AN OPTIMAL LINEAR OPERATOR FOR STEP EDGE-DETECTION

Step edge detection is an important subject in image processing and computer vision and many methods, including some optimal filters, have been proposed. In this paper, we propose an optimal linear operator of an infinite window size for step edge detection. This operator is at first derived from the well-known mono-step edge model by use of a signal/noise ratio adapted to edge detection. Because of the infinite window size of the operator, we propose then a statistic multiedge model and analyze the optimal operator by spectral analysis. It is shown that the Infinite Symmetric Exponential Filter (ISEF) is optimal for both mono- and multiedge detection. Recursive realization of ISEF and the derivatives is presented and generalized to multidimensional cases also. The performance of ISEF is analyzed and compared with that of Gaussian and Canny filters, and it is shown that ISEF has a better performance in precision of edge localization, insensibility to noise, and computational complexity. Edge detection based on the optimal filter ISEF is thus presented and the essential difference between ISEF and some other optimal edge detectors is shown. The experimental results for computer-generated and real images, which confirm our theoretical analysis, are reported. © 1992.