Implementing a Gaussian blur kernel in MATLAB from scratch - matlab

Question

I recently implemented a box average filter in MATLAB. I found it to be a fun exercise. I wanted to do the same thing with a Gaussian blur filter, so as to eventually solve some super-resolution problems. But I have found this much more challenging. There are several questions on here about such a topic. All of the answers in those topics have been very helpful. However, I have not been able to create the kernel successfully. Currently my code simply implements an averaging filter. Wiki page for Gaussian blur: https://en.wikipedia.org/wiki/Gaussian_blur
Here is my code:
function out_im = GaussianBlur(in_im, sigma, N) %input image, sigma, Number of iterations
[rows, cols] = size(in_im);
orig_im = in_im;
Filter = zeros(rows,cols);
w2 = 0;
for k = 1 : N
for LR_ROWS = 2 : 1 : rows - 1
for LR_COLS = 2 : 1 : cols -1
for i = -1 : 1
for j = -1 : 1
w1 = exp(-(orig_im(LR_ROWS, LR_COLS).^2/(2*sigma^2)));
w2 = w2 + w1;
Filter(LR_ROWS, LR_COLS) = Filter(LR_ROWS, LR_COLS) + ...
w1*orig_im(LR_ROWS+i, LR_COLS+j);
end
end
Filter(LR_ROWS, LR_COLS) = Filter(LR_ROWS, LR_COLS)./w2;
w2 = 0;
end
end
orig_im = Filter;
Filter = zeros(rows, cols);
end
out_im = orig_im;
end
Any suggestions or advice is greatly appreciated! Thank you.