Implementing Gaussian Blur - How to calculate convolution matrix (kernel)

Question

My question is very close to this question: How do I gaussian blur an image without using any in-built gaussian functions?

The answer to this question is very good,

Answer 1

It's as simple as it sounds:

double sigma = 1;
int W = 5;
double kernel[W][W];
double mean = W/2;
double sum = 0.0; // For accumulating the kernel values
for (int x = 0; x < W; ++x) 
    for (int y = 0; y < W; ++y) {
        kernel[x][y] = exp( -0.5 * (pow((x-mean)/sigma, 2.0) + pow((y-mean)/sigma,2.0)) )
                         / (2 * M_PI * sigma * sigma);

        // Accumulate the kernel values
        sum += kernel[x][y];
    }

// Normalize the kernel
for (int x = 0; x < W; ++x) 
    for (int y = 0; y < W; ++y)
        kernel[x][y] /= sum;