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On the Decomposition of Interval-Valued Fuzzy Morphological Operators

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Abstract

Interval-valued fuzzy mathematical morphology is an extension of classical fuzzy mathematical morphology, which is in turn one of the extensions of binary morphology to greyscale morphology. The uncertainty that may exist concerning the grey value of a pixel due to technical limitations or bad recording circumstances, is taken into account by mapping the pixels in the image domain onto an interval to which the pixel’s grey value is expected to belong instead of one specific value. Such image representation corresponds to the representation of an interval-valued fuzzy set and thus techniques from interval-valued fuzzy set theory can be applied to extend greyscale mathematical morphology. In this paper, we study the decomposition of the interval-valued fuzzy morphological operators. We investigate in which cases the [α 1,α 2]-cuts of these operators can be written or approximated in terms of the corresponding binary operators. Such conversion into binary operators results in a reduction of the computation time and is further also theoretically interesting since it provides us a link between interval-valued fuzzy and binary morphology.

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Authors and Affiliations

  1. Dept. of Appl. Math. and Computer Science, Fuzziness and Uncertainty Modelling Research Unit, Ghent University, Krijgslaan 281 (Building S9), 9000, Ghent, Belgium

    Tom Mélange, Mike Nachtegael & Etienne E. Kerre

  2. Dept. of Applied Mathematics, University of Campinas, Campinas, SP, 13083 859, Brazil

    Peter Sussner

Authors
  1. Tom Mélange
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  2. Mike Nachtegael
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  3. Peter Sussner
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  4. Etienne E. Kerre
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Corresponding author

Correspondence to Tom Mélange.

Additional information

This work was financially supported by the GOA project B/04138/01 IV 1 of Ghent University and by CNPq under grant no. 306040/2006-9.

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Mélange, T., Nachtegael, M., Sussner, P. et al. On the Decomposition of Interval-Valued Fuzzy Morphological Operators. J Math Imaging Vis 36, 270–290 (2010). https://doi.org/10.1007/s10851-009-0185-7

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