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.