translation invariant unit template with a specific support such as the 3 × 3 support of the Moore template t shown in Figure 1.7.1. Suppose further that we would like this template to be used with a variety of reduction operations, for instance, summation and maximum. In fact, we cannot describe such an operand without regard of the image-template operation by which it will be used. For us to derive the expected results, the template must map all points in its support to the unitary value with respect to the combining operation . Thus, for the reduce operation of summation , the unit values in the support must be 1, while for the maximum reduce operation , the values in the support must all be 0. Therefore, we cannot define a single template operand to characterize a neighborhood for reduction without regard to the image-template operation to be used to reduce the values within the neighborhood. However, we can capture exactly the information of interest in unit templates with the simple notion of neighborhood function. Thus, for example, the Moore