Optimal, efficient, recursive edge detection filters

The design of an optimal, efficient, infinite-impulse-response (IIR) edge detection filter is described. J. Canny (1986) approached the problem by formulating three criteria designed in any edge detection filter: good detection, good localization, and low spurious response. He maximized the product of the first two criteria while keeping the spurious response criterion constant. Using the variational approach, he derived a set of finite extent step edge detection filters corresponding to various values of the spurious response criterion, approximating the filters by the first derivative of a Gaussian. A more direct approach is described in this paper. The three criteria are formulated as appropriate for a filter of infinite impulse response, and the calculus of variations is used to optimize the composite criteria. Although the filter derived is also well approximated by first derivative of a Gaussian, a superior recursively implemented approximation is achieved directly. The approximating filter is separable into two linear filters operating in two orthogonal directions allowing for parallel edge detection processing. The implementation is very simple and computationally efficient