function f = DoG(x, sigma, scale)
% f = DoG(x, sigma, scale)
% Difference of Gaussians
% INPUT: vectors 'x' and parameters
% OUTPUT: vector 'f'
%  = G_{scale*sigma)-G_{sigma}
%    (G is gaussian)
% Note: the function is scale-invariant

G_scale = 1/sqrt(2*pi)/(scale*sigma)*exp(-x.^2./2./(scale^2*sigma^2));
G = 1/sqrt(2*pi)/sigma*exp(-x.^2./2./sigma^2);
f=G_scale-G;