In this dissertation, a new approach for determining gaze direction is presented. This approach is based on the existence of a visual axes center for the human eye, the location of which is invariant with respect to the head. The vector from the visual axes center of an eye through the pupil center provides a reliable approximation for a gaze vector. Calibration camera images of human subjects looking at known points on a computer monitor are collected in a non-intrusive manner. Algorithms are applied to the images from two independent cameras whose spatial relationship is known with respect to the monitor. The calibration algorithms allow determination of physical distances between selected facial features visible in the images and the invariant location of the visual axes center for each eye (not visible) with respect to these features. Given these invariant relationships between a subject's facial features and eye visual axes centers, optimization techniques are applied to subsequent images collected from a single camera to obtain the three-dimensional locations of the visible facial features and the visual axes centers, and from these, the gaze direction. The results of experiments conducted to determine the viability and accuracy of the visual axes center approach in determining the gaze direction are presented. The results show that the approach can provide acceptable gaze direction error values when high accuracy (< 1° angular error) is not required. Techniques to improve accuracy are discussed as well as potential limitations of the approach.