Order statistic filters: minimal collection of minimum weight vectors

Weighted order statistic (WOS) filters are a generalization of the standard order statistic filters. Usually, they are characterized by a weight vector and a threshold value. Rather than considering individual filters, it is possible to consider the whole set of filters related to a given weight vector as a class of filters by allowing the threshold values vary from 0 to the sum of the weights. A major question is to find out if two weight vectors are equivalent or not as classes of filters. Some equivalent weight vectors as well as discussions on minimal collections of weight vectors are presented in this paper.