Image distortions produced by mean, median and mode filters

The paper reviews earlier continuum models of image distortions produced by mean, median and mode filters, and shows that rigorous discrete calculatio ns are required to give predictions that agree accurately with experimental measurements in the median case. In addition, the paper describes what is believed to be the first discrete model of the distortions produced by medi an filters that is able to predict essentially exact numerical values of re levant boundary shifts. Not only does it take proper account of the actual discrete processes that are involved in the median computation, but also it reveals important intricacies about the operation of median filters and de monstrates clearly the unexpectedly large anisotropy that this type of filt ering produces.