Simplified Boolean LUM smoothers

The field of the research related to the implementation of nonlinear order-statistic filters through their equivalent expression by positive Boolean functions (PBF) lies in the conversion between the traditional filtering functions and their corresponding PBF. In the case of the order-statistic LUM smoothers, the complexity of minimal PBF depends on a smoothing parameter and window size. In order to speed up the binary operations, this paper focuses on the binary analysis of the LUM smoothers in the dependence on the configuration of ones and zeros inside binary input sets, too. The proposed 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 neighborhood play the key role.