Canny edge algorithm has 5 stages, from here1. Apply Gaussian filter to smooth the image in order to remove the noise2. Find the intensity gradients of the image3. Apply non-maximum suppression to get rid of spurious response to edge detection4. Apply double threshold to determine potential edges5. Track edge by hysteresis: Finalize the detection of edges by suppressing all the other edges that are weak and not connected to strong edges.This algorithm was originally developed for antiasymmetric edges $(f(x) = - f(-x)$, where the true edge point is at $x = 0$) such as ridge, roof and step edges, discussing here about visualization of these edegs. (Source Academic Press, Handbook Imaging Processing Analysis) They say only that requirements for reliable performance are good detection and good localization. Good detection means that a true edge is highly likely to be a detected and that the likelihood of detecting an edge where there is none is low. Good localization means that the error in the location of a detected edge relative to that of the true edge should be small.In summaryCanny developed mathematical forms for the criteria for low error rate and  good localization and showed that there is a trade-off between the two  that dictates a unique shape for the impulse response of the optimal  detector.Canny algorithm and Central Limit TheoremIt assumes the same assumptions to all data sets. If Central Limit Theorem holds for the data sample, you include two such samples in one measurement. The average of the result will be normally distributed because Canny algorithm cannot affect it, since it applies to all data sets.Canny algorithm follows the maximum value. This may cause it go side tract, for instance here of the paper Optical quality assurance of GEM foils by T. Hilden et al:Possible defects in Canny algorithmThere are some situations which cause me systematic error. I think some disturbances/defects in the corners of images may cause some systematic deviation in Canny algorithm. This is what I do not understand and cannot specify better. How can use estimate the situations when Canny algorithm fails? 
Better Alternatives for Canny algorithm in Edge Detection?
algorithms;algorithm analysis;discrete mathematics