title: Relation between sigma and radius on the Gaussian blur
body: <p>I have seen the following relation between sigma and the radius in a gaussian blur (from <a href="http://en.wikipedia.org/wiki/Talk%3AGaussian_blur#Radius_again" rel="nofollow noreferrer">http://en.wikipedia.org/wiki/Talk%3AGaussian_blur#Radius_again</a> and also from the implementation of some programs, for example <a href="http://imagej.nih.gov/ij/source/ij/plugin/filter/GaussianBlur.java" rel="nofollow noreferrer">http://imagej.nih.gov/ij/source/ij/plugin/filter/GaussianBlur.java</a> line 526)</p>
  
  <p><img src="https://i.stack.imgur.com/bk7lV.png" alt="$$ r = \sigma \sqrt{2 log 255} - 1$$"></p>
  
  <p>Where does this relation come from? (I think the 255 has to do with the precision (255 = 2^8-1 => 8 bits images)</p>