# A Method of Free-Space Point-of-Regard Estimation Based on 3D Eye Model and Stereo Vision
## 3 Methods
### 3D Point-of-Regard Estimation  
3D model-based gaze estimation method is a kind of precise gaze tracking method. Since the spatial coordinates of the eye features' parameters can be calculated and after combining with the 3D geometric model, the relative position of the head and the viewed object could not be fixed. In addition, the accuracy will not deteriorate even the head is far away from the calibration position. Another advantage is that when this kind of method is applied to remote-camera type gaze tracking device, stereo cameras can also be used to solve head movement.  
However, some existing 3D model-based methods, such as the method in [35], because of the need of estimating the corneal center, need at least two light sources to estimate corneal sphere [7]. Moreover, it is also necessary to calibrate the relationship between the light source, the screen and the stereo cameras, which also makes it more difficult to deploy this kind of devices.  
Although the 3D model-based gaze estimation has some shortcomings, its line-of-sight model is still fine. The angle between the optical axis and the visual axis is an important factor in human vision mechanism, and this is a major feature of the classic 3D eye model. Therefore, we intend to preserve most of the features of the 3D line-of-sight model while removing some details to enhance our method's practicality. The proposed model is based on a simplified 3D eye model, and then we establish a gaze estimation method suitable for the proposed head-mounted device.  
We propose a 3D point-of-regard (PoR) estimation model. The model simplifies corneal spherical center from classic eye model, but estimates the spatial coordinates of the eyeball center by using the pupil center normal through the pupil center. In addition, the pupil center normal is assumed as the initial value for estimating the eyeball center. In order to enable the head-mounted device to be worn repeatedly, the model uses the vector between the left and the right inner eye corners as the aligning reference to calculate the relative poses of the head and the device, and in the following sections, it is named as the inner eye corner vector. Finally, the paper proposes using the middle point of the nearest point of the binocular visual axes as the 3D PoR.  
The eyeball center \(e\) and the angle \(\theta\) between optical axis and visual axis of both eyes will be estimated in the personal calibration process. The gaze estimation model is shown in Figure 6. The personal calibration process is realized by the user looking at the calibration target board several times. Theoretically, the eyeball features' parameters can be solved by looking at the calibration target board twice, but the eyeball features' parameters obtained by watching more times are reliable due to the calculation error of stereo vision and the uncertainty of human visual attention. The inner eye corner \(P_{A}\) is not actually involved in the calculation of binocular visual axes. In fact, only eyeball center \(e\) is needed to calculate its spatial coordinates in this model, and the inner eye corner \(P_{A}\) is used as a reference to describe the position of the eyeball center relative to the gaze tracking system.  
Figure 6: The diagram of the 3D eye model and the definition of the eyeball features. All the 3D points refer to positions in the device coordinate system (as the stereo cameras coordinate system shown in the figure). The 3D point-of-regard is considered as the intersection point of the left and right eyes’ visual axes.