ISSN: 1941-0506
• Publisher: Institute of Electrical and Electronics Engineers
• Peer Reviewed: Peer Reviewed
• Volume: 26
• Issue: 1
• Pages: 270 - 279
• DOI: https://doi.org/10.1109/tvcg.2019.2934314
• Keywords: Signal Processing; Software; Computer Vision and Pattern Recognition; Computer Graphics and Computer-Aided Design
• Public URL: https://nottingham-repository.worktribe.com/output/4571462
• Publisher URL: https://ieeexplore.ieee.org/document/8805436
• Additional Information: © 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.