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Despite the crisp clear details and blended colours, a photo is just a series of dots, called pixels, of different colours. Any photo, including one of your own lovely visage, is represented in a computer as a long string of numbers, each representing the colour at a particular pixel. Just as a string of three numbers marks a point in three-dimensional space (it gives its coordinates), so a string of N numbers sits in what mathematicians think of as N-dimensional space: so mathematically you can think of a photo as a point in an N-dimensional space, where N is the number of pixels in the photo.

First of all the researchers calculate the average face by simply averaging the values at each pixel over all the photos in the set. This new string of numbers represents the average face and the position of the points representing the other faces show how they differ from the average face.

Principal component analysis uses a statistical concept called variance to measure how the set of faces, viewed as points in N-dimensional space, is spread out. It calculates the first principal component to be the direction from the average face in which the set spreads out the most. Then it looks for the second principal component: the direction that is perpendicular to the first component, in which the set spreads out the most. Then for a third principal component, perpendicular to the first two, in which the set spreads out the most, and so on.