Gaussian Filter Normailisation

Hi All,

Can anyone point me to some information on how to properly normalise
Gaussian and Gaussian derivative filters...?

The Smoothing filter case is simple (i think), as I just sum my
original filter weights to get the correct factor, then divide out
each of my filter weights. The resulting kernel is stable when
convolved with an image.

But what about the higher derivatives? As I can't just sum them.

I have seen this for the 1st derivative:

<code>
int i = 0;
double A = 0;
for (x = -halflength; x <= halflength; x++, i++)
{
    G[i] = // gaussian function
    A += (double)x * G[i];
}

A = 1.0 / A;

for (i = 0; i < length; i++)
{
    G[i] *= A;
}
</code>

But why normalise like this????
Thanks...