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Computing the weighted average of the pixel values in a window is a basic module in many computer vision operators. The process is reformulated in a linear vector space and the role of the different subspaces is emphasized. Within this framework wellknown artifacts of the gradient-based edge detectors, such as large spurious responses can be explained quantitatively. It is also shown that template matching with a template derived from the input data is meaningful since it provides an independent measure of confidence in the presence of the employed edge model. The widely used three-step edge detection procedure - gradient estimation, non-maxima suppression, hysteresis thresholding - is generalized to include the information provided by the confidence measure. The additional amount of computation is minimal and experiments with several standard test images show the ability of the new procedure to detect weak edges.
Meer et al. (2001) studied this question.