Deletion of (26,6)-simple points as multivalued retractions

Authors:
Carmen Escribano;Antonio Giraldo;María Asunción Sastre
Affiliations:
Departamento de Matemática Aplicada, Facultad de Informática, Universidad Politécnica, Boadilla del Monte, Madrid, Spain;Departamento de Matemática Aplicada, Facultad de Informática, Universidad Politécnica, Boadilla del Monte, Madrid, Spain;Departamento de Matemática Aplicada, Facultad de Informática, Universidad Politécnica, Boadilla del Monte, Madrid, Spain
Venue:
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
Year:
2012

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Abstract

In a recent paper we have introduced a notion of multivalued continuity in digital spaces which extends the usual notion of digital continuity and allows to define topological notions, like retractions, in a far more realistic way than by using just single-valued digitally continuous functions. In particular, we have characterized the deletion of simple points in 2-D, one of the most important processing operations in digital topology, as a particular kind of retraction. In this work we extend some of these results to 3-dimensional digital sets.