The Dual Representation of Gray-Scale Morphological Filters

Dougherty, Edward R.

doi:10.1109/CVPR.1989.37846

The Dual Representation of Gray-Scale Morphological Filters

Edward R. Dougherty

CVPR 1989 pp. 172-177

doi:10.1109/CVPR.1989.37846 /cvpr/1989/dougherty1989cvpr-dual/

Abstract

One of the classic results of mathematical morphology is the filter-representation theorem of G. Matheron (1975) for black-and-white images. The theorem states that any morphological filter can be represented as a union of erosions by elements in the filter's kernel. In its dual form, it states that the erosion representation can be replaced by an intersection of dilations by elements of the dual filter's kernel. Here, the dual-form of the gray-scale representation is derived in terms of a minimum of dilations by elements in the dual filter's kernel.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>

CVPR Semantic Scholar

Cite

Text

Dougherty. "The Dual Representation of Gray-Scale Morphological Filters." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 1989. doi:10.1109/CVPR.1989.37846

Markdown

[Dougherty. "The Dual Representation of Gray-Scale Morphological Filters." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 1989.](https://mlanthology.org/cvpr/1989/dougherty1989cvpr-dual/) doi:10.1109/CVPR.1989.37846

BibTeX

@inproceedings{dougherty1989cvpr-dual,
  title     = {{The Dual Representation of Gray-Scale Morphological Filters}},
  author    = {Dougherty, Edward R.},
  booktitle = {IEEE/CVF Conference on Computer Vision and Pattern Recognition},
  year      = {1989},
  pages     = {172-177},
  doi       = {10.1109/CVPR.1989.37846},
  url       = {https://mlanthology.org/cvpr/1989/dougherty1989cvpr-dual/}
}