The effect of position sources on estimated eigenvalues in intensity modeled data

In biometrics, often models are used in which the data distributions are approximated with normal distributions. In particular, the eigenface method models facial data as a mixture of fixed-position intensity signals with a normal distribution. The model parameters, a mean value and a covariance matrix, need to be estimated from a training set. Scree plots showing the eigenvalues of the estimated covariance matrices have two very typical characteristics when facial data is used: firstly, most of the curve can be approximated by a straight line on a double logarithmic plot, and secondly, if the number of samples used for the estimation is smaller than the dimensionality of these samples, using more samples for the estimation results in more intensity sources being estimated and a larger part of the scree plot curve is accurately modeled by a straight line. One explanation for this behaviour is that the fixed-position intensity model is an inaccurate model of facial data. This is further supported by previous experiments in which synthetic data with the same second order statistics as facial data gives a much higher performance of biometric systems. We hypothesize that some of the sources in face data are better modeled as position sources, and therefore the fixed-position intensity sources model should be extended with position sources. Examples of features in the face which might change position between either images of different people or images of the same person are the eyes, the pupils within the eyes and the corners of the mouth. We show experimentally that when data containing a limit number of position sources is used in a system based on the fixed-position intensity sources model, the resulting scree plots have similar characteristics as the scree plots of facial data, thus supporting our claim that facial data at least contains sources inaccurately modeled by the fixed position intensity sources model, and position sources might provide a better model for these sources.