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Scalar Field Comparison with Topological Descriptors: Properties and Applications for Scientific Visualization
Author(s) -
Yan Lin,
Masood Talha Bin,
Sridharamurthy Raghavendra,
Rasheed Farhan,
Natarajan Vijay,
Hotz Ingrid,
Wang Bei
Publication year - 2021
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.14331
Subject(s) - topological data analysis , visualization , persistent homology , computer science , merge (version control) , scalar field , cluster analysis , data field , scientific visualization , field (mathematics) , data visualization , topology (electrical circuits) , data mining , pattern recognition (psychology) , set (abstract data type) , artificial intelligence , mathematics , algorithm , pure mathematics , combinatorics , mathematical physics , information retrieval , programming language
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.