School of Electrical Engineering, Purdue University, West Lafayette, IN 49707; Bell Laboratories, Holmdel, NJ 07733.
IEEE Trans Pattern Anal Mach Intell. 1984 Feb;6(2):188-201. doi: 10.1109/tpami.1984.4767502.
A new method for locating edges in digital data to subpixel values and which is invariant to additive and multiplicative changes in the data is presented. For one-dimensional edge patterns an ideal edge is fit to the data by matching moments. It is shown that the edge location is related to the so-called ``Christoffel numbers.'' Also presented is the study of the effect of additive noise on edge location. The method is extended to include two-dimensional edge patterns where a line equation is derived to locate an edge. This in turn is compared with the standard Hueckel edge operator. An application of the new edge operator as an edge detector is also provided and is compared with Sobel and Hueckel edge detectors in presence and absence of noise.
本文提出了一种新的方法，可以将数字数据中的边缘定位到亚像素值，并且对数据的加性和乘性变化具有不变性。对于一维边缘模式，通过匹配矩来拟合理想边缘。结果表明，边缘位置与所谓的“克里斯托费尔数”有关。还研究了加性噪声对边缘位置的影响。该方法扩展到包括二维边缘模式，其中导出了一条线方程来定位边缘。这反过来又与标准的休克尔边缘算子进行了比较。还提供了新边缘算子作为边缘检测器的应用，并在存在和不存在噪声的情况下与索贝尔和休克尔边缘检测器进行了比较。
