How to determine the window size of a Gaussian filter

Question

Gaussian smoothing is a common image processing function, and for an introduction of Gaussian filtering, please refer to here. As we can see, one parameter: standard derivation

Answer 1

Here is a good reference.

1. After discretizing, pixel with distance greater than 3 sigma have negligible weights. See this

2. As already pointed, 6sigma, implies 3sigma both ways

3. Size of convolution matrix to be used for filtering would inadvertently be 6sigma by 6sigma, because of points 1 and 2 above.

Here how you can obtain the discrete Gaussian.

Finally, the size of the standard deviation(and therefore the Kernel used) depends on how much noise you suspect to be in the image. Clearly, a larger convolution kernel implies farther pixels get to contribute to the new value of the centre pixel as opposed to a smaller kernel.