A novel mathematical index about edge detection is constructed to indicate both conspicuous edges and inconspicuous edges in a gray-level image. The index called Sum of Gradient Direction (SGD) is derived from the basic idea that the gradient directions of the points surrounding the real edge point have good consistency while the gradient directions of those surrounding the noise point have poor consistency. According to the SGD index a new adaptive thresholding method to detect edges is proposed. A great quantity of experiments show that: the SGD index has the ability to distinguish both conspicuous edge points and inconspicuous edge points from the noisy points; the proposed novel edge detector utilizing the SGD to regulate the gradient threshold has the ability of detecting weak edges and suppressing noisy points at the same time.