Thinning algorithms as multivalued N-retractions

  • Authors:

  • Carmen Escribano;Antonio Giraldo;María Asunción Sastre

  • Affiliations:

  • Departamento de Matemática Aplicada, Facultad de Informática, Universidad Politécnica de Madrid, Madrid, Spain;Departamento de Matemática Aplicada, Facultad de Informática, Universidad Politécnica de Madrid, Madrid, Spain;Departamento de Matemática Aplicada, Facultad de Informática, Universidad Politécnica de Madrid, Madrid, Spain

  • Venue:
  • DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
  • Year:
  • 2009

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Abstract

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.