Deterministic properties of separable and cross median filters with an application to block truncation coding

Abstract

In this paper, we present some deterministic properties of separable and cross median filters. It is proved that in the absence of vertical binary oscillations, the roots of a separable median filter are included in a subset of root signals of the corresponding cross median filter. Moreover, the sufficient and necessary condition is given for a point to be invariant to cross median filtering. On the root structures of cross median filters, we indicate that there exist three different types of regions based on the one-dimensional features of rows and columns. Finally, an application example is discussed where the roots of separable and cross median filters are used in block truncation coding (BTC) for image compression.