Binary Analysis of Center-weighted Median Filters

This paper focuses on the binary analysis of the center-weighted median (CWM) filters. This subclass of nonlinear stack filters is based on minimal positive Boolean functions (PBFs), the complexity of which depends on two parameters only, such as a window size and a weight of the central sample. It can be easily seen that the complexity of PBFs corresponding with CWMs increases with the increasing window size and the central weight. The above mentioned fact makes the implementation of CWMs in practical applications rather complicated. In order to simplify the implementation, a new analysis, based on the determination of binary outputs according to the configuration of ones and zeros inside binary input sets, is provided. By this way, the outputs of binary filters are practically known at once with no PBF generation and the calculation of binary operations. The achieved simplification is described in the form of the elementary expressions, where the binary value of the central sample and a number of the ones in its neighbourhood play the key role. Thus, the proposed method makes the implementation of CWM filters more flexible, since it is possible to extend it for the arbitrary combination of the window size and the central weight.