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Abstract
Digital images are generally created as discrete measurements of light, as performed by dedicated sensors. Consequently, each pixel contains a discrete approximation of the light inciding in a sensor element. The nature of this measurement implies certain uncertainty due to discretization matters. In this work we propose to model such uncertainty using intervals, further leading to the generation of so-called interval-valued images. Then, we study the partial differentiation of such images, putting a spotlight on antisymmetric convolution operators for such task. Finally, we illustrate the utility of the interval-valued images by studying the behaviour of an extended version of the well-known Canny edges detection method.
Keywords
FUZZY-LOGIC, EDGE-DETECTION, Canny method, Edge detection, Interval-valued information, Image processing, IMAGES, MORPHOLOGY, COLOR

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Citation

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Chicago
Lopez-Molina, Carlos, Cedric Marco-Detchart, Juan Cerron, Humberto Bustince, and Bernard De Baets. 2015. “Gradient Extraction Operators for Discrete Interval-valued Data.” In Advances in Intelligent Systems Research, ed. JM Alonso, H Bustince, and M Reformat, 89:836–843. Paris, France: Atlantis Press.
APA
Lopez-Molina, Carlos, Marco-Detchart, C., Cerron, J., Bustince, H., & De Baets, B. (2015). Gradient extraction operators for discrete interval-valued data. In JM Alonso, H. Bustince, & M. Reformat (Eds.), Advances in Intelligent Systems Research (Vol. 89, pp. 836–843). Presented at the 16th World congress of the International Fuzzy Systems Association (IFSA) ; 9th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), Paris, France: Atlantis Press.
Vancouver
1.
Lopez-Molina C, Marco-Detchart C, Cerron J, Bustince H, De Baets B. Gradient extraction operators for discrete interval-valued data. In: Alonso J, Bustince H, Reformat M, editors. Advances in Intelligent Systems Research. Paris, France: Atlantis Press; 2015. p. 836–43.
MLA
Lopez-Molina, Carlos, Cedric Marco-Detchart, Juan Cerron, et al. “Gradient Extraction Operators for Discrete Interval-valued Data.” Advances in Intelligent Systems Research. Ed. JM Alonso, H Bustince, & M Reformat. Vol. 89. Paris, France: Atlantis Press, 2015. 836–843. Print.
@inproceedings{7258295,
  abstract     = {Digital images are generally created as discrete measurements of light, as performed by dedicated sensors. Consequently, each pixel contains a discrete approximation of the light inciding in a sensor element. The nature of this measurement implies certain uncertainty due to discretization matters. In this work we propose to model such uncertainty using intervals, further leading to the generation of so-called interval-valued images. Then, we study the partial differentiation of such images, putting a spotlight on antisymmetric convolution operators for such task. Finally, we illustrate the utility of the interval-valued images by studying the behaviour of an extended version of the well-known Canny edges detection method.},
  author       = {Lopez-Molina, Carlos and Marco-Detchart, Cedric and Cerron, Juan and Bustince, Humberto and De Baets, Bernard},
  booktitle    = {Advances in Intelligent Systems Research},
  editor       = {Alonso, JM and Bustince, H and Reformat, M},
  isbn         = {9789462520776},
  issn         = {1951-6851},
  language     = {eng},
  location     = {Gijon, Spain},
  pages        = {836--843},
  publisher    = {Atlantis Press},
  title        = {Gradient extraction operators for discrete interval-valued data},
  volume       = {89},
  year         = {2015},
}

Web of Science
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