Normalized edge detector

A normalized Gaussian operator that can be separated into normalized functions in the x and y directions is presented. The behavior of the gradient values of step and ramp edges and combinations of pairs of these idealized edges obtained using this operator are analyzed. It is shown that the slope of a ramp edge can be estimated using the gradient operator at a single small scale and that the contrast and width of a ramp can also be estimated using only gradient information. Thus, the gradient is shown to contain much more information than is typically used in gradient-based edge detectors. Simulations were performed on ideal edges and edge pairs to demonstrate the actual behavior of the operator for intermediate values. The operator was also applied to real images, and slope, contrast, and scale were obtained at gradient maxima points