The Asymptotic Optimal Frequency Domain Filter for Edge Detection

In an earlier paper by Shanmugam, Dickey, and Green, an edge detection filter was derived which maximized the energy within a specified interval about an edge feature. The initial expression of this filter involved a prolate spheroidal wave function. However, a careful analysis of the application of an asymptotic approximation to this function uncovered a major dimensional error. The corrected derivation of the asymptotic optimal filter forms the subject of this paper. To verify the results, the filter found is compared to a similar filter developed independently by Marr and Hildreth.