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International Conference on Relational and Algebraic Methods in Computer Science

RAMICS 2017: Relational and Algebraic Methods in Computer Science pp 43–59Cite as

Relations as Images

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10226))

Abstract

Boolean matrices constitute an immediate representation of black and white images, with 1 and 0 representing the black and white pixels, respectively. We give relational expressions for calculating two morphological operations on images, namely dilation and erosion. These operations have been implemented under RelView and we compare the performance of RelView with that of Matlab and Mathematica, which have a package for computing various morphological operations. Heijmans et al. have defined dilation and erosion for undirected graphs with vertices weighted by grey-level values. Graphs generalise images by allowing irregular “grids”. We propose a definition of dilation and erosion for nonweighted directed graphs (i.e., relations) along the same lines. These operations have been implemented under RelView too.

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Notes

  1. 1.

    In these expressions, the first \(o_2\) is a vector and the second one is an origin; the vector \(o_2\) is composed with an \(\mathsf {L}\) of the appropriate type to ensure the compatibility of the codomain of \(o_2 \mathbin {\mathrm{;}}\mathsf {L}\) with that of \(\mathsf {I}_1\). We write xRy for \((x,y) \in R\).

References

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Acknowledgements

We gratefully acknowledge the input of the anonymous referees and the financial support of NSERC (Natural Sciences and Engineering Research Council of Canada).

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Authors and Affiliations

  1. Département d’informatique et de génie logiciel, Université Laval, Québec, QC, Canada

    Mathieu Alain & Jules Desharnais

Authors
  1. Mathieu Alain
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  2. Jules Desharnais
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Corresponding author

Correspondence to Jules Desharnais .

Editor information

Editors and Affiliations

  1. Data61, CSIRO, Sydney, New South Wales, Australia

    Peter Höfner

  2. CNRS, Lyon, France

    Damien Pous

  3. University of Sheffield, Sheffield, United Kingdom

    Georg Struth

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Alain, M., Desharnais, J. (2017). Relations as Images. In: Höfner, P., Pous, D., Struth, G. (eds) Relational and Algebraic Methods in Computer Science. RAMICS 2017. Lecture Notes in Computer Science(), vol 10226. Springer, Cham. https://doi.org/10.1007/978-3-319-57418-9_3

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  • DOI: https://doi.org/10.1007/978-3-319-57418-9_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-57417-2

  • Online ISBN: 978-3-319-57418-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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