Edge detection is the process that attempts to characterize the intensity changes in the image in terms of the physical processes that have originated them. A critical, intermediate goal of edge detection is the detection and characterization of significant intensity changes. This paper discusses this part fo the edge detection problem. To characterize the types of intensity changes derivatives of different types, and possibly different scales, are needed. Thus we consider this part of edge detection as a problem in numerical differentiation. We show that numerical differentiation of images is an ill-posed problem in the sense of Hadamard. Differentiation needs to be regularized by a regularizing filtering operation before differentiation. This shows that his part of edge detection consists of two steps, a filtering step and differentiation step.
