Time-varying Extremum Graphs

TL;DR

This paper introduces the time-varying extremum graph (TVEG), a novel topological structure for analyzing and visualizing dynamic scalar fields by capturing salient features and their topological events over time.

Contribution

It presents the formal definition, construction algorithm, and application of TVEG for dynamic scalar field analysis, extending the extremum graph concept to time-varying data.

Findings

Successfully captures feature tracks in dynamic scalar fields

Identifies topological events like creation, deletion, split, and merge

Demonstrates effectiveness on fluid dynamics datasets

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 substructure 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 K\'arm\'an vortex street dataset.