Suppose you store the images as column vectors of length NxN (the 
number of pixels in each image) and that you have M images, you'll end 
up with a matrix G (N^2 x M) : 

1 
CovMat = -------- G G^T 
M - 1 

this is what you are trying to find the eigenvalues/eigenvectors for, 
right? 

There is a trick widely used when doing PCA on sets of images, it is 
based on the fact that the (M x M) matrix: 


1 
lmCovMat = -------- G^T G 
M - 1 


has the same non-zero eigenvalues of CovMat. So what you do is to 
compute the eigenvalues and eigenvectors of this low memory covariance 
matrix and then, for the eigenvectors, compute: 

E = G lmE 

where E is a matrix containing the wanted eigenvectors and lmE is the 
matrix of the eigenvectors compouted from the lmCovMat. 

This is implemented already in the OpenCV libraries. 

Hope it helps.

 

clear
[x]=load_imgs('training');
x=x(1:100,:);
a1=x*x';
b=x'*x;
[va,p]=eig(a1/27);
[vb,q]=eig(b/27);
%b/27*vb(:,1)==q(1)*vb(:,1);