Question

(Using Matlab) Write a function to "smooth" a black-and-white image by replacing each pixel by the average of itself and its neighbors. In MATLAB a black-and-white image is just a matrix of 1s and 0s - 1 represents white, and 0 represents black.

To keep the algorithm simple, ignore the edges of the image - that is, do not change the first and last rows and columns.

function name = smooth_image()

input argument = input matrix

output argument = output matrix

The algorithm can be described as follows:

• Given an NxM input matrix
• make a copy of the matrix - this will be the output matrix
• loop over rows 2 to N-1 of the input matrix
• loop over columns 2 to M-1 of the input matrix
• take the average of the 3x3 submatrix centered on the current row & column
• set the corresponding element of the output matrix equal to this average

Answer 1

function f=smooth(arrIn)

%copy the matrix
y=arrIn;

side1 = size(y)(1,1); %determine the row of the matrix
side2 = size(y)(1,2); %determine the column of the matrix

t = ones(3)/9;   % create a smoothing filter .. it is matrix of ones divided by 9 to give average value

for m = 2:side1-1 %traverse the matrix from row 2 to previous to the end row
    for n=2:side2-1 % traverse the matrix from column 2 to previous to the end of column
    mat = arrIn(m-1:m+1,n-1:n+1); % get the 3x3 matrix to be processed
    y(m,n)=round(conv2(mat,t)(3,3)); % convolution is done between the matrices and centre value which represents the mean value is taken and put back into y matrix
   end

end

f=y; % y matrix returned

end

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example matrix and its smoothed matrix

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N.B: convolution of two matrix is simply multiplying the given matrix by the other matrix while shifting the other matrix over the first matrix.

So for each location in the matrix, that location is aligned with the center of the other matrix and respective elements are multiplied together and summed.

Here in this case the other matrix is 3x3, so when 3x3 matrix convoluted with 3x3 matrix it will give 5x5 matrix. element (3,3) will be the one needed because it will be the one where each of the respective element will be multiplied with each other and summed up..