A generalized model of the geometric distortions produced by rank-order filters

Abstract

This paper considers the shifts produced by rank-order filters on curved boundaries and contours and provides a generalized continuum model of these shifts, covering as special cases median, maximum and minimum filters. As for median filters, linear intensity variations and step edges are two extreme situations whose shifts are nevertheless predicted by the same formulae. This work should be valuable in leading to greater understanding of the properties and wider use of this important class of filters, which is crucial to the rigorous design of morphological filters.

Keywords:

• median
• maximum and minimum filters
• rank-order filters
• edge shifts
• geometric distortions
• morphology
• noise suppression