On achievable accuracy in edge localization

Edge localization occurs when an edge detection algorithm is able to accurately determine the location of an edge in an image. Edge localization is formulated as a parameter estimation problem, and the authors derive a Cramer-Rao bound on achievable accuracy as measured by mean squared error. The bound reveals the effect on localization of factors such as signal to noise ratio, observation window size, scale of smoothing filter, and a priori uncertainty about edge intensity. The authors analyze the Canny (1986) algorithm and show that the variance of its localization error is only a factor of two higher than the lower limit established by the Cramer-Rao bound. Although this is very good, it is shown that the maximum-likelihood estimator, which is derived in this work, virtually achieves the lower bound