Extension of Canny´s discrete criteria to second derivative filters, towards a unified approach

Second derivative filters are used to detect edges by the location of the zero crossing of the filters response. We define analytical expressions of the probabilities for the good detections in the good location and for the false detections. Then we compare these expressions to those obtained for the first derivative filters used to detect edges with the gradient approach. We prove that there is no difference between these two approaches and that the performances are linked to those of a smooth filters from which first and second derivative filters have been deduced. We discuss the impact of the thresholding strategy and show some results for different kind of classical filters