Thinning Algorithms as Multivalued \({\mathcal{N}}\)-Retractions

  • Carmen Escribano
  • Antonio Giraldo
  • María Asunción Sastre
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5810)


In a recent paper we have introduced a notion of continuity in digital spaces which extends the usual notion of digital continuity. Our approach, which uses multivalued maps, provides a better framework to define topological notions, like retractions, in a far more realistic way than by using just single-valued digitally continuous functions. In particular, we characterized the deletion of simple points, one of the most important processing operations in digital topology, as a particular kind of retraction.

In this work we give a simpler algorithm to define the retraction associated to the deletion of a simple point and we use this algorithm to characterize some well known parallel thinning algorithm as a particular kind of multivalued retraction, with the property that each point is retracted to its neighbors.


Digital images digital topology continuous multivalued function simple point retraction thinning algorithm 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Carmen Escribano
    • 1
  • Antonio Giraldo
    • 1
  • María Asunción Sastre
    • 1
  1. 1.Departamento de Matemática Aplicada, Facultad de InformáticaUniversidad Politécnica de MadridMadridSpain

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