The exploitation of natural symmetries (mirror images) in a well-defined family of patterns (human faces) is discussed within the framework of the Karhunen-Lo&e expansion. This results in an extension of the data and imposes even and odd symmetry on the eigenfunctions of the covariance matrix, without increasing the complexity of the calculation. The resulting approximation of faces projected from outside of the data set onto this optimal basis is improved on average.

A method is presented for the representation of (pictures of) faces. Within a specified framework the representation is ideal. This results in the characterization of a face, to within an error bound, by a relatively low-dimensional vector. The method is illustrated in detail by the use of an ensemble of pictures taken for this purpose.

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