Scalar Field Comparison with Topological Descriptors: Properties and Applications for Scientific Visualization
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arXiv
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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866911903847022592 |
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| author | Yan, Lin Masood, Talha Bin Sridharamurthy, Raghavendra Rasheed, Farhan Natarajan, Vijay Hotz, Ingrid Wang, Bei |
| author_facet | Yan, Lin Masood, Talha Bin Sridharamurthy, Raghavendra Rasheed, Farhan Natarajan, Vijay Hotz, Ingrid Wang, Bei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_00157 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Scalar Field Comparison with Topological Descriptors: Properties and Applications for Scientific Visualization Yan, Lin Masood, Talha Bin Sridharamurthy, Raghavendra Rasheed, Farhan Natarajan, Vijay Hotz, Ingrid Wang, Bei Human-Computer Interaction Computational Geometry 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. |
| title | Scalar Field Comparison with Topological Descriptors: Properties and Applications for Scientific Visualization |
| topic | Human-Computer Interaction Computational Geometry |
| url | https://arxiv.org/abs/2106.00157 |