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The dual representation of gray-scale morphological filters
Dougherty, E.R.
Center for Imaging Sci., Rochester Inst. of Technol., NY;

This paper appears in: Computer Vision and Pattern Recognition, 1989. Proceedings CVPR '89., IEEE Computer Society Conference on
Publication Date: 4-8 Jun 1989
On page(s): 172-177
Meeting Date: 06/04/1989 - 06/08/1989
Location: San Diego, CA, USA
ISBN: 0-8186-1952-x
References Cited: 10
INSPEC Accession Number: 3471668
Digital Object Identifier: 10.1109/CVPR.1989.37846
Current Version Published: 2002-08-06

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

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