Statistical behavior of edge detectors

In this paper we present a method for estimating the statistical properties of two well-known edge detectors: the non maxima suppression and the zero crossing of the Laplacian algorithms. Assuming the data are corrupted by an additive Gaussian noise we derive the probability density function (pdf) of the detected edge. Thanks to this approach the computed pdf explicitly depends on the parameters of the edge detector. Experimental results on real images and comparisons with Monte Carlo simulations are presented in order to characterize the performance of this method.