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Lesson 3 of the Edge Detection unit. The second derivative crosses zero at an edge instead of peaking, which locates a step edge at exactly x = 3.5 from integer pixels. It also has no smoothing in it: nine pixels disturbed by 0.03 produce four sign changes where there should be one. Measured on a photo, noise multiplies the zero-crossing pixels by 2.76x at sigma = 1.0 and 1.02x at sigma = 3.0, and only 33% of the resulting contours are closed.
