Bias in the Localization of Curved Edges

This paper presents a theoretical and experimental analysis of the bias in the localization of edges detected from the zeros of the second derivative of the image in the direction of its gradient, such as the Canny edge detector. Its contributions over previous art are: a quantification of the localization bias as a function of the scale σ of the smoothing filter and the radius of curvature R of the edge, which unifies, without any approximation, previous results that independently studied the case of R σ or σ R; the determination of an optimal scale at which edge curvature can be accurately recovered for circular objects; and a technique to compensate for the localization bias which can be easily incorporated into existing algorithms for edge detection. The theoretical results are validated by experiments with synthetic data, and the bias correction algorithm introduced here is reduced to practice on real images.