Time-varying Extremum Graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913417275637760 |
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| author | Das, Somenath Sridharamurthy, Raghavendra Natarajan, Vijay |
| author_facet | Das, Somenath Sridharamurthy, Raghavendra Natarajan, Vijay |
| contents | We introduce time-varying extremum graph (TVEG), a topological structure to support visualization and analysis of a time-varying scalar field. The extremum graph is a substructure of the Morse-Smale complex. It captures the adjacency relationship between cells in the Morse decomposition of a scalar field. We define the TVEG as a time-varying extension of the extremum graph and demonstrate how it captures salient feature tracks within a dynamic scalar field. We formulate the construction of the TVEG as an optimization problem and describe an algorithm for computing the graph. We also demonstrate the capabilities of \TVEG towards identification and exploration of topological events such as deletion, generation, split, and merge within a dynamic scalar field via comprehensive case studies including a viscous fingers and a 3D von Kármán vortex street dataset. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17652 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Time-varying Extremum Graphs Das, Somenath Sridharamurthy, Raghavendra Natarajan, Vijay Graphics Computational Geometry Computer Vision and Pattern Recognition We introduce time-varying extremum graph (TVEG), a topological structure to support visualization and analysis of a time-varying scalar field. The extremum graph is a substructure of the Morse-Smale complex. It captures the adjacency relationship between cells in the Morse decomposition of a scalar field. We define the TVEG as a time-varying extension of the extremum graph and demonstrate how it captures salient feature tracks within a dynamic scalar field. We formulate the construction of the TVEG as an optimization problem and describe an algorithm for computing the graph. We also demonstrate the capabilities of \TVEG towards identification and exploration of topological events such as deletion, generation, split, and merge within a dynamic scalar field via comprehensive case studies including a viscous fingers and a 3D von Kármán vortex street dataset. |
| title | Time-varying Extremum Graphs |
| topic | Graphics Computational Geometry Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2406.17652 |