Page 168 of Digital Image Processing, Global Edition says:
we know that the values of a Gaussian function at a distance larger than 3π from the mean are small enough that they can be ignored.
If we get the mean
of Gaussian to be 0
and π = 1
, then It seems above says elements in kernel which their values are equal to $\frac{1}{\sqrt{2\pi}} e^{-\frac{9}{2}}$ or less than it, can be ignored. I calculated its value:
(1/sqrt(2*pi))*e^(-9/2)
ans = 4.4318e-03
Although it is a small number; but if we multiply it by 255
the result will be 1.1301
that will round to 1
and not to the 0
. So the first question is: why we ignore elements which may affect on result, at least for white pixels?
Then the book continues and says:
This means that if we select the size of a Gaussian kernel to be
β‘6πβ€ Γ β‘6πβ€
(...), we are assured of getting essentially the same result as if we had used an arbitrarily large Gaussian kernel.
Now another question rises: If 3π
is enough for ignoring, why surely select β‘6πβ€ Γ β‘6πβ€
for size of kernel, and not β‘3πβ€ Γ β‘3πβ€
or β‘4πβ€ Γ β‘4πβ€
?