Threshold decomposition algorithm for gray-scale soft morphological operations. II. Erosion

Gray-scale soft mathematical morphology is the natural extension of binary soft mathematical morphology which has been proved 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 the present paper, a superposition property called threshold decomposition and another property called stacking are introduced and have been found to apply successfully to gray-scale soft morphology operation. These properties allow the gray-scale signals and structuring elements to be decomposed into their binary sets, respectively operated by only logic gates in new VLSI architecture, and then these binary results are combined to produce the desired output as the time-consuming gray-scale processing. The threshold decomposition algorithm for gray-scale soft morphological erosion is developed and presented. The theorems developed may significantly improve speed as well as give new theoretical insight into the operations