Persistence Modules, Shape Description, and Completeness

  • Francesca Cagliari
  • Massimo Ferri
  • Luciano Gualandri
  • Claudia Landi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7309)

Abstract

Persistence modules are algebraic constructs that can be used to describe the shape of an object starting from a geometric representation of it. As shape descriptors, persistence modules are not complete, that is they may not distinguish non-equivalent shapes. In this paper we show that one reason for this is that homomorphisms between persistence modules forget the geometric nature of the problem. Therefore we introduce geometric homomorphisms between persistence modules, and show that in some cases they perform better. A combinatorial structure, the H 0-tree, is shown to be an invariant for geometric isomorphism classes in the case of persistence modules obtained through the 0th persistent homology functor.

Keywords

geometric homomorphism rank invariant H0-tree 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Francesca Cagliari
    • 1
  • Massimo Ferri
    • 1
    • 3
  • Luciano Gualandri
    • 1
  • Claudia Landi
    • 2
    • 3
  1. 1.Dip. di MatematicaUniv. di BolognaItaly
  2. 2.Dip. di Scienze e Metodi dell’IngegneriaUniv. di Modena e Reggio EmiliaItaly
  3. 3.ARCESUniv. di BolognaItaly

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