# Gaussian filter study matlab codes

This program show the effect of Gaussian filter. The output are four subfigures shown in the same figure:

• Subfigure 1: The initial noise free "lena"
• Subfigure 2: The noisy "lena"
• Subfigure 3: Filtered the initial "lena"
• Subfigure 4: Filtered the noisy "lena"

```The matlab codes:
%%%%%%%%%%%%% The main.m file  %%%%%%%%%%%%%%%
clear;
% Parameters of the Gaussian filter:
n1=10;sigma1=3;n2=10;sigma2=3;theta1=0;
% The amplitude of the noise:
noise=0.1;

x=ind2gray(w,map);
filter1=d2gauss(n1,sigma1,n2,sigma2,theta);
x_rand=noise*randn(size(x));
y=x+x_rand;
f1=conv2(x,filter1,'same');
rf1=conv2(y,filter1,'same');
figure(1);
subplot(2,2,1);imagesc(x);
subplot(2,2,2);imagesc(y);
subplot(2,2,3);imagesc(f1);
subplot(2,2,4);imagesc(rf1);
colormap(gray);
%%%%%%%%%%%%%% End of the main.m file %%%%%%%%%%%%%%%

%%%%%%% The functions used in the main.m file %%%%%%%
% Function "d2gauss.m":
% This function returns a 2D Gaussian filter with size n1*n2; theta is
% the angle that the filter rotated counter clockwise; and sigma1 and sigma2
% are the standard deviation of the gaussian functions.
function h = d2gauss(n1,std1,n2,std2,theta)
r=[cos(theta) -sin(theta);
sin(theta)  cos(theta)];
for i = 1 : n2
for j = 1 : n1
u = r * [j-(n1+1)/2 i-(n2+1)/2]';
h(i,j) = gauss(u(1),std1)*gauss(u(2),std2);
end
end
h = h / sqrt(sum(sum(h.*h)));

% Function "gauss.m":
function y = gauss(x,std)
y = exp(-x^2/(2*std^2)) / (std*sqrt(2*pi));
%%%%%%%%%%%%%% end of the functions %%%%%%%%%%%%%%%%
```

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