Time-varying Extremum Graphs
This work addresses the need for better visualization and analysis tools for time-varying scalar fields in scientific domains, representing an incremental advancement in topological data analysis.
The authors tackled the problem of analyzing dynamic scalar fields by introducing the time-varying extremum graph (TVEG), a topological structure that captures feature tracks and identifies topological events like deletion, generation, split, and merge, as demonstrated through case studies including a viscous fingers dataset and a 3D von Kármán vortex street dataset.
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 Kármán vortex street dataset.