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Which one is robust to detect weak edges while going unresponsive to noise? Sobel or Canny edge detectors?
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I would recommend you to try out all and see which one works better in your case. I had to do it once and I applied edge enhancement algorithms before using edge detection. In the following paper http://staff.science.uva.nl/~rein/nldiffusionweb/ named nldiffusioncode.pdf you can read about three algorithms they developed. The code is free and the link is matlab.zip. I could not find the actual webpage.
I also used adapthisteq function from matlab to enhance contrast before before edge enhancement and detection
Perhaps you could try testing and comparing them for your application: