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