The influence of edge direction on the estimation of edge contrast and orientation

This paper concerns the in#uence of edge direction on the estimation of edge contrast and orientation. We present an analytical study of general "rst-order detectors. We show that the gradient estimated using radial "lters is not a!ected by edge orientation. For non-radial "lters, the gradient may be a!ected by edge orientation. For instance, we "nd that the estimated edge orientation using a non-radial "lter may be biased, even if the image is noise-free. However, there are non-radial "lters for which gradient is una!ected by edge orientation, as in the case of radial "lters. The properties of these functions are given in this paper. The results are illustrated by studying the detectors of Canny, Deriche, and Shen & Castan. We take into account discretization e!ects such as subpixel and tesselation of the image plane. The quantitative results provide insights into the estimation of gradient by these commonly used detectors. Taken together, the theoretical and experimental results give a clear indication of the e!ect of the rotation invariance property of an edge detector on its response, thus providing a more precise meaning for this property in edge detection. ( 2001 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.