An Empirical Performance Evaluation Technique for Discrete Second Derivative Edge Detectors

The problem of edge evaluation in relation to image gradient-based edge detectors has been widely studied, and there exist a range of edge evaluation techniques that are appropriate to such edge detectors. Although discrete second derivative operators often form the basis of edge detection methods, whereby zero-crossings are used to locate edge pixels, rather less attention has been paid to the development of edge evaluation techniques that are directly appropriate to zero-crossing methods. We propose a new evaluation technique that performs edge sensitivity analysis with respect to angular orientation and displacement errors for edges located by such discrete second derivative operators. The technique applies a finite element interpolation to the output values of the second derivative operator. Hence the method is used to directly evaluate edges located by a second derivative operator without the need to use a supplementary first derivative operator for gradient approximation.