Feature Tracking Utilizing a Maximum-Weight Independent Set Problem

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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Time‐varying Extremum Graphs

Das,

Sridharamurthy,

Natarajan

2024

Computer Graphics Forum

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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.

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Feature Tracking Utilizing a Maximum-Weight Independent Set Problem

Cited by 4 publications

References 34 publications

Comparing Morse Complexes Using Optimal Transport: An Experimental Study

Comparing Morse Complexes Using Optimal Transport: An Experimental Study

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

Time‐varying Extremum Graphs

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