Weight conditions of recursive weighted median filters

The authors consider some root properties of recursive weighted median (RWM) filters. Specifically, a set of conditions on weights for an RWM filter to preserve monotone or locally monotone sequences is found. The authors also find the weight conditions under which any input sequence will converge to a locally monotone sequence after a finite number of passes and those under which the output of an RWM filter is equivalent to that of an RM filter