We do a principal component analysis of the matrix of vectorized training samples, separate for right eye and left eye. The resulting principal components (eigeneyes) span a subspace [4] which is a good representation for right and left eye images. Examples of these eigeneyes are given in figures 2 and 3, ordered according to eigenvalues. One important notice about this technique is that its aim is representation and not discrimination. Thus, we should act with care when selecting the number of eigeneyes to keep for spanning the subspace (eigeneyes with small corresponding eigenvalues might still be important for discrimination).
One limitation which also needs to be pointed out in the way we apply eigeneyes in this paper, is that the training set is relatively small. Ideally, we would have a large separate set of eyes to compute a more general subspace of eigeneyes. We would also expect a degradation in performance due to the large variation in the dataset. We normalize the images by keeping the center point fixed, which gives us some invariance with respect to positioning of the eye, but a better way would perhaps be to locate the corners of the eye so we might be able to normalize with respect to rotation and size in addition to position.
