curvature(S)

Fast and efficient computation of the Gaussian and Mean curvatures of a surface S = f(x,y).

[K,H] = CURVATURE(S) computes the gaussian and mean curvatures of the
surface S defined by S = f(x,y), where (x,y) is the
rectangular grid on which f is defined.

Example: Define gaussians on a rectangular grid, and find its
curvatures:
f = @(mu1,mu2,s1,s2,x,y) exp(-(x-mu1).^2/(s1.^2)-(y-mu2).^2/(s2.^2));
[X,Y] = meshgrid(linspace(-5,5,200));
S = f(-2,0,2,2,X,Y) - f(2,0,2,2,X,Y)
figure; mesh(S);
[K,H] = curvature(S);
figure;mesh(K); title('Gaussian Curvature','FontSize',20);
figure;mesh(H); title('Mean Curvature','FontSize',20);