On Edge Detection,
MASSACHUSETTS INST OF TECH CAMBRIDGE ARTIFICIAL INTELLIGENCE LAB
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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 of 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 this part of edge detection consists of two steps, a filtering step and a differentiation step. We discuss recent results on the behavior and the information content of zero crossings obtained with filters of different sizes. These results imply a specific order in the sequence of filtering and differentiation operations. Topological properties are preserved by level-crossings.