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An edge in an image corresponds to a discontinuity in the intensity surface of the underlying scene. It can be approximated by a piecewise straight curve composed of edgels, i.e., short, linear edge-elements, each characterized by a direction and a position. The approach to edgel-detection here, is to fit a series of one-dimensional surfaces to each window (kernel of the operator) and accept the surface-description which is adequate in the least squares sense and has the fewest parameters. (A one-dimensional surface is one which is constant along some direction.) The tanh is an adequate basis for the stepedge and its combinations are adequate for the roofedge and the line-edge. The proposed method of step-edgel detection is robust with respect to noise; for (step-size/Â¿noise) Â¿ 2.5, it has subpixel position localization (Â¿position < Â¿) and an angular localization better than 10Â°; further, it is designed to be insensitive to smooth shading. These results are demonstrated by some simple analysis, statistical data, and edgelimages. Also included is a comparison of performance on a real image, with a typical operator (Difference-of-Gaussians). The results indicate that the proposed operator is superior with respect to detection, localization, and resolution.