Scalar Field Comparison with Topological Descriptors: Properties and Applications for Scientific Visualization
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.
Cite
@article{arxiv.2106.00157,
title = {Scalar Field Comparison with Topological Descriptors: Properties and Applications for Scientific Visualization},
author = {Lin Yan and Talha Bin Masood and Raghavendra Sridharamurthy and Farhan Rasheed and Vijay Natarajan and Ingrid Hotz and Bei Wang},
journal= {arXiv preprint arXiv:2106.00157},
year = {2024}
}