I understand that including the mirror image of each face in an ensemble of faces doubles the ensemble. But I don't understand why it is "interesting and useful" that doing this makes every eigenfunction either even or odd in the midline. Specifically, if you go to this website, http://camelot.mssm.edu/imaging/publications_imaging/review2.pdf and look at Fig 2 (p 9) the text above the figure says that the first 5 eigenfaces in the ensemble are even, but the sixth is odd. I see that the 6th face looks a lot different from the first 5, but I don't understand how exactly this works. Please explain?