a Matlab code snippet to compress a RGB image to a two-component image, two basis vectors and an offset.

image_comp_svd.m

orignalImage = im2double(imread('grass.tif'));

m = size(orignalImage, 1);
n = size(orignalImage, 2);
piexelNum = m * n;

X = reshape(orignalImage, [piexelNum, 3]);
avg = mean(X);
X2 = X - avg;

[U, S, V] = svd(X2, 'econ');
U2 = U(:, [1 2]);
S2 = S([1 2], [1 2]);
V2 = V(:, [1 2]);

% Reconstruct the image
% avg : offset color vector for the entire image
% S2 * V2' : an 2x3 matrix where each row corresponds to a basis vector
% U2 : two coefficients per pixel with respect to the two basis
reconstructedImage = U2 * (S2 * V2') + avg;

figure;
axis off;
subplot(1, 3, 1);
image(reshape(orignalImage, [m, n, 3]));
title('original');
subplot(1, 3, 2);
image(reshape(reconstructedImage, [m, n, 3]));
title('reconstructed');
subplot(1, 3, 3);
% scaled by a factor of 100 to see the differences
diff = rgb2gray(imabsdiff(X, reconstructedImage)) * 100; 
imagesc(reshape(diff, [m, n, 3]));
title('diff (×100)');