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The Discrete Morse Complex of Images: Algorithms, Modeling and Applications

Authors Ricardo Dutra da Silva , Helio Pedrini , Bernd Hamann

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Ricardo Dutra da Silva
  • Department of Informatics, Federal University of Technology, Curitiba, PR, Brazil
Helio Pedrini
  • Institute of Computing, University of Campinas, SP, Brazil
Bernd Hamann
  • Department of Computer Science, University of California, Davis, CA 95616, USA

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Ricardo Dutra da Silva, Helio Pedrini, and Bernd Hamann. The Discrete Morse Complex of Images: Algorithms, Modeling and Applications. In 2nd International Conference of the DFG International Research Training Group 2057 – Physical Modeling for Virtual Manufacturing (iPMVM 2020). Open Access Series in Informatics (OASIcs), Volume 89, pp. 18:1-18:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/OASIcs.iPMVM.2020.18

Abstract

The Morse complex can be used for studying the topology of a function, e.g., an image or terrain height field when understood as bivariate functions. We present an algorithm for the computation of the discrete Morse complex of two-dimensional images using an edge-based data structure. By using this data structure, it is possible to perform local operations efficiently, which is important to construct the complex and make the structure useful for areas like visualization, persistent homology computation, or construction of a topological hierarchy. We present theoretical and applied results to demonstrate benefits and use of our method.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Image processing
Keywords
  • Discrete Morse Complex
  • Image Topology
  • Cell Complexes

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