Time-varying Extremum Graphs

Das, S and Sridharamurthy, R and Natarajan, V (2024) Time-varying Extremum Graphs. [Preprint]

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Abstract

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 sub-structure 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. © 2024 Eurographics - The European Association for Computer Graphics and John Wiley & Sons Ltd.

Item Type:	Preprint
Publication:	Computer Graphics Forum
Publisher:	John Wiley and Sons Inc
Additional Information:	The copyright for this article belongs to authors.
Keywords:	Data visualization; High energy physics; Topology, Extrema graph; Morse decomposition; Morse-Smale complex; Salient features; Scalar fields; Sub-structures; Time varying; Topological methods; Topological structure; Visualization and analysis, Visualization
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	18 Dec 2024 12:12
Last Modified:	18 Dec 2024 12:12
URI:	http://eprints.iisc.ac.in/id/eprint/85884

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