hw2_02.m

function [x_filtered_std_dev] = hw2_02

    % generate 10 images of size 256x256 of pixel value 128
    x = ones(10,256,256)*128;

    % apply gaussian noise
    x = imnoise(x, 'gaussian', 0, 2.0);
    
    % solution for homework problem 2
    x_filtered = apply_box_filter(x, 3);
    x_filtered_std_dev = generate_std_dev(x_filtered);

end

%% function for finding the mean of all images
%  used in generate_std_dev function
function [outputMatrix] = matrix_mean(inputMatrix)
    number_of_images = length(inputMatrix);
    
    % memory allocation
    temp_matrix = zeros(size(inputMatrix(1)));
    
    % summation of all image values
    for i = 1:number_of_images
        temp_matrix = temp_matrix + inputMatrix(i);
    end
    
    % returns matrix where each pixel value is the mean of all the other
    % pixels at that index for all images
    outputMatrix = (1/number_of_images) * temp_matrix;
end

%% function for finding the stddev of all images
function [output_val] = generate_std_dev(input_matrix)

    number_of_images = length(input_matrix);
    
    % memory allocation
    temp_matrix = zeros(size(input_matrix(1)));
    
    % calls function to get avg matrix
    matrix_average = matrix_mean(input_matrix);
    
    % summation of all squared values
    for i = 1:number_of_images
        temp_matrix = temp_matrix + (matrix_average - input_matrix(i)).^2;
    end
    
    % divide temp
    temp_matrix = temp_matrix * (1/(number_of_images-1));
    
    % return sqrt value
    output_val = sqrt(temp_matrix);

end

%% function for applying the filter for #2
function [filtered_matrix] = apply_box_filter (input_matrix, filter_size)

    % generate the filter (variable size so i can do different filters)
    box_filter = ones(filter_size, filter_size) * 1/(filter_size.^2);
    
    temp_matrix = zeros(size(input_matrix(1)));
    
    % convolve the filter over the matrix
    for i = 1:length(input_matrix)
        temp_matrix(i) = conv2(input_matrix(i), box_filter, 'same');
    end
    
    % return the filtered matrix
    filtered_matrix = temp_matrix;
    
end