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Digitally Continuous Multivalued Functions, Morphological Operations and Thinning Algorithms

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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.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, Facultad de Informática, Universidad Politécnica, Campus de Montegancedo, Boadilla del Monte, 28660, Madrid, Spain

    Carmen Escribano, Antonio Giraldo & María Asunción Sastre

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  1. Carmen Escribano
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  2. Antonio Giraldo
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  3. María Asunción Sastre
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Correspondence to Antonio Giraldo.

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Escribano, C., Giraldo, A. & Sastre, M.A. Digitally Continuous Multivalued Functions, Morphological Operations and Thinning Algorithms. J Math Imaging Vis 42, 76–91 (2012). https://doi.org/10.1007/s10851-011-0277-z

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