How to make a 2D gaussian Blur terms?

Question

I want to make a 2D gaussian Blur coeffients. Now I am making 1D gaussian Blur term as following.

double Cmfc_test5Dlg::Guassian(int x, double sigma)
{
        double c = 2.0 * sigma * sigma;
        return exp(-x * x / c) / sqrt(c * 3.141592f);
}
double Cmfc_test5Dlg::GuassianTerms(int kernalSize, double sigma, int *terms)
{
        for (int i = 0; i < kernalSize; ++i) {
                terms[i] = Guassian(i - kernalSize / 2, sigma)*1024;
        }
        return 1;
}

But I want to make 2D instead of 1D. What should I do ?

Answer 1

It's real easy. Multi-dimensional Gaussian functions are separable, that is they can be calculated as the product of the Gaussian function along all axes. For the 2-d case it means:

terms[x, y] = terms[x]*terms[y]

Note that separability also means that you obtain the same result as by using the 2-d filter, by first 1-d filtering along one axis and then 1-d filtering the output along the other axis.