how to obtain 2d Gaussian kernel in matlab

Question

How do I obtain 2D circularly symmetric Gaussian weighting function sampled out to 3 standard deviations (3 x 3) and re scaled to unit volume?

Solution

Try fspecial (Image Processing Toolbox) with the 'gaussian' option. For example,

z = fspecial('gaussian', [30 30], 4);

generates values on a 30×30 grid with sampling step 1 and standard deviation 4.

surf(z)

produces the graph

The function is normalized to unit volume. To check this, note that the sampling step is 1, so that the Riemann sum approximating the integral is just the sum of all function values:

>> sum(z(:))
ans =
    1.0000