Eigenface

Eigenfaces (English also called eigenfaces ) is a method for face detection based on the principal component analysis. Was developed the method of Matthew Turk and Alex Pentland.

History of the procedure

The eigenfaces are based on a method of Sirovich and Kirby, faces can be efficiently compressed and restored with the. This is done with the help of some main components of the principal component analysis.

Description of the procedure

Training images of faces are read in lexicographic order and stored in vectors.

An average face is formed from the training set:

From each a difference face is formed:

With the help of the difference images a covariance matrix is created:

Being. The eigenvectors of the matrix are the main components that have been designated as eigenfaces because of their face-like appearance of Turk and Pentland. However, the calculation of the eigenvectors is impossible in this form for desktop computers because of the very large memory requirements. There is another more efficient way, since there is only important eigenvectors. To this end, the new matrix is calculated:

The eigenvectors may be calculated without any problems, as much smaller dimensions. In addition, the following must be done:

Or otherwise

The vectors thus obtained are the eigenvectors of, with only the ' s interest to us with the highest eigenvalues. The ' s have to be orthonormal, that is, they still need to be normalized.

Application

Using the determined natural faces images can be projected into the face space (the image is decomposed into its eigenface components).

The vector thus obtained may be used by a pattern recognition algorithm for face recognition.