Optimal edge detectors for ramp edges

It is argued that the best way to model an edge is by assuming all ideal mathematical function passed through a low-pass filter and and immersed in noise. Using techniques similar to those developed by J. Canny (1983, 1986) and L.A. Spacek (1986), optimal filters are derived for ramp edges of various slopes. The optimal nonrecursive filter for ideal step edges is then derived as a limiting case of the filters for ramp edges. Because there are no step edges in images, edge detection is improved when the ramp filter is used instead of the filters developed for step edges. For practical purposes, some convolution masks are given which can be used directly for edge detection without the need to go into the details of the subject