Threshold decomposition of soft morphological filters

Frank Y. Shih, Christopher C. Pu

Abstract: The properties of soft morphological operations and the new definitions of binary soft morphological operations are presented. It is shown that soft morphological filtering on an arbitrary signal is equivalent to decomposing the signal into binary signals, filtering each binary signal with a binary soft morphological filter, and then reversing the decomposition. This equivalence allows problems in the analysis and the implementation of soft morphological operations in real time by using only logic gates for binary signals instead of sorting numbers.<