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On the decomposition of interval-valued fuzzy morphological operators

Tom Mélange (UGent) , Mike Nachtegael (UGent) , Peter Sussner and Etienne Kerre (UGent)
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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 [alpha (1),alpha (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.
Keywords
SET-THEORY, DUALITY, Interval-valued fuzzy sets, Mathematical morphology, Decomposition, MATHEMATICAL MORPHOLOGIES

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Please use this url to cite or link to this publication:

Chicago
Mélange, Tom, Mike Nachtegael, Peter Sussner, and Etienne Kerre. 2010. “On the Decomposition of Interval-valued Fuzzy Morphological Operators.” Journal of Mathematical Imaging and Vision 36 (3): 270–290.
APA
Mélange, T., Nachtegael, M., Sussner, P., & Kerre, E. (2010). On the decomposition of interval-valued fuzzy morphological operators. JOURNAL OF MATHEMATICAL IMAGING AND VISION, 36(3), 270–290.
Vancouver
1.
Mélange T, Nachtegael M, Sussner P, Kerre E. On the decomposition of interval-valued fuzzy morphological operators. JOURNAL OF MATHEMATICAL IMAGING AND VISION. 2010;36(3):270–90.
MLA
Mélange, Tom, Mike Nachtegael, Peter Sussner, et al. “On the Decomposition of Interval-valued Fuzzy Morphological Operators.” JOURNAL OF MATHEMATICAL IMAGING AND VISION 36.3 (2010): 270–290. Print.
@article{2132596,
  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 [alpha (1),alpha (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.},
  author       = {M{\'e}lange, Tom and Nachtegael, Mike and Sussner, Peter and Kerre, Etienne},
  issn         = {0924-9907},
  journal      = {JOURNAL OF MATHEMATICAL IMAGING AND VISION},
  keyword      = {SET-THEORY,DUALITY,Interval-valued fuzzy sets,Mathematical morphology,Decomposition,MATHEMATICAL MORPHOLOGIES},
  language     = {eng},
  number       = {3},
  pages        = {270--290},
  title        = {On the decomposition of interval-valued fuzzy morphological operators},
  url          = {http://dx.doi.org/10.1007/s10851-009-0185-7},
  volume       = {36},
  year         = {2010},
}

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