Digitally Continuous Multivalued Functions, Morphological Operations and Thinning Algorithms

Escribano Iglesias, M. del Carmen and Giraldo Carbajo, Antonio and Sastre Rosa, María de la Asunción (2011). Digitally Continuous Multivalued Functions, Morphological Operations and Thinning Algorithms. "Journal of Mathematical Imaging and Vision" ; ISSN 0924-9907. https://doi.org/10.1007/s10851-011-0277-z.

Description

Title: Digitally Continuous Multivalued Functions, Morphological Operations and Thinning Algorithms
Author/s:
  • Escribano Iglesias, M. del Carmen
  • Giraldo Carbajo, Antonio
  • Sastre Rosa, María de la Asunción
Item Type: Article
Título de Revista/Publicación: Journal of Mathematical Imaging and Vision
Date: December 2011
ISSN: 0924-9907
Subjects:
Freetext Keywords: Digital space, Continuous function, Mathematical morphology, Simple point, Retraction, Thinning
Faculty: Facultad de Informática (UPM)
Department: Matemática Aplicada
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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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⟶X∖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.

More information

Item ID: 8628
DC Identifier: http://oa.upm.es/8628/
OAI Identifier: oai:oa.upm.es:8628
DOI: 10.1007/s10851-011-0277-z
Official URL: http://www.springerlink.com/content/b77871r1477016n6/
Deposited by: Memoria Investigacion
Deposited on: 12 Dec 2011 12:50
Last Modified: 20 Apr 2016 17:20
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