Image distortions produced by mean, median and mode filters

Median filters are probably the most widely used of the noise suppression filters that are commonly applied to digital images. They are vastly superior to mean filters since the latter are well known to blur images as well as removing noise. Median filters do not suffer from this disadvantage. Although median filters do not blur images, it has been found that they can cause a certain amount of image distortion by shifting edges (Davies 1997). This paper reviews previous work on the computation of shifts produced by mean, median and mode filters using continuum models. The paper proceeds to show how, in the case of median filters, it can be extended using discrete models to give more accurate predictions that are in line with experimental measurements.