A Review and Analysis of Eye-Gaze Estimation Systems, Algorithms and Performance Evaluation Methods in Consumer Platforms <s> C. Cross-ratio based methods <s> One of the main limitations of current remote eye gaze tracking (REGT) techniques is that the user's head must remain within a very limited area in front of the monitor screen. In this paper, we present a free head motion REGT technique. By projecting a known rectangular pattern of lights, the technique estimates the gaze position relative to this rectangle using an invariant property of projective geometry. We carry extensive analysis of similar methods using an eye model to compare their accuracy. Based on these results, we propose a new estimation procedure that compensates the angular difference between the eye visual axis and optical axis. We have developed a real time (30 fps) prototype using a single camera and 5 light sources to generate the light pattern. Experimental results shows that the accuracy of the system is about 1deg of visual angle <s> BIB001 </s> A Review and Analysis of Eye-Gaze Estimation Systems, Algorithms and Performance Evaluation Methods in Consumer Platforms <s> C. Cross-ratio based methods <s> Of gaze tracking techniques, video-oculography (VOG) is one of the most attractive because of its versatility and simplicity. VOG systems based on general purpose mapping methods use simple polynomial expressions to estimate a user's point of regard. Although the behaviour of such systems is generally acceptable, a detailed study of the calibration process is needed to facilitate progress in improving accuracy and tolerance to user head movement. To date, there has been no thorough comparative study of how mapping equations affect final system response. After developing a taxonomic classification of calibration functions, we examine over 400,000 models and evaluate the validity of several conventional assumptions. The rigorous experimental procedure employed enabled us to optimize the calibration process for a real VOG gaze tracking system and, thereby, halve the calibration time without detrimental effect on accuracy or tolerance to head movement. <s> BIB002 </s> A Review and Analysis of Eye-Gaze Estimation Systems, Algorithms and Performance Evaluation Methods in Consumer Platforms <s> C. Cross-ratio based methods <s> Homography normalization is presented as a novel gaze estimation method for uncalibrated setups. The method applies when head movements are present but without any requirements to camera calibration or geometric calibration. The method is geometrically and empirically demonstrated to be robust to head pose changes and despite being less constrained than cross-ratio methods, it consistently performs favorably by several degrees on both simulated data and data from physical setups. The physical setups include the use of off-the-shelf web cameras with infrared light (night vision) and standard cameras with and without infrared light. The benefits of homography normalization and uncalibrated setups in general are also demonstrated through obtaining gaze estimates (in the visible spectrum) using only the screen reflections on the cornea. <s> BIB003 </s> A Review and Analysis of Eye-Gaze Estimation Systems, Algorithms and Performance Evaluation Methods in Consumer Platforms <s> C. Cross-ratio based methods <s> 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. <s> BIB004 </s> A Review and Analysis of Eye-Gaze Estimation Systems, Algorithms and Performance Evaluation Methods in Consumer Platforms <s> C. Cross-ratio based methods <s> Cross-ratio (CR) based methods offer many attractive properties for remote gaze estimation using a single camera in an uncalibrated setup by exploiting invariance of a plane projectivity. Unfortunately, due to several simplification assumptions, the performance of CR-based eye gaze trackers decays significantly as the subject moves away from the calibration position. In this paper, we introduce an adaptive homography mapping for achieving gaze prediction with higher accuracy at the calibration position and more robustness under head movements. This is achieved with a learning-based method for compensating both spatially-varying gaze errors and head pose dependent errors simultaneously in a unified framework. The model of adaptive homography is trained offline using simulated data, saving a tremendous amount of time in data collection. We validate the effectiveness of the proposed approach using both simulated and real data from a physical setup. We show that our method compares favorably against other state-of-the-art CR based methods. <s> BIB005
These methods work by projecting a known rectangular pattern of NIR lights on the eye of the user and estimating the gaze position using invariant property of projective geometry. Four LEDs on four corners of a computer screen are used to produce glints on the surface of the cornea (Fig. 5) . From the glint positions, the pupil and the size of the monitor screen, gaze location is estimated using two perspective projections. The first projection comprises of the virtual images of the corneal reflections of the LEDs (scene plane). The second projection is the camera projection, that is the images of the corneal reflections on the camera's imaging plane. With these two projections a single projective transformation relating the scene and camera image plane is obtained. Then the projection of the PoG on the scene plane to the image of the pupil center on the camera plane can be estimated BIB005 . Key works on the development and experimental verification of the cross ratio based methods can be found in Yoo  and Hansen BIB003 . Coutinho et al. presents a detailed analysis of methods and comparison of their accuracy in BIB001 [68]. They also suggest improvements by including a fifth LED on the optical axis of the camera and using a calibration procedure to improve accuracy BIB004 . Error compensation with polynomial-based regression have been proposed by Cerrolaza BIB002 or Gaussian process regression BIB003 . Error correction by homography mapping that eliminates the need of the fifth light source has been proposed by Kang  .