Discrete & Computational Geometry

, Volume 47, Issue 2, pp 347–377 | Cite as

Optimal Topological Simplification of Discrete Functions on Surfaces

  • Ulrich Bauer
  • Carsten Lange
  • Max Wardetzky
Open Access


Given a function f on a surface and a tolerance δ>0, we construct a function f δ subject to ‖f δ fδ such that f δ has a minimum number of critical points. Our construction relies on a connection between discrete Morse theory and persistent homology and completely removes homological noise with persistence ≤2δ from the input function f. The number of critical points of the resulting simplified function f δ achieves the lower bound dictated by the stability theorem of persistent homology. We show that the simplified function can be computed in linear time after persistence pairs have been computed.


Discrete Morse theory Persistent homology Topological denoising 


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Copyright information

© The Author(s) 2011

Authors and Affiliations

  1. 1.Institute for Numerical and Applied MathematicsUniversity of GöttingenGöttingenGermany
  2. 2.Department of Mathematics and Computer ScienceFreie Universität BerlinBerlinGermany

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