A New Class of Alternating Sequential Filters

A well-known class of morphological filters are the alternating sequential filters. Such filters are obtained by composing openings and closings with increasingly large structuring elements. This paper shows that this class can be extended substantially by composing overfilters and underfilters. 1 Introduction Idempotence of an image operator is a useful property: it guarantees that a second pass of the operator has no further effect on the image. In mathematical morphology, operators / which are increasing and idempotent (i.e., / 2 = /) are called (morphological) filters. Here the increasingness condition refers to some underlying partial ordering. For the sake of simplicity we restrict ourselves to operators on the collection of 2dimensional, discrete, binary images. Mathematically, this collection can be modeled by P(Z 2 ), the subsets of Z 2 . The corresponding partial ordering is the usual set inclusion. The construction of morphological filters, as well as related notions..