Topological feature extraction and tracking

Abstract

Scientific datasets obtained by measurement or produced by computational simulations must be analyzed to understand the phenomenon under study. The analysis typically requires a mathematically sound definition of the features of interest and robust algorithms to identify these features, compute statistics about them, and often track them over time. Because scientific datasets often capture phenomena with multi-scale behaviour, and almost always contain noise the definitions and algorithms must be designed with sufficient flexibility and care to allow multi-scale analysis and noise-removal. In this paper, we present some recent work on topological feature extraction and tracking with applications in molecular analysis, combustion simulation, and structural analysis of porous materials.