Asymmetric rank-order filters and their morphological representations

Rank-order filters are represented by type-1 and type-2 asymmetric rank-order filters, and some interesting properties of the latter are presented. Among other results, it is shown that a signal that is not required to be finite is a root of the kth rank-order filter if and only if it is also a root of the kth type-1 and type-2 asymmetric rank-order filters, and (2) asymmetric median filters can bound a median much tighter than that of morphological filters by taking opening/closing with a structuring,element B that is a one-dimensional convex set having N+1 elements in the set of integers