%% Face recognition
% This algorithm uses the eigenface system (based on pricipal component
% analysis - PCA) to recognize faces. For more information on this method
% refer to http://cnx.org/content/m12531/latest/

%% Download the face database
% You can find the database at the follwoing link, 
% http://www.cl.cam.ac.uk/research/dtg/attarchive/facedatabase.html The
% database contains 400 pictures of 40 subjects. Download the zipped
% database and unzip it in the same directory as this file. 

%% Loading the database into matrix v
w=load_database();

%% Initializations
% We randomly pick an image from our database and use the rest of the
% images for training. Training is done on 399 pictues. We later
% use the randomly selectted picture to test the algorithm.

ri=round(400*rand(1,1));            % Randomly pick an index.
r=w(:,ri);                          % r contains the image we later on will use to test the algorithm
v=w(:,[1:ri-1 ri+1:end]);           % v contains the rest of the 399 images. 

N=20;                               % Number of signatures used for each image.
%% Subtracting the mean from v
O=uint8(ones(1,size(v,2))); 
m=uint8(mean(v,2));                 % m is the maen of all images.
vzm=v-uint8(single(m)*single(O));   % vzm is v with the mean removed. 

%% Calculating eignevectors of the correlation matrix
% We are picking N of the 400 eigenfaces.
L=single(vzm)'*single(vzm);
[V,D]=eig(L);
V=single(vzm)*V;
V=V(:,end:-1:end-(N-1));            % Pick the eignevectors corresponding to the 10 largest eigenvalues. 


%% Calculating the signature for each image
cv=zeros(size(v,2),N);
for i=1:size(v,2);
    cv(i,:)=single(vzm(:,i))'*V;    % Each row in cv is the signature for one image.
end


%% Recognition 
%  Now, we run the algorithm and see if we can correctly recognize the face. 
subplot(121); 
imshow(reshape(r,112,92));title('Looking for ...','FontWeight','bold','Fontsize',16,'color','red');

subplot(122);
p=r-m;                              % Subtract the mean
s=single(p)'*V;
z=[];
for i=1:size(v,2)
    z=[z,norm(cv(i,:)-s,2)];
    if(rem(i,20)==0),imshow(reshape(v(:,i),112,92)),end;
    drawnow;
end

[a,i]=min(z);
subplot(122);
imshow(reshape(v(:,i),112,92));title('Found!','FontWeight','bold','Fontsize',16,'color','red');