Question

Perform 3x3, 5x5 and 11x11 average filtering of the noisy the image in ImageSet3 ( image attached below). Do median filtering on the same data using 3x3,5x5 and 11x11 kernels. Compare your results.

You may use the matlab built-in functions/library to expedite your work

Answer 1

3*3 Average Filtering:

windowSize = 3; % Whatever odd number you want. Larger = more blur.
kernel = ones(windowSize) / windowSize ^ 2 ;
y = imread('ImageSet3.png');
blurredImage = conv2(single(y), kernel, 'same');
imshow(blurredImage, []); % or imshow(uint8(blurredImage), [0 255]);

3*3 Averaged image:

:

5*5 Average Filtering:

windowSize = 5; % Whatever odd number you want. Larger = more blur.
kernel = ones(windowSize) / windowSize ^ 2 ;
y = imread('ImageSet3.png');
blurredImage = conv2(single(y), kernel, 'same');
imshow(blurredImage, []); % or imshow(uint8(blurredImage), [0 255]);

5*5 averaged image:

11*11 Average Filtering:

windowSize = 11; % Whatever odd number you want. Larger = more blur.
kernel = ones(windowSize) / windowSize ^ 2 ;
y = imread('ImageSet3.png');
blurredImage = conv2(single(y), kernel, 'same');
imshow(blurredImage, []); % or imshow(uint8(blurredImage), [0 255]);

11*11 averaged image:

3*3 Median Filtering:

I = imread('ImageSet3.png'); % Reading an Image
display(size(I)); %Shows the Size of read Image

figure,imshow(I);title('Grayscale Image'); %Shows the read Image


%DEFINE THE WINDOW SIZE MXN
M=3;
N=3;

%PAD THE MATRIX WITH ZEROS ON ALL SIDES
modifyA=padarray(I,[floor(M/2),floor(N/2)]); %%padarray is a builtin matlab
%%function to pad zeros and floor function rounds the number to negative infinite, as M=3
%%N =3 , M/2 = N/2 = 1.5 which when floor applied to them gives 1 as
%%floor(1.5) is 1. So kernel matrix size is 1*1, so 0 is padded to the
%%image
figure,imshow(uint8(modifyA)); title('PADDED WITH ZEROS'); %This is the Zero Paddedimage

%%Median is the middle point of the series. The index that is obtained by dividing the total number of elements in a window by 2 gives the position.
B = zeros([size(I,1) size(I,2)]);
med_indx = round((M*N)/2); %MEDIAN INDEX

%%A sliding window of size M x N is used and the elements in the window are sorted and the middle element from the sorted array is chosen.
for i=1:size(modifyA,1)-(M-1)
for j=1:size(modifyA,2)-(N-1)


temp=modifyA(i:i+(M-1),j:j+(N-1),:);
tmp_sort = sort(temp(:));%tmp(:) converts 2D matrix to 1D matrix
B(i,j) = tmp_sort(med_indx);
  
  

end
end


%CONVERT THE IMAGE TO UINT8 FORMAT.
B=uint8(B);
figure,imshow(B);
title('IMAGE AFTER MEDIAN FILTERING');

3*3 Median Filtered Image:

5*5 Median Filtering:

IMAGE AFTER MEDIAN FILTERING

I = imread('ImageSet3.png');
display(size(I));

figure,imshow(I);title('Grayscale Image');


%DEFINE THE WINDOW SIZE MXN
M=5;
N=5;

%PAD THE MATRIX WITH ZEROS ON ALL SIDES
modifyA=padarray(I,[floor(M/2),floor(N/2)]);
%%padarray is a builtin matlab
%%function to pad zeros and floor function rounds the number to negative infinite, as M=3
%%N =5 , M/2 = N/2 = 2.5 which when floor applied to them gives 1 as
%%floor(2.5) is 2. So kernel matrix size is 2*2, so zero matrix of size 2*2 is padded to the
%%image
figure,imshow(uint8(modifyA)); title('PADDED WITH ZEROS');


%%Median is the middle point of the series. The index that is obtained by dividing the total number of elements in a window by 2 gives the position.
B = zeros([size(I,1) size(I,2)]);
med_indx = round((M*N)/2); %MEDIAN INDEX
%%A sliding window of size M x N is used and the elements in the window are sorted and the middle element from the sorted array is chosen.
for i=1:size(modifyA,1)-(M-1)
for j=1:size(modifyA,2)-(N-1)


temp=modifyA(i:i+(M-1),j:j+(N-1),:);
tmp_sort = sort(temp(:));%tmp(:) converts 2D matrix to 1D matrix
B(i,j) = tmp_sort(med_indx);
  
  

end
end


%CONVERT THE IMAGE TO UINT8 FORMAT.
B=uint8(B);
figure,imshow(B);
title('IMAGE AFTER MEDIAN FILTERING');

5*5 Median Filtered Image:

IMAGE AFTER MEDIAN FILTERING

11*11 Median Filtering:

I = imread('ImageSet3.png');
display(size(I));

figure,imshow(I);title('Grayscale Image');


%DEFINE THE WINDOW SIZE MXN
M=11;
N=11;

%PAD THE MATRIX WITH ZEROS ON ALL SIDES
modifyA=padarray(I,[floor(M/2),floor(N/2)]);
%%padarray is a builtin matlab
%%function to pad zeros and floor function rounds the number to negative infinite, as M=3
%%N =5 , M/2 = N/2 = 2.5 which when floor applied to them gives 1 as
%%floor(2.5) is 2. So kernel matrix size is 2*2, so zero matrix of size 2*2 is padded to the
%%image
figure,imshow(uint8(modifyA)); title('PADDED WITH ZEROS');


%%Median is the middle point of the series. The index that is obtained by dividing the total number of elements in a window by 2 gives the position.
B = zeros([size(I,1) size(I,2)]);
med_indx = round((M*N)/2); %MEDIAN INDEX
%%A sliding window of size M x N is used and the elements in the window are sorted and the middle element from the sorted array is chosen.
for i=1:size(modifyA,1)-(M-1)
for j=1:size(modifyA,2)-(N-1)


temp=modifyA(i:i+(M-1),j:j+(N-1),:);
tmp_sort = sort(temp(:));%tmp(:) converts 2D matrix to 1D matrix
B(i,j) = tmp_sort(med_indx);
  
  

end
end


%CONVERT THE IMAGE TO UINT8 FORMAT.
B=uint8(B);
figure,imshow(B);
title('IMAGE AFTER MEDIAN FILTERING');

11*11 Median Filtered Image:

IMAGE AFTER MEDIAN FILTERING