Artificial Intelligence Laboratory and the Information Systems Laboratory, Stanford University, Stanford, CA 94305.
IEEE Trans Pattern Anal Mach Intell. 1986 Jun;8(6):699-714. doi: 10.1109/tpami.1986.4767852.
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 edgeelements, 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 surfacedescription 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 step-edge and its combinations are adequate for the roof-edge and the line-edge. The proposed method of step-edgel detection is robust with respect to noise; for (step-size/noise) > 2.5, it has subpixel position localization (position < 3) and an angular localization better than 100; further, it is designed to be insensitive to smooth shading. These results are demonstrated by some simple analysis, statistical data, and edgel-images. 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.
图像中的边缘对应于基础场景强度表面的不连续。它可以通过由边缘组成的分段直线曲线来近似，即短的线性边缘元素，每个元素都具有方向和位置。这里的边缘检测方法是为每个窗口（算子的核）拟合一系列一维曲面，并接受在最小二乘意义上足够准确且参数最少的曲面描述。（一维曲面是指沿某个方向保持不变的曲面。）双曲正切函数是阶跃边缘的合适基函数，其组合是屋顶边缘和线边缘的合适基函数。所提出的阶跃边缘检测方法对噪声具有鲁棒性；对于（阶跃大小/噪声）>2.5，它具有亚像素位置定位（位置<3）和优于 100 的角度定位；此外，它被设计为对平滑阴影不敏感。这些结果通过一些简单的分析、统计数据和边缘图像得到了证明。还包括与典型算子（高斯差分）在真实图像上的性能比较。结果表明，所提出的算子在检测、定位和分辨率方面具有优越性。
