Determining optimal scales for edge detection using regularization

A regularization method for determining the scales of an edge detector adaptively for each part of the image is proposed. The optimal-filter concept of T. Poggio et al. (1984) and the scale space concept of A. Witkin (1983) are extended to an adaptive scale parameter. An energy function defined over continuous scale space is first introduced. Natural constraints for edge detection are incorporated into the energy function. To obtain a set of optimal scales which can minimize the energy function, a parallel relaxation algorithm is introduced. Experiments for synthetic and natural scenes show the advantages of the new algorithm over the edge detectors by B. Marr and E. Hildreth (1980) or J.F. Canny (1986)