Could you describe the effects for varying different parameters of a canny edge detector?
Following http://www.kerrywong.com/2009/05/07/canny-edge-detection-auto-thresholding/ is one of the few resources that shows how to choose thresholds Tlow and Thigh 

According to this, for a picture which is sufficiently spread in historgram, one can choose T_low = 0.66 * mean value of image and T_high = 1.33 * mean value. 

However, when the image is not sufficiently spread, one should use median as opposed to mean value of the image.

If the gap between T_low and T_high is very small, the resultant edges will be smaller in continuity and hence there will be more fractions. As the gap increases, you will have more single line edges. 

As regards to sigma, as the sigma increases, the smoothing increases and noisy edges will go away, but at the same time, the location of edges may also move little. See this document, http://www.cse.unr.edu/~bebis/CS791E/Notes/EdgeDetection.pdf and results at page 29 shows this effect.