Threshold decomposition of gray-scale soft morphology into binary soft morphology

Gray-scale soft mathematical morphology is the natural extension of binary soft mathematical morphology which has been shown to be less sensitive to additive noise and to small variations. But gray-scale soft morphological operations are difficult to implement in real time. In this Note, a superposition property called threshold decomposition and another property called stacking are applied successfully on gray-scale soft morphological operations. These properties allow gray-scale signals and structuring elements to be decomposed into their binary sets respectively and operated by only logic gates in new VLSI architectures, and then these binary results are combined to produce the desired output as of the time-consuming gray-scale processing.