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Self-faces (English also Eigenfaces called) a procedure for the face recognition is based on the main component analysis. The procedure of Matthew Turk and Alex Pentland was developed.

History of the procedure

The self-faces are based on the procedure by Sirovich and Kirby and Kirby and Sirovich with that efficiently faces to be compressed and restored can with the help of some main components from the main component analysis.

Description of the procedure

Training pictures of the faces \ Gamma_1, \ Gamma_2, \ Gamma_3 \ cdots \ Gamma_M are read in in lexikografischer order and stored in vectors.

From the training set an average face becomes \ psi \! formed:

\ Psi = \ frac {1} {M} \ sum_ {n=1} ^M \ Gamma_N.

Of everyone \ gamma \! becomes a difference face \ Phi \! formed:

\ Phi_i = \ Gamma_i - \ psi \!.

With the help of the difference pictures \ Phi_i \! second order statistics C are provided:

C = \ frac {1} {M} \ sum_ {n=1} ^M \ Phi_n \ Phi_n^T = AA^T

whereby A = [\ Phi_1 \ Phi_2 \ cdots \ Phi_M] is. The self-vectors of the matrix C are the main components, which were designated because of their face-similar appearance, of Turk and Pentland as self-faces (Eigenfaces). The calculation of the self-vectors from C is however in this form for Desktop computer impossible, because of the very much-very storage requirement. In addition there is however another more efficient way, there it only M - 1 important self-vector-gives. In addition the new matrix L is computed:

L = A^TA \!

The self-vectors v_l of L can be computed without problems, since L has many smaller dimensions. Further the following must be made:

u_l = \ sum_ {k=1} ^M v_ {process card} \ Phi_k, \ qquad l = 1, \ cdots, M

or differently

u_l = A v_l \!

The vectors thus received u_l are the self-vectors of C, whereby only the M' interests us u's with the highest eigenvalues. U's must be orthonormal, i.e. they must be still normalized.

Application

With the help of the determined self-faces u_l pictures can be projected into the face area (the picture is divided into its self-faces components).

\ omega_k = u_k^T (\ gamma - \ psi) \ qquad k = 1 \ cdots M'

In such a way received vector \ Omega^T = [\ omega_1, \ cdots, \ omega_ {M'}] can be used by one pattern recognition algorithm for a face recognizing.

Further details in the PAPER.

Literature

Turk, M., and Pentland, A., "Eigenfaces for Recognition", journal OF Cognitive Neuroscience, volume. 3, No. 1, pp. 71-86, winters 1991.
L. Sirovich and M. Kirby (1987), Low dimensional procedure for the characterization OF of human faces. Journal OF the Optical Society OF America A, 4 (3), 519-524.
M. Kirby and L. Sirovich. Application OF the karhunen loeve procedure for the characterization OF of human faces., IEEE Transactions on Pattern analysis and Machine Intelligence, 12 (1): 103--108, January 1990.