Which sigma to use for edge detection
The $\sigma$ decides the scale of objects being simplified. This is explained here:


  The size of the Gaussian filter: the smoothing filter used in the first stage directly affects the results of the Canny algorithm. Smaller filters cause less blurring, and allow detection of small, sharp lines. A larger filter causes more blurring, smearing out the value of a given pixel over a larger area of the image. Larger blurring radii are more useful for detecting larger, smoother edges – for instance, the edge of a rainbow.


Thus the support size of the Gaussian function decides the level of details that are simplified. Simplest way is to test with binary squares/circles.