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

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