The dual representation of gray-scale morphological filters Conference Paper uri icon


  • 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.

name of conference

  • Proceedings CVPR '89: IEEE Computer Society Conference on Computer Vision and Pattern Recognition

published proceedings

  • 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)

author list (cited authors)

  • Dougherty, E. R.

citation count

  • 6

complete list of authors

  • Dougherty, ER

publication date

  • January 1989