Order-statistics based filters that were originally provided bynthe robust estimation theory have proved to be efficient in image/signalnfiltering in the presence of additive white noise or impulsive noise.nTheir algorithms are simple and easy to implement. Their analysis,nhowever, is not straightforward. In this paper, we show that filtersnbased on order statistics can be explained by using the theory ofnpiecewise-linear (PWL) functions which was established originally forncircuit analysis and has recently been applied to nonlinear filtering.nWe also prove that an L-filter is a PWL filter defined on IRnnand a median filter by threshold decomposition is a piecewise-constantn(PWC) filter on [0,M-1]n. The main results lead to thenunification of order-statistics based filters with the PWL filter class.nBased on the fact that PWL functions are a general class ofnapproximation functions which are uniformly dense in the domainnconcerned, it is expected that the results obtained can provide a newnway to the extension, as well as further study of, order-statisticsnbased filters
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