Extended Permutation Filters and Their Applicationto Edge

Extended permutation (EP) lters are deened and analyzed in this paper. In particular, we focus on extended permutation rank selection (EPRS) lters. These lters 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 lters exhibit excellent edge enhancement properties. We also show that several previously deened classes of rank order based edge enhancers (CS, LUM, and WMMR sharpeners) can be formulated as subclasses of EPRS lters. These sharpening subclasses are in addition to the smoothing subclasses, which include rank conditioned rank selection, permutation , stack, and weighted order statistic lters. Thus, this novel class of lters provides a broad framework within which many rank order based smoothers and edge enhancers can be uniied. Edge enhancement properties are developed and an L norm EPRS lter optimization procedure is presented. Finally, extensive computer simulation results are presented comparing the performance of EPRS and other sharpening lters in edge enhancement applications. EDICS Number: IP 1.4 Permission to publish this abstract separately is granted. 1 Example of a sequence containing a convex/concave increasing/decreasing edge and the output of an order statistic (OS) lter (N = 15, k = 3) operating on the sequence. The increasing edge has been retarded while the decreasing edge has been advanced. Neither transition region duration has been r 1 ]), where ~ r 1 is the center sample rank and ~ r 1 is the rank of the LUM midpoint t l. 3 Example of a step edge showing the rank of the mean ~ r 1 for size N = 9 lter window (= 1). Notice that for each lter position which spans the edge, the mean takes on a unique 4 Example of a ramp edge showing the rank of the mean ~ r 1 for size N = 9 lter window where = 1. Notice that mean rank provides detailed edge location information. : : 14 5 A convex/concave edge with innection point at time index 0. On the left (right) side of the edge the rank of {trimmed mean is bound by ~ 6 A convex/concave edge ltered by …