On the localization performance measure and optimal edge detection

Summary form only given, as follows. Two measures have been suggested in the literature to characterize the localization performance of an edge detector. The first one was proposed by Abdou and Pratt (1979) and the second one by Canny (1986). The limitations of these localization measures are shown. The former is heuristic, while Canny´s measure has not been formulated correctly. The problem of localization of an edge detector has been formulated with the help of the theory of zero-crossings of stochastic processes. The measure of localization of the edge detector proposed is the extent to which it causes the density of maxima to be reduced as we get farther away from the true edge. It is possible to show that with this localization measure and a constraint of the width of the filter, the optimal linear filter for edge detection is the derivative of a Gaussian