TADD: a computational framework for data analysis using discrete Morse theory

Authors:
Jan Reininghaus;David Günther;Ingrid Hotz;Steffen Prohaska;Hans-Christian Hege
Affiliations:
Zuse Institute Berlin, Berlin, Germany;Zuse Institute Berlin, Berlin, Germany;Zuse Institute Berlin, Berlin, Germany;Zuse Institute Berlin, Berlin, Germany;Zuse Institute Berlin, Berlin, Germany
Venue:
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
Year:
2010

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Abstract

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.