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Towards a Certified Computation of Homology Groups for Digital Images

  • Jónathan Heras
  • Maxime Dénès
  • Gadea Mata
  • Anders Mörtberg
  • María Poza
  • Vincent Siles
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7309)

Abstract

In this paper we report on a project to obtain a verified computation of homology groups of digital images. The methodology is based on programming and executing inside the Coq proof assistant. Though more research is needed to integrate and make efficient more processing tools, we present some examples partially computed in Coq from real biomedical images.

Keywords

Homology Discrete Morse Theory Proof assistant tools Coq SSReflect Synapses 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jónathan Heras
    • 1
  • Maxime Dénès
    • 2
  • Gadea Mata
    • 1
  • Anders Mörtberg
    • 3
  • María Poza
    • 1
  • Vincent Siles
    • 3
  1. 1.Department of Mathematics and Computer ScienceUniversity of La RiojaSpain
  2. 2.INRIA Sophia AntipolisMéditerranéeFrance
  3. 3.University of GothenburgSweden

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