Arguably the most important decision to be made when developing an object recognition algorithm is selecting the scene measurements or features on which to base the algorithm. In appearance-based object recognition, the features are chosen to be the pixel intensity values in an image of the object. These pixel intensities correspond directly to the radiance of light emitted from the object along certain rays in space. The set of all such radiance values over all possible rays is known as the plenoptic function or light-field. In this paper, we develop a theory of appearance-based object recognition from light-fields. This theory leads directly to an algorithm for face recognition across pose that uses as many images of the face as are available, from one upwards. All of the pixels, whichever image they come from, are treated equally and used to estimate the (eigen) light-field of the object. The eigen light-field is then used as the set of features on which to base recognition, analogously to how the pixel intensities are used in appearance-based face and object recognition.