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

12 comments:

  1. How did you find Gaussian kernel kindly explain briefly

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

    ReplyDelete
  3. nice code i want to get the kernel how can i do that?all the reference are not downloading it

    ReplyDelete
  4. nice code i want to get the kernel i don't have it and all the reference not useful can you give me an excellent one?

    ReplyDelete
  5. How is the center pixel = 0 for the exp(-(x^2+y^2)/(2*sigma^2))? When x and y are both zero, the exponent = 0 and exp(0) = 1.

    ReplyDelete
  6. @rock_hound

    The explanation is for -x^2+y^2)/(2*sigma*sigma).
    Thank you

    ReplyDelete
  7. Very Interesting code !! please i want to get the kernel i don't have it and all the reference not useful can you give me an excellent one?

    ReplyDelete
  8. we need a correct one line matlab command using gaussian filter to remove noise

    ReplyDelete
  9. hi, can you explain me the different between denoising image with gaussian filter in spatial domain and frequency domain? how to differentiate it with your code?

    ReplyDelete