A validated edge model technique for the empirical performance evaluation of discrete zero-crossing methods

A new evaluation technique is presented to enable edge sensitivity analysis with respect to angular orientation and displacement errors for edges located by discrete zero-crossing operators. The technique is validated by using a Gaussian edge model and is shown to provide an effective mechanism for characterising the quality of second derivative feature detection operators in terms of quantitative measures of correctness of edge location and orientation. The technique applies a finite element interpolation to the output values of the discrete operator in order to extract sub-pixel level information about zero-crossings; in general, the displacement and orientation of a local line segment along which the line integral of the output interpolant is zero may then be readily found as the solution of a pair of simultaneous algebraic equations. A significant advantage over earlier edge sensitivity techniques is that the method does not require the use of a supplementary first derivative operator for gradient approximation. The method can therefore be used to make direct comparisons between zero-crossing operators in terms of basic performance standards without reference to particular test images; such standards are also important as they form the necessary basis for investigating the potential for the use of proxies for operator performance in relation to subsequent higher-level image processing tasks.