Question

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

Here, we have to implement an average filter. Input is an NxM matrix. The approach is to iterate the input matrix using for loop and for every cell in the matrix, iterate the submatrix surrounding it. Calculate the mean of all the values in the submatrix and update the corresponding cell of the output matrix. Following is the MATLAB program :

function output_matrix = smooth_image(input_matrix)

% MatLab function average filter; input is NxM matrix;

% submatrix size is 3x3

[N,M] = size(input_matrix); % find the number of rows and columns of input matrix

output_matrix = input_matrix; % creates copy of the input matrix

for i = 2:N-1 % for loop to iterate input matrix; leaves the values at edges

for j = 2:M-1

sum = 0; % initialize sum to zero

for i1 = i-1:i+1 % for loop to iterate submatrix

for j1 = j-1:j+1

sum = sum + input_matrix(i1,j1); % sum of values in submatrix

end

end

output_matrix(i,j) = floor(sum/9); % update the values of output matrix with average values

% floor function is used to

% keep only the integer part of the average value

% sum value is divided by 9 because size of submatrix is 3x3

end

end

end

Note: This function will work for both whether the values in the input matrix are integers or just 1s and 0s.

Output for integer matrix:

Output for input matrix with 1s and 0s: