The Canny Edge Detector Revisited

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文件名称：The Canny Edge Detector Revisited
文件大小：307KB
文件格式：PDF
更新时间：2014-08-31 08:59:15
Canny Canny (1986) suggested that an optimal edge detector should maximize both signal-to-noise ratio and localization, and he derived mathematical expressions for these criteria. Based on these criteria, he claimed that the optimal step edge detector was similar to a derivative of a gaussian. However, Canny’s work suffers from two problems. First, his derivation of localization criterion is incorrect. Here we provide a more acurate localization criterion and derive the optimal detector from it. Second, and more seriously, the Canny criteria yield an infinitely wide optimal edge detector. The width of the optimal detector can however be limited by considering the effect of the neighbouring edges in the image. If we do so, we find that the optimal step edge detector, according to the Canny criteria, is the derivative of an ISEF filter, proposed by Shen and Castan (1992). In addition, if we also consider detecting blurred (or non-sharp) gaussian edges of different widths, we find that the optimal blurred-edge detector is the above optimal step edge detector convolved with a gaussian. This implies that edge detection must be performed at multiple scales to cover all the blur widths in the image. We derive a simple scale selection procedure for edge detection, and demonstrate it in one and two dimensions.