Time-varying Extremum Graphs

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 K & aacute;rm & aacute;n vortex street dataset. The TVEG is a time-varying extension of the extremum graph. It is a topological structure that support visualization and analysis of a time-varying scalar field. Temporal tracks from the TVEG aid in the visualization of the viscous fingers dataset. The tracks indicate typical growing behavior of fingers along the z-axis. The 3D domain is scaled along the z-axis and stacked to visualize the tracks over time. Individual tracks may be selected and inspected further to understand the dynamics of the associated fingers. image