Digitally Continuous Multivalued Functions, Morphological Operations and Thinning Algorithms

  • Authors:

  • Carmen Escribano;Antonio Giraldo;María Asunción Sastre

  • Affiliations:

  • Departamento de Matemática Aplicada, Facultad de Informática, Universidad Politécnica, Madrid, Spain 28660;Departamento de Matemática Aplicada, Facultad de Informática, Universidad Politécnica, Madrid, Spain 28660;Departamento de Matemática Aplicada, Facultad de Informática, Universidad Politécnica, Madrid, Spain 28660

  • Venue:
  • Journal of Mathematical Imaging and Vision
  • Year:
  • 2012

Quantified Score

Hi-index 0.00

Visualization

Abstract

In a recent paper (Escribano et al. in Discrete Geometry for Computer Imagery 2008. Lecture Notes in Computer Science, vol. 4992, pp. 81---92, 2008) we have introduced a notion of continuity in digital spaces which extends the usual notion of digital continuity. Our approach, which uses multivalued functions, 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 this work we develop properties of this family of continuous functions, now concentrating on morphological operations and thinning algorithms. We show that our notion of continuity provides a suitable framework for the basic operations in mathematical morphology: erosion, dilation, closing, and opening. On the other hand, concerning thinning algorithms, we give conditions under which the existence of a retraction F:X驴X驴D guarantees that D is deletable. The converse is not true, in general, although it is in certain particular important cases which are at the basis of many thinning algorithms.