A theoretical study of some nonlinear edge preserving smoothing filters

Good edge-preserving filters must be robust against large deviations from the nominal stationarity model. The extended influence function (EIF) has been proposed to study the effect of large proportions of outliers on an estimator's value. This extends the definition of the influence function which is mainly an infinitesimal tool. It is shown that the EIF may be used to predict qualitatively, useful performance measures like the output mean and the mean-square error. Specifically, the EIF is used to investigate the performance of the modified trimmed mean filter. Performance predictions are compared with results obtained through statistical simulations.<>