Morphological properties of rank ordering filters

When performing tasks such as image segmentation and region coding, it is important to preserve the shape of the regions as closely as possible to those of the original object shapes. For the purposes of data compression it may then be prudent to allow some simplification of the region boundaries in a controlled manner (Beaumont 1996). To improve the segmentation of the image it is usual to filter the image to remove noise, and limit the generation of unnatural regions. The author found that the standard methods for spatial noise filtering such as low pass filtering and median filtering proved unsatisfactory. This is because they also filtered the shape of the region boundaries. A set of nonlinear filters were developed that preserved more of the structure of region boundaries. The constraints of the project also required the filters to be local (i.e mask based) and perform in real time (i.e. computationally fast). While developing the above filters the author uncovered the following 2 classes of filters which did not seem to be well documented in the literature: rank ordering clipping filters-nonlinear low pass; and low deviation filters-nonlinear edge enhancement