Differential operator based edge and line detection

Edge detection in sampled images may be viewed as a problem of numerical differentiation. In fact, most point edge operators function by estimating the local gradient or Laplacian. Adopting this view, Torre and Poggio [2] apply regularization techniques to the problem of computing derivatives, and arrive at a class of simple linear estimators involving derivatives of a low-pass Gaussian kernel. In this work, we further develop the approach by examining statistical properties of such estimators, and investigate the effectiveness of various combinations of the partial derivative estimates in detecting blurred steps and lines. We also touch briefly on the problem of sensitivity to various types of edge structures, and develop an isotropic operator with reduced sensitivity to isolated spikes.