Examination of the concept of a row-column separated median filter

The two-dimensional median filter is not a linear filter and is therefore not separable into a set of smaller one-dimensional filters. Despite this theoretical barrier to simplification, the separation of a two-dimensional median filter into a set of row medians followed by a column median has been reported by others as an effective image processing tool. In this paper, it is shown that the quality of the image output is actually similar for the two implementations. It is further shown that there are situations in which the row/column median filter produces a higher quality image than a two dimensional median for the same Area or Area-Time hardware metric.