This paper presents a computational framework that allows for a robust extraction of the extremal structure of scalar and vector fields on 2D manifolds embedded in 3D. This structure consists of critical points, separatrices, and periodic orbits. The framework is based on Forman's discrete Morse theory, which guarantees the topological consistency of the computed extremal structure. Using a graph theoretical formulation of this theory, we present an algorithmic pipeline that computes a hierarchy of extremal structures. This hierarchy is defined by an importance measure and enables the user to select an appropriate level of detail. © 2010 Springer-Verlag.
CITATION STYLE
Reininghaus, J., Günther, D., Hotz, I., Prohaska, S., & Hege, H. C. (2010). TADD: A computational framework for data analysis using discrete morse theory. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6327 LNCS, pp. 198–208). https://doi.org/10.1007/978-3-642-15582-6_35
Mendeley helps you to discover research relevant for your work.