Efficient facet edge detection and quantitative performance evaluation

In this paper, we "rst introduce a recursive procedure for e$ciently computing cubic facet parameters for edge detection. The procedure allows to compute facet parameters in a "xed number of operations independent of kernel size. We then introduce an image independent quantitative criterion for analytically evaluating di!erent edge detectors (both gradient and zero-crossing based methods) without the need of ground-truth information. Our criterion is based on our observation that all edge detectors make a decision of whether a pixel is an edgel or not based on the result of convolution of the image with a kernel. The variance of the convolution output therefore directly a!ects the performance of an edge detector. We propose to analytically compute the variance of the convolution output and use it as a measure to characterize the performance of four well-known edge detectors. 2001 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.