ML Anthology

Closed-Form Representation of Convolution, Dilation, and Erosion in the Context of Image Algebra

Edward R. Dougherty, Charles R. Giardina
CVPR 1988 pp. 754-759
doi:10.1109/CVPR.1988.196319 /cvpr/1988/dougherty1988cvpr-closed/

Abstract

Using fundamental operators from image algebra, the authors present simple closed-form expressions for dilation, erosion, and convolution. Algebraically, these expressions appear as terms within the algebra. Moreover, the methodology for obtaining the expressions reveals a universal operational structure within image algebra, of which the three aforementioned operations are particular instances. The result is a natural parallel mechanism for computation and a representation of convolution that naturally overcomes the difficulties arising from the variability of image domains in the defining relation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

CVPR Semantic Scholar

Cite

Text

Dougherty and Giardina. "Closed-Form Representation of Convolution, Dilation, and Erosion in the Context of Image Algebra." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 1988. doi:10.1109/CVPR.1988.196319

Markdown

[Dougherty and Giardina. "Closed-Form Representation of Convolution, Dilation, and Erosion in the Context of Image Algebra." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 1988.](https://mlanthology.org/cvpr/1988/dougherty1988cvpr-closed/) doi:10.1109/CVPR.1988.196319

BibTeX

@inproceedings{dougherty1988cvpr-closed,
  title     = {{Closed-Form Representation of Convolution, Dilation, and Erosion in the Context of Image Algebra}},
  author    = {Dougherty, Edward R. and Giardina, Charles R.},
  booktitle = {IEEE/CVF Conference on Computer Vision and Pattern Recognition},
  year      = {1988},
  pages     = {754-759},
  doi       = {10.1109/CVPR.1988.196319},
  url       = {https://mlanthology.org/cvpr/1988/dougherty1988cvpr-closed/}
}