%
%
% for the illustration of SVD over 2D image for the course of "Multimedia
% Analysis and Indexing"
%
% Winston Hsu <winston@csie.ntu.edu.tw>
% -- last update, 04/03/2007
%
% demo.
% test if vectors in U, V are orthogonal
% the engery of those sigma (or singular values) 
%


IMG_SRC = 'nj_gray';

egNs = [1, 5, 10, 50, 200];

gim = imread([IMG_SRC, '.jpg']);

figure;  imagesc(gim); colormap(gray); title('original image');

[U,S,V] = svd(double(gim)); % X = U*S*V';

Sd = diag(S); %the 
for n=egNs
    if n > min(size(S)), continue; end;
    
    St = zeros(size(S)); 
    for i=1:n, St(i, i) = Sd(i); end;
    
    imgT = U*St*V'; 
    
    msg = sprintf('%d dim.', n);
    figure; imagesc(imgT); colormap(gray); title(msg); axis off;
end;