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 calculations 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 median filters that is able to predict essentially exact numerical values of relevant 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 demonstrates clearly the unexpectedly large anisotropy that this type of filtering produces.