Quantitative evaluation of edge detectors using the minimum kernel variance criterion

In this paper, we introduce a new criterion for analytically evaluating different edge detectors (both gradient and zero-crossing based methods) without the need of ground-truth information. The criterion is based on the observation that most 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 affects the performance of an edge detector. We show how to compute the variance of a convolution. We then describe results from comparing four well-known edge detectors using the proposed criterion.