by the operators of smaller size. Note that the larger operators leave a larger border (since new
values cannot be computed in that region) and this can be seen in the increase in border size for
the larger operators, in Figure 3.15(b) and (c).
3.4.4 Gaussian averaging operator
The Gaussian averaging operator has been considered to be optimal for image smoothing. The
template for the Gaussian operator has values set by the Gaussian relationship. The Gaussian
function g at coordinates x y is controlled by the variance
2
according to:
gx y  =
1
2
2
e
x
2
+y
2
2
2
(3.24)
Equation 3.24 gives a way to calculate coefficients for a Gaussian template which is then
convolved with an image. The effects of selection of Gaussian templates of differing size are
shown in Figure 3.16. The Gaussian function essentially removes the influence of points greater
than 3