ACCURACY OF THE ZERO CROSSINGS OF THE 2ND DIRECTIONAL DERIVATIVE AS AN EDGE DETECTOR

In this paper the accuracy of the second directional derivative edge detector is analyzed, based on a number of idealized edge models. The results are compared with those for the Laplacian edge detector. Errors are shown to be small under a number of conditions. These conditions are less severe for the second directional derivative than for the Laplacian edge detector. Spurious or phantom edges can be removed by checking the sign of the third directional derivative, though this is not enough to remove all large errors. Indeed, it is also shown that large errors will be obtained if no threshold is set on the magnitude of a third order derivative.