Recently, mathematical morphology has been applied to image processing and analysis, because of its simplicity and shift-invariance. We propose novel morphological operations of image differentiation like the erosion and dilation for morphological smoothing. It is named bipolar morphological operation. We show that bipolar morphological operation is closely related to a differential operator we recently proposed5). This operator, we call it RONDO(Rank-Order based Nonlinear Differential Operator), is a generalized weighted median filter with positive and negative weight coefficients.
image processing, mathematical morphology, image differentiation, edge detection