Morphological operators such as erosion, dilation, opening and closing have been used for image processing. These classical operators modify an image feature based only on the size and polarity of that feature. We introduce a 3 by 3 pixel operator which can be used to perform repeated erosion and dilation like operations that are functions of not only size and polarity, but also local derivatives or ratios of adjacent pixel values. These operations can be mixed to implement new types of nonlinear filtering functions. Examples are given in 1 and 2 dimensions.