Generating Second Order (Co)homological Information within AT-Model Context

  • Pedro Real
  • Helena Molina-Abril
  • Fernando Díaz del Río
  • Darian Onchis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11382)


In this paper we design a new family of relations between (co)homology classes, working with coefficients in a field and starting from an AT-model (Algebraic Topological Model) AT(C) of a finite cell complex C These relations are induced by elementary relations of type “to be in the (co)boundary of” between cells. This high-order connectivity information is embedded into a graph-based representation model, called Second Order AT-Region-Incidence Graph (or AT-RIG) of C. This graph, having as nodes the different homology classes of C, is in turn, computed from two generalized abstract cell complexes, called primal and dual AT-segmentations of C. The respective cells of these two complexes are connected regions (set of cells) of the original cell complex C, which are specified by the integral operator of AT(C). In this work in progress, we successfully use this model (a) in experiments for discriminating topologically different 3D digital objects, having the same Euler characteristic and (b) in designing a parallel algorithm for computing potentially significant (co)homological information of 3D digital objects.


Cell complex Algebraic-topological model Homology computation Primal and dual AT-segmentation AT-model region-incidence-graph nD digital object 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Pedro Real
    • 1
  • Helena Molina-Abril
    • 1
  • Fernando Díaz del Río
    • 1
  • Darian Onchis
    • 2
    • 3
  1. 1.H.T.S. Informatics’ EngineeringUniversity of SevilleSevilleSpain
  2. 2.Faculty of MathematicsUniversity of ViennaViennaAustria
  3. 3.Faculty of Mathematics and Computer ScienceWest University of TimisoaraTimişoaraRomania

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