How to make a Gaussian filter in Matlab

Question

I have tried to make a Gaussian filter in Matlab without using imfilter() and fspecial(). I have tried this but result is not like the one I have with imfilter and fspecial.

Here is my codes.

function Gaussian_filtered = Gauss(image_x, sigma)

% for single axis
% http://en.wikipedia.org/wiki/Gaussian_filter
Gaussian_filtered = exp(-image_x^2/(2*sigma^2)) / (sigma*sqrt(2*pi)); 
end

for 2D Gaussian,

function h =  Gaussian2D(hsize, sigma)

n1 = hsize;
n2 = hsize;

for i = 1 : n2 
        for j = 1 : n1
        % size is 10;
        % -5<center<5 area is covered.
        c = [j-(n1+1)/2 i-(n2+1)/2]';                
        % A product of both axes is 2D Gaussian filtering
        h(i,j) = Gauss(c(1), sigma)*Gauss(c(2), sigma);        
        end
    end
end

and the final one is

function Filtered = GaussianFilter(ImageData, hsize, sigma)

%Get the result of Gaussian
filter_ = Gaussian2D(hsize, sigma);

%check image
[r, c] = size(ImageData);
Filtered = zeros(r, c);    

for i=1:r
    for j=1:c
        for k=1:hsize
            for m=1:hsize
                    Filtered =  Filtered + ImageData(i,j).*filter_(k,m);    
            end
        end
    end
end
end

But the processed image is almost same as the input image. I wonder the last function GaussianFiltered() is problematic...

Thanks.

Answer 1

here's an alternative:

Create the 2D-Gaussian:

  function f=gaussian2d(N,sigma)
  % N is grid size, sigma speaks for itself
 [x y]=meshgrid(round(-N/2):round(N/2), round(-N/2):round(N/2));
 f=exp(-x.^2/(2*sigma^2)-y.^2/(2*sigma^2));
 f=f./sum(f(:));

Filtered image, given your image is called Im:

 filtered_signal=conv2(Im,gaussian2d(N,sig),'same');

Here's some plots:

imagesc(gaussian2d(7,2.5))

 Im=rand(100);subplot(1,2,1);imagesc(Im)
 subplot(1,2,2);imagesc(conv2(Im,gaussian2d(7,2.5),'same'));

Answer 2

This example code is slow because of the for-loops. In matlab you can better use conv2, as suggested by user:bla, or just use filter2.

I = imread('peppers.png'); %load example data
I = I(:,:,1);
N=5; %must be odd
sigma=1;
figure(1);imagesc(I);colormap gray
x=1:N;
X=exp(-(x-((N+1)/2)).^2/(2*sigma^2));
h=X'*X;
h=h./sum(h(:));
%I=filter2(h,I); %this is faster
[is,js]=size(I);
Ib = NaN(is+N-1,js+N-1); %add borders
b=(N-1)/2 +1;
Ib(b:b+is-1,b:b+js-1)=I;
I=zeros(size(I));
for i = 1:is
    for j = 1:js
        I(i,j)=sum(sum(Ib(i:i+N-1,j:j+N-1).*h,'omitnan'));
    end
end
figure(2);imagesc(I);colormap gray