An ideal image edge detection scheme

This paper introduces a scale-invariant and contrast-invariant multi-scale differential edge detector. The method is a direct consequence of two key discoveries: (1) a precise scale normalization method and (2) a formula to verify scale-invariant detectors. The new scale normalization method provides differential operators with respect to scale, among them the scale-invariant edge detectors. To investigate these differential detectors quantitatively, mathematical functions were used to represent the edges and to solve for the parameters, including position, width, contrast, offset, and orientation, in closed form. Noise is filtered as a low-contrast feature. The method has been tested with various kinds of synthesized edge functions and can extract edge features accurately. It is suitable for real-world images of several kinds of degradation.