An Optimal Recursive Step Edge Detector

In this paper, a new class of step edge detection IIR filters derived from the Shen–Castan and Deriche edge detection filters is proposed. To avoid the discontinuity drawback of Shen–Castan edge detector, we multiply its impulse response by a proper function. This function exhibits a behavior closed to the sign(.) for large values of x, and similar to the line f(x) = k.x, for small values of x. Hence, the new edge detector preserves good behaviors of both Deriche and Shen–Castan operators, while a detection-localization product larger than 2 is achieved. Furthermore, it is shown that the proposed edge detector is optimal according to Canny’s criteria. In addition, a recursive implementation of the new operator is proposed that provides a fast edge detection algorithm. Experimental results confirm the high performance of the proposed edge detector.