% equalize takes an image, displays it's histogram, generates a transform,
% transforms (and outputs) the equalized image, and displays it's
% histogram, and it's mean and Standard Deviation
%
% Syntax:
% equalize(image)
%
% Input: an mxn grayscale image as a uint8 matrix
%
% Output:
% an image of size mxn and type uint8
%
% History:
% Nikolai Norona created and finished 10/22
function equalize = equalize(image)
    M = size(image,1);
    N = size(image,2);
    %plots hist of input image
    hist = compute_histogram(image);
    plot_histogram(hist);
    figure();
    T = histogram_transform(hist);
    %round T because it needs to represent real pixel values, not doubles
    T = round(T);
    equalize = zeros([M N],'uint8');
    %iterate through old image, using T to assign values to new image
    for i = 1:M
        for j = 1:N
            equalize(i,j) = T(image(i,j)+1);
        end
    end
    %display histogram of new image
    hist2 = compute_histogram(equalize);
    plot_histogram(hist2);
    %mean and standard deviation of equalized image
    %code section written in collaboration with Jonathan Garache
    equalizedImage = double(equalize(:));
    inputImage = double(image(:));
    A = ['mean: ', num2str(mean(inputImage)), ' standard deviation: ', num2str(std(inputImage))];
    B = ['mean: ', num2str(mean(equalizedImage)), ' standard deviation: ', num2str(std(equalizedImage))];
    disp('orignal image:');
    disp(A);
    disp('new image:');
    disp(B);
end