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arXiv · 2106.00157

Scalar Field Comparison with Topological Descriptors: Properties and Applications for Scientific Visualization

Lin Yan·Talha Bin Masood·Raghavendra Sridharamurthy·Farhan Rasheed·Vijay Natarajan·Ingrid Hotz·Bei Wang
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Abstract

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.

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Lin Yan, Talha Bin Masood, Raghavendra Sridharamurthy, Farhan Rasheed, Vijay Natarajan, Ingrid Hotz, Bei Wang. 2021-06-01. Scalar Field Comparison with Topological Descriptors: Properties and Applications for Scientific Visualization. https://doi.org/10.1111/cgf.14331

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