ON OPTIMAL INFINITE IMPULSE-RESPONSE EDGE-DETECTION FILTERS

In this paper, we outline the design of an optimal, computationally efficient, infinite impulse response edge detection filter. We compute the optimal filter based on Canny's high signal to noise ratio, good localization criteria, and a criterion on the spurious response of the filter to noise. In our design procedure, we incorporate an expression for the width of the filter, which is appropriate for infinite length filters, directly in the expression for spurious responses. The three criteria are maximized using the variational method and nonlinear constrained optimization. The optimal filter parameters are tabulated for various values of the filter performance criteria. A complete methodology for implementing the optimal filters using approximating recursive digital filtering is presented. The approximating recursive digitial filter is separable into two linear filters operating in two orthogonal directions. The implementation is very simple and computationally efficient. It has a constant time of execution for different sizes of the operator and is readily amenable to real time hardware implementation.