Using the SVD rather than covariance matrix to calculate eigenfaces

Question

I'm using the set of n = 40 faces from AT&T (http://www.cl.cam.ac.uk/research/dtg/attarchive/facedatabase.html) to try and generate eigenfaces via the SVD.

First I calculate the average vector:

Then I subtract it from every vector in the training set, reshape the new vector into a 1 by (p*q) column vector of a n by (p*q) matrix x, and calculate a matrix X such that X = (1/sqrt(n))*x. (here's where the issue is: all my results in X are rounded to 0, resulting in a black image result for eigenface as seen below)

Then I calculate the SVD of this matrix X and try to get the first eigenface of the first column of the unitary matrix by reshaping it back into a p by q matrix

However, this is my result:

Can anyone spot my error in the code below? Any answer is much appreciated

n = 40;
%read images
A = double(imread('faces_training/1.pgm'));
f(:, :, 1) = A;
for j = 2:n
    f(:, :, j) = double(imread(['faces_training/',num2str(j),'.pgm']));
    A = A + f(:, :, j);
end
%calculate average
a = (1/n)*A;
%imshow(uint8(a))
for i = 1:n
%subtract from images
    x_vector(:, i) = reshape(f(:, :, i) - a, [], 1);
end
X = (1/sqrt(n))*x_vector;
%svd
[U S V] = svd(X);
B = reshape(U(:, 1), [size(a, 1) size(a, 2)]);
imshow(uint8(B))

Answer 1

Doing the same thing and had the same problem. The short answer is you have to normalize your eigenvector to get a good image. Before normalizing, you’ll notice your vector values are very close to 0 (probably because of how svd was done) which probably means they’re close to black.

Anyway, use this equation on the eigenvectors you wanna transform: newpixel[i,j]=(oldpixel[i,j]-min(oldpixel[:,j]))/(max(oldpixel[:,j])--min(oldpixel[:,j]))