Facial recognition systems based on eigenfaces are based on a very simple idea: Calculate an orthonormal basis for the subspace spanned by all facial images. This subspace is calculated from a collection of representative faces, the training set. In this paper we analyze the properties of the training set and derive sufficient conditions that will guarantee an efficient system. The idea behind the analysis is based on perturbation theory and also leads to an efficient algorithm for updating the eigenfaces when a new face is added to the training set
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