TADD: A Computational Framework for Data Analysis Using Discrete Morse Theory

  • Jan Reininghaus
  • David Günther
  • Ingrid Hotz
  • Steffen Prohaska
  • Hans-Christian Hege
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6327)

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.

Keywords

Discrete Morse theory data analysis scalar fields vector fields 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Jan Reininghaus
    • 1
  • David Günther
    • 1
  • Ingrid Hotz
    • 1
  • Steffen Prohaska
    • 1
  • Hans-Christian Hege
    • 1
  1. 1.Zuse Institute Berlin (ZIB)BerlinGermany

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