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One More Step Towards Well-Composedness of Cell Complexes over nD Pictures

  • Nicolas Boutry
  • Rocio Gonzalez-Diaz
  • Maria-Jose JimenezEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11414)

Abstract

An nD pure regular cell complex K is weakly well-composed (wWC) if, for each vertex v of K, the set of n-cells incident to v is face-connected. In previous work we proved that if an nD picture I is digitally well composed (DWC) then the cubical complex Q(I) associated to I is wWC. If I is not DWC, we proposed a combinatorial algorithm to “locally repair” Q(I) obtaining an nD pure simplicial complex \(P_S(I)\) homotopy equivalent to Q(I) which is always wWC. In this paper we give a combinatorial procedure to compute a simplicial complex \(P_S(\bar{I})\) which decomposes the complement space of \(|P_S(I)|\) and prove that \(P_S(\bar{I})\) is also wWC. This paper means one more step on the way to our ultimate goal: to prove that the nD repaired complex is continuously well-composed (CWC), that is, the boundary of its continuous analog is an \((n-1)\)-manifold.

Notes

Acknowledgments

This research has been partially supported by MINECO, FEDER/UE under grant MTM2015-67072-P and Instituto de Matematicas de la Universidad de Sevilla (IMUS).

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Nicolas Boutry
    • 1
  • Rocio Gonzalez-Diaz
    • 2
  • Maria-Jose Jimenez
    • 2
    Email author
  1. 1.EPITA Research and Development Laboratory (LRDE)Le Kremlin-BicêtreFrance
  2. 2.Departamento Matematica Aplicada IUniversidad de SevillaSevillaSpain

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