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The fundamentals of fuzzy mathematical morphology, part 1 : basic concepts

Author
Organization
Abstract
Fuzzy mathematical morphology provides an alternative extension of the binary morphological operations to gray-scale images based on the theory of fuzzy sets. This paper introduces the basic concepts of fuzzy mathematical morphology, starting from the original definitions of the morphological operations by Serra. More specifically, the fuzzy dilation, erosion, closing and opening operations are introduced. Their basic properties such as monotonicity and interaction with union and intersection are discussed in detail. Some important relationships between the fuzzy erosion and fuzzy dilation are established.
Keywords
FUZZY MATHEMATICAL MORPHOLOGY, BINARY MATHEMATICAL MORPHOLOGY, FUZZY SETS, GRAY-SCALE IMAGES, DILATION, EROSION, CLOSING, OPENING

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

Chicago
De Baets, Bernard, Etienne Kerre, and Madan Gupta. 1995. “The Fundamentals of Fuzzy Mathematical Morphology, Part 1 : Basic Concepts.” International Journal of General Systems 23 (2): 155–171.
APA
De Baets, Bernard, Kerre, E., & Gupta, M. (1995). The fundamentals of fuzzy mathematical morphology, part 1 : basic concepts. INTERNATIONAL JOURNAL OF GENERAL SYSTEMS, 23(2), 155–171.
Vancouver
1.
De Baets B, Kerre E, Gupta M. The fundamentals of fuzzy mathematical morphology, part 1 : basic concepts. INTERNATIONAL JOURNAL OF GENERAL SYSTEMS. 1995;23(2):155–71.
MLA
De Baets, Bernard, Etienne Kerre, and Madan Gupta. “The Fundamentals of Fuzzy Mathematical Morphology, Part 1 : Basic Concepts.” INTERNATIONAL JOURNAL OF GENERAL SYSTEMS 23.2 (1995): 155–171. Print.
@article{195440,
  abstract     = {Fuzzy mathematical morphology provides an alternative extension of the binary morphological operations to gray-scale images based on the theory of fuzzy sets. This paper introduces the basic concepts of fuzzy mathematical morphology, starting from the original definitions of the morphological operations by Serra. More specifically, the fuzzy dilation, erosion, closing and opening operations are introduced. Their basic properties such as monotonicity and interaction with union and intersection are discussed in detail. Some important relationships between the fuzzy erosion and fuzzy dilation are established.},
  author       = {De Baets, Bernard and Kerre, Etienne and Gupta, Madan},
  issn         = {0308-1079},
  journal      = {INTERNATIONAL JOURNAL OF GENERAL SYSTEMS},
  keyword      = {FUZZY MATHEMATICAL MORPHOLOGY,BINARY MATHEMATICAL MORPHOLOGY,FUZZY SETS,GRAY-SCALE IMAGES,DILATION,EROSION,CLOSING,OPENING},
  language     = {eng},
  number       = {2},
  pages        = {155--171},
  title        = {The fundamentals of fuzzy mathematical morphology, part 1 : basic concepts},
  url          = {http://dx.doi.org/10.1080/03081079508908037},
  volume       = {23},
  year         = {1995},
}

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