OPTIMAL EDGE DETECTORS FOR RAMP EDGES

We argue that the best way to model an edge is by assuming an ideal mathematical function passed through a low pass filter and emersed in noise. Using techniques similar to those developed by Canny and Spacek, we derive optimal filters for ramp edges of various slopes. We also derive the optimal nonrecursive filter for ideal step edges as a limiting case of the filters for ramp edges. Because there are no step edges in images, we show that edge detection is improved when the ramp filter is used instead of the filters developed for step edges. For practical purposes we give in Table IV some convolution masks which can be used directly for edge detection without the need to go into the details of the subject.