Abstract: Remote gaze estimation using a single non-calibrated camera, simple user calibration or calibration free, and robust to head movements are very desirable features of eye tracking systems. Because cross-ratio (CR) is an invariant property of projective geometry, gaze estimation methods that rely on this property have the potential to provide these features, though most current implementations rely on a few simplifications that compromise the performance of the method. In this paper, the CR method for gaze tracking is revisited, and we introduce a new method that explicitly compensates head movements using a simple 3 parameter eye model. The method uses a single non-calibrated camera and requires a simple calibration procedure per user to estimate the eye parameters. We have conducted simulations and experiments with real users that show significant improvements over current state-of-the-art CR methods that do not explicitly compensate for head motion.