Equality in soft erosion, soft dilation and soft close in multi scale environment

In this paper, equality is established and discussed among soft erosion, soft dilation and 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 (47). 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. As part of that, in this paper equality may be established in between soft erosion, soft dilation and soft close in multi scale environment. A very important point is that equality does not exist in mathematical morphology but will exist in soft mathematical morphology.