Correlation between sigma and radius on a Gaussian blur

Question

I saw the following relationship between sigma and radius in Gaussian blur (from http://en.wikipedia.org/wiki/Talk%3AGaussian_blur#Radius_again , as well as from the implementation of some programs, for example http://imagej.nih.gov/ij /source/ij/plugin/filter/GaussianBlur.java line 526)

$r = \ sigma \ sqrt {2 log 255} - 1$

Where does this relation come from? (I think 255 has to do with accuracy (255 = 2 ^ 8-1 => 8 bit images)

+3

José D. Feb 24 '14 at 10:02

1 answer

Mercury · Accepted Answer · 2014-02-24T10:30:49+0000

When using a Gaussian kernel with sigma as its parameter, you actually use: enter image description here

, , 1 ( ), . - , , r, : enter image description here

+1 , , . , : enter image description here

, .