Extended permutation (EP) filters are defined and analyzed. In particular, we focus on extended permutation rank selection (EPRS) filters. These filters are constrained to output an order statistic from an extended observation vector. This extended vector includes N observation samples and K statistics that are functions of the observation samples. The rank permutations from selected samples in this extended observation vector are used as the basis for selecting an order statistic output. We show that by including the sample mean in the extended observation vector, the filters exhibit excellent edge enhancement properties. We also show that several previously defined classes of rank-order-based edge enhancers (CS, LUM, and WMMR sharpeners) can be formulated as subclasses of EPRS filters. These sharpening subclasses are in addition to the smoothing subclasses, which include rank conditioned rank selection, permutation stack, and weighted order statistic filters. Thus, this novel class of filters provides a broad framework within which many rank-order-based smoothers and edge enhancers can be unified. Edge enhancement properties are developed and an Ln norm EPRS filter optimization procedure is presented. Finally, extensive computer simulation results are presented, comparing the performance of EPRS and other sharpening filters in edge enhancement applications