Question

I’m trying to implement a very basic eigenface calculation in Matlab. It kind of works but I get only two meaningful eigenvalues – the rest are zero. The corresponding eigenvectors seem to be right since most of them will show an eigenface when converting to an image.

So why are most of my eigenvalues zero? I need them to be different from zero in order to sort the eigenfaces by their significance (greatest magnitude eigenvalues).

I am reading 400 images, each size h/w = 112/92 px
They can be found here: http://www.cl.cam.ac.uk/Research/DTG/attarchive/pub/data/att_faces.zip

The code:

clear all;

files = dir('eigenfaces2/training/*.pgm');
[numFaces, discard] = size(files);

h = 112;
w = 92;
s = h * w;

%calculate average face
avgFace = zeros(s, 1);
faces = [];
for i=1:numFaces
  file = strcat('eigenfaces2/training/', files(i).name);
  im = double(imread(file));
  im = reshape(im, s, 1);
  avgFace = avgFace + im;
  faces(:,i) = im;
end
avgFace = avgFace ./ numFaces;

A = [];
for i=1:numFaces
  diff = avgFace - faces(i);
  A(:,i) = diff;
end

numEigs = 20;

L = (A' * A) / numFaces; 
[tmpEigs, discard] = eigs(L, numEigs);
eigenfaces = [];
for i=1:numEigs
  v = tmpEigs(:,i);
  eigenfaces(:,i) = A * v;
end

%visualize largest eigenfaces
figure;
for i=1:numEigs
  eigface = eigenfaces(:,i);
  mmax = max(eigface);
  mmin = min(eigface);
  eigface = 255 .* (eigface-mmin) ./ (mmax-mmin);
  eigface = reshape(eigface, h, w);
  subplot(4,5,i); imshow(uint8(eigface));
end

Answer 1

I’ve don’t have much experience with computer vision/image recognition, but I think you might want

diff = avgFace - faces(:,i);

in your second for loop. Otherwise it’s just subtracting a constant from avgFace each time, and so A (and hence L) only gets a rank of 2.