The use of Hilbert Transform on DSNR analysis of step and ridge edge detection

In this paper, the analytical expressions of Discriminative Signal to Noise Ratio (DSNR) of step-edge and ridge-edge via Hilbert Transform (HT) have been derived. Firstly we revisit those expressions evaluated for step-edge by using Canny´s Edge Detector (CED) and Step Expansion Filter (SEF). Although SEF is optimal for step edges in terms of DSNR criterion, it is not optimal with respect to a variety of edge types. The matching filter has to be modified for different edge types. But a local energy measure obtained via HT can detect any kind of edges. The results obtained by HT are compared with the results of SEF and CED.