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Abstract
While classical image processing algorithms were designed for scalar-valued (binary or grayscale) images, new technologies have made it commonplace to work with vector-valued ones. These technologies can involve new types of sensors, as in remote sensing, but also mathematical models leading to an increased cardinality at each pixel. This work analyzes the role of first-order differentiation in vector-valued images; specifically, we explore a novel operator to produce a 2D vector from a Jacobian matrix, in order to represent the variation in a vector-valued image as a planar feature.
Keywords
EDGE-DETECTION, ANISOTROPIC DIFFUSION, MULTISPECTRAL IMAGES, SCALE-SPACE, FILTERS, Vector-valued images, Differentiation, Jacobian matrix, Information fusion

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MLA
Lopez-Molina, Carlos, et al. “Gradient Fusion Operators for Vector-Valued Image Processing.” ADVANCES IN FUZZY LOGIC AND TECHNOLOGY 2017, VOL 2, vol. 642, Springer, 2018, pp. 430–42, doi:10.1007/978-3-319-66824-6_38.
APA
Lopez-Molina, C., Montero, J., Bustince, H., & De Baets, B. (2018). Gradient fusion operators for vector-valued image processing. ADVANCES IN FUZZY LOGIC AND TECHNOLOGY 2017, VOL 2, 642, 430–442. https://doi.org/10.1007/978-3-319-66824-6_38
Chicago author-date
Lopez-Molina, Carlos, Javier Montero, Humberto Bustince, and Bernard De Baets. 2018. “Gradient Fusion Operators for Vector-Valued Image Processing.” In ADVANCES IN FUZZY LOGIC AND TECHNOLOGY 2017, VOL 2, 642:430–42. Cham: Springer. https://doi.org/10.1007/978-3-319-66824-6_38.
Chicago author-date (all authors)
Lopez-Molina, Carlos, Javier Montero, Humberto Bustince, and Bernard De Baets. 2018. “Gradient Fusion Operators for Vector-Valued Image Processing.” In ADVANCES IN FUZZY LOGIC AND TECHNOLOGY 2017, VOL 2, 642:430–442. Cham: Springer. doi:10.1007/978-3-319-66824-6_38.
Vancouver
1.
Lopez-Molina C, Montero J, Bustince H, De Baets B. Gradient fusion operators for vector-valued image processing. In: ADVANCES IN FUZZY LOGIC AND TECHNOLOGY 2017, VOL 2. Cham: Springer; 2018. p. 430–42.
IEEE
[1]
C. Lopez-Molina, J. Montero, H. Bustince, and B. De Baets, “Gradient fusion operators for vector-valued image processing,” in ADVANCES IN FUZZY LOGIC AND TECHNOLOGY 2017, VOL 2, Warsaw, POLAND, 2018, vol. 642, pp. 430–442.
@inproceedings{8669399,
  abstract     = {{While classical image processing algorithms were designed for scalar-valued (binary or grayscale) images, new technologies have made it commonplace to work with vector-valued ones. These technologies can involve new types of sensors, as in remote sensing, but also mathematical models leading to an increased cardinality at each pixel. This work analyzes the role of first-order differentiation in vector-valued images; specifically, we explore a novel operator to produce a 2D vector from a Jacobian matrix, in order to represent the variation in a vector-valued image as a planar feature.}},
  author       = {{Lopez-Molina, Carlos and Montero, Javier and Bustince, Humberto and De Baets, Bernard}},
  booktitle    = {{ADVANCES IN FUZZY LOGIC AND TECHNOLOGY 2017, VOL 2}},
  isbn         = {{9783319668239}},
  issn         = {{2194-5357}},
  keywords     = {{EDGE-DETECTION,ANISOTROPIC DIFFUSION,MULTISPECTRAL IMAGES,SCALE-SPACE,FILTERS,Vector-valued images,Differentiation,Jacobian matrix,Information fusion}},
  language     = {{eng}},
  location     = {{Warsaw, POLAND}},
  pages        = {{430--442}},
  publisher    = {{Springer}},
  title        = {{Gradient fusion operators for vector-valued image processing}},
  url          = {{http://doi.org/10.1007/978-3-319-66824-6_38}},
  volume       = {{642}},
  year         = {{2018}},
}

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