Optimum edge detection filter.

Edge detection and enhancement are required in a number of important image processing applications. In this paper we consider the problem of optimizing spatial frequency domain filters for detecting a class of edges in images. The filter is optimum in that it produces maximum energy in the vicinity of the location of the edge for a given spatial resolution I and the bandwidth ?. We show that the filter transfer function can be specified in terms of the prolate spheroidal wavefunctions for a given space-bandwidth product I?. Further we show that for values of I? less than 2, the optimal filter represents the Laplacian operator in image space followed by a low pass filter with a cutoff frequency ?.