Binary LUM smoothing

In this letter, valuable simplification and analysis related to Boolean lower-upper middle (LUM) smoothers are provided. Thus, a class of nonlinear order-statistic LUM smoothers can be implemented as stack filters fast and effectively. An acquisition of the proposed method lies in the simple determination of the binary output according to the configuration of binary samples inside the filter window, where the proposed method takes advantage of the previously developed conversion algorithm between LUM smoothers and positive Boolean functions. Besides the important theoretical aspect, the proposed analysis allows to implement the LUM smoothers in small-area chips that can be successfully used in real image and video applications.