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Modeling and Simplifying Morse Complexes in Arbitrary Dimensions

  • Lidija ČomićEmail author
  • Leila De Floriani
Chapter
Part of the Mathematics and Visualization book series (MATHVISUAL)

Abstract

Ascending and descending Morse complexes, defined by a scalar function f over a manifold domain M, decompose M into regions of influence of the critical points of f, thus representing themorphology of the scalar function f over M in a compact way. Here, we introduce two simplification operators on Morse complexes which work in arbitrary dimensions and we discuss their interpretation as n-dimensional Euler operators. We consider a dual representation of the two Morse complexes in terms of an incidence graph and we describe how our simplification operators affect the graph representation. This provides the basis for defining a multi-scale graph-based model of Morse complexes in arbitrary dimensions.

Keywords

Simplicial Complex Morse Theory Morse Function Integral Line Incidence Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

Acknowledgements

This work has been partially supported by the National Science Foundation under grant CCF-0541032, by the MIUR-FIRB project SHALOM under contract number RBIN04HWR8, and by the Ministry of Science of the Republic of Serbia through Project 23036.

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Copyright information

© Springer Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Faculty of EngineeringUniversity of Novi SadNovi SadSerbia
  2. 2.Department of Computer ScienceUniversity of GenovaGenovaItaly

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