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

摘要

This paper concerns the influence of edge direction on the estimation of edge contrast and orientation. We present an analytical study of general first-order detectors. We show that the gradient estimated using radial filters is not affected by edge orientation. For non-radial filters, the gradient may be affected by edge orientation. For instance, we find that the estimated edge orientation using a non-radial filter may be biased, even if the image is noise-free. However, there are non-radial filters for which gradient is unaffected by edge orientation, as in the case of radial filters. 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 effects 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 effect of the rotation invariance property of an edge detector on its response, thus providing a more precise meaning for this property in edge detection.