The authors deduce the first and second directional derivative operators for 2-D and 3-D images for a symmetric exponential filter and realize them by a first-order recursive algorithm. The edges are detected according to the gradient maxima or the zero crossing of the second derivative along the gradient direction. Experimental results show that the new methods are less sensitive to noise and have a much better precision of edge localization. Theoretical and experimental studies comparing the performances of the filters were performed, showing that the exponential filter is superior to other current filters. >