%% Compress colored image with PCA algorithm
clear
close all
clc

A = double(imread('blue_bird.jpg'));

% Display original image
subplot(1, 2, 1);
imagesc(A/255)
title('Original image')

% Convert image to 2d
img_size = size(A);
X = reshape(A, img_size(1) * img_size(2), 3);

% Normalize data before performing PCA
[X_norm, mu, sigma] = featureNormalize(X);

% Run PCA
[U, S] = pca(X_norm);

% Reduce data to the first 2 eigenvectors
K = 2;
Z = projectData(X_norm, U, K);

% Convert back to 3d and display compressed image
Q = reshape((X_norm+mu).*sigma, img_size(1),img_size(2), 3);
subplot(1, 2, 2);
imagesc(Q/255);
title('Compressed image')

% Create the new compressed image
imwrite(Q,'blue_bird_compressed.jpg');

% Find out how much space we saved
original = dir('blue_bird.jpg');
compressed = dir('blue_bird_compressed.jpg');
oSize = original.bytes;
cSize = compressed.bytes;
saved = (1-(cSize/oSize))*100;

disp(['Before: ', num2str(oSize), ' bytes']);
disp(['After: ', num2str(cSize), ' bytes']);
disp([num2str(saved), '% space saved']);