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Gaussian Filter without using the MATLAB built_in function

Gaussian Filter



Gaussian Filter is used to blur the image. It is used to reduce the noise and the image details.










          The Gaussian kernel's center part  ( Here 0.4421 )  has the highest value and  intensity of other pixels                 decrease as the distance from the center part increases.


               On convolution of the local region and the Gaussian kernel gives the highest intensity value to the center part of the local region(38.4624) and the remaining pixels have less intensity as the distance from the center increases.
               Sum up the result and store it in the current pixel location(Intensity = 94.9269) of the image.




MATLAB CODE:
%Gaussian filter using MATLAB built_in function
%Read an Image
Img = imread('coins.png');
A = imnoise(Img,'Gaussian',0.04,0.003);
%Image with noise
figure,imshow(A);

H = fspecial('Gaussian',[9 9],1.76);
GaussF = imfilter(A,H);
figure,imshow(GaussF);


MATLAB CODE for Gaussian blur WITHOUT built_in function:
%Read an Image
Img = imread('coins.png');
A = imnoise(Img,'Gaussian',0.04,0.003);
%Image with noise
figure,imshow(A);
 
Image with Noise
I = double(A);

%Design the Gaussian Kernel
%Standard Deviation
sigma = 1.76;
%Window size
sz = 4;
[x,y]=meshgrid(-sz:sz,-sz:sz);

M = size(x,1)-1;
N = size(y,1)-1;
Exp_comp = -(x.^2+y.^2)/(2*sigma*sigma);
Kernel= exp(Exp_comp)/(2*pi*sigma*sigma);
 
Gaussian Kernel 9x9 size with Standard Deviation =1.76
%Initialize
Output=zeros(size(I));
%Pad the vector with zeros
I = padarray(I,[sz sz]);

%Convolution
for i = 1:size(I,1)-M
    for j =1:size(I,2)-N
        Temp = I(i:i+M,j:j+M).*Kernel;
        Output(i,j)=sum(Temp(:));
    end
end
%Image without Noise after Gaussian blur
Output = uint8(Output);
figure,imshow(Output);
After Filtering

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3 comments:

Ηλιάνα Ποτσίκα said... Reply to comment

Geat job!! Thanks.!

OSAMA PAK said... Reply to comment

How did you find Gaussian kernel kindly explain briefly

Unknown said... Reply to comment

hi can you please send me mathematical equation for 3D images

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