Recall
that convolution is commutative.
Suppose I use the templates gx = exp(-i2/2 s2) and By = gy = exp(-j2/2
s2) Then
gx *
(gy * I) = (gx * gy) * I
but, it is not hard to show that the first convolution is
simply the 2-D Gaussian that we defined previously!
In
general, this means that we can separate the 2-D Gaussian convolution into 2
1-D convolutions with great computational cost savings.
A good
exercise is to show that the box filter is also separable.