Duality in soft open and soft close in multi scale morphological environment

In this paper, duality is discussed in soft open as well as soft close in multi scale environment. Soft erosion and soft dilation will exist for various thresholds. So soft open and soft close also exist for various thresholds. If definition for soft erosion and soft dilation are studied (5), then some type of equalities are viewed among soft morphological operations. So equality may be established in between soft erosion and soft dilation in multi scale environment (149). Open and close are composite operations. So soft open and soft close are also composite operations which will exist at various thresholds. Equality may be viewed among all soft morphological operations. In the same way duality also will exist for all soft morphological operations because duality will exist for all morphological operations, for example dual of erosion is dilation, dual of dilation is erosion, dual of open is close and dual of close is open. In this paper, duality is discussed in soft open and soft close operations, in multi scale as environment. A very important point is that equality does not exist in mathematical morphology but will exist in soft mathematical morphology. So various duals will occur for each soft morphological operation.