A class of multi-shell min/max median filters

Abstract

A novel extension of median filters from one dimension to higher dimensions is presented. Unlike the standard and separable median filters, this class of filters is able to preserve features of lower dimensionality, such as thin lines in two-dimensional space. Also, unlike the max/median filter, it does not have to trace exhaustively all the possible lines through the central sample. Hence, this class of filters does not blur sharp images while removing impulse noise and is highly computationally efficient. With minor modifications, missing line noise can also be removed with similar performance. Moreover, this class of filters is able to perform feature selective filtering by which isolated features of any particular shape can be removed from an image with a set of custom-tailored shells.