A probabilistic framework for edge detection and scale selection

We devise a statistical framework for edge detection by performing a statistical analysis of zero crossings of the second derivative of an image. This analysis enables us to estimate at each pixel of an image the probability that an edge passes through the pixel. We present a statistical analysis of the the Lindeberg operators that we use to compute image derivatives. We also introduce a confidence probability that tells us how reliable the edge probability is, given the image's noise level and the operator's scale. Combining the edge and confidence probabilities leads to a probabilistic scale selection algorithm. We present the results of experiments on natural images.