I find on the OpenCV documentation for cvSmooth that sigma can be calculated from the kernel size as follows: sigma = 0.3(n/2 - 1) + 0.8
I would like to know the theoretical background of this equation.
Thank you.
I find on the OpenCV documentation for cvSmooth that sigma can be calculated from the kernel size as follows: sigma = 0.3(n/2 - 1) + 0.8
I would like to know the theoretical background of this equation.
Thank you.
Using such a value for sigma, the ratio between the value at the centre of the kernel and on the edge of the kernel, found for y=0
and x=n/2-1
, is:
g_edge / g_center = exp(-(x²+y²)/(2σ²))
= exp(-(n/2-1)²/(2*(0.3(n/2-1)+0.8)²))
The limit of this value as n
increases is:
exp(-1/(2*0.3²)) = 0.00386592
Note that 1/256
is 0.00390625
. Images are often encoded in 256-value ranges. The choice of 0.3
ensures that the kernel considers all pixels that may significantly influence the resulting value.
I am afraid I do not have an explanation for the 0.8
part, but I imagine it is here to ensure reasonable values when n
is small.
g_edge / g_center
, as it appears on both sides of the division.
Feb 19 '20 at 22:37