I want to write code in matlab to find a characteristic scale of an image patch.
I have an image patch X, I need to maximize function `F(X,sigma)` and that sigma is the characteristic sigma.

For my experiments, F can be the laplacian of the image, sigma is the "power" of a gaussian filter on the image. `F(x,sigma)` should return for each x (image/patch values) its response over scale sigma (i.e. a discrete value for each X and sigma).
My questions are:

 1. The laplacian is obtained by convolving laplacian kernel with the image, where
does the sigma takes place ? (is it by smoothing the image before (the laplace) with `G(sigma)`?)
 2. How can I define `F(X,sigma)` to return discrete value (X is nXm), ? i.e. what does this function do exactly.