# 2D Gaze Estimation Based on Pupil-Glint Vector Using an Artificial Neural Network
## 4 Conclusions  
In this paper, a novel 2D gaze estimation method based on pupil-glint vector is proposed on the basis of conventional gaze tracking methods. In order to realize the accurate estimation of gaze direction, an improved artificial neural network (DLRS-ANN) based on direct least squares regression is developed. Learning rate parameter, weighting function, and corresponding coefficients are determined according to trial and experience. Detected coordinates of pupil-glint vectors are applied as inputs to train an improved neural network. The mapping function model is solved and then utilized to calculate gaze point coordinates. An array of four NIR LEDs is employed to form quadrangular glints. The NIR LEDs array can generate well-distributed illumination around the human eye, which contributes to extracting pupil and glint characteristics more stably and precisely. In addition, the center coordinates of quadrangular NIR LEDs, considered as additional inputs of neural network, can further compensate for the error caused during the process of calculating the gaze point, which can enhance the accuracy of gaze point coordinates. When the gaze tracking system is established, calibration models with different numbers of markers are utilized to validate the proposed method. When a four-, six-, nine-, or 16-marker calibration model is employed for the calibration process, the proposed method can achieve an accuracy of 1.29\({}^{\circ}\), 0.89\({}^{\circ}\), 0.52\({}^{\circ}\), and 0.39\({}^{\circ}\), respectively. Taking into account error compensation, the proposed method can achieve an accuracy of 1.17\({}^{\circ}\), 0.79\({}^{\circ}\), 0.47\({}^{\circ}\), and 0.36\({}^{\circ}\), respectively, when a four-, six-, nine-, or 16-marker calibration model is employed. When considering error compensation, the improvement percentage of gaze estimation accuracy for a four-, six-, nine-, or 16-marker calibration model is 9.3%, 11.2%, 9.6%, and 7.6%, respectively. The experimental results show that the training process of the proposed method is stable. The gaze estimation accuracy of the proposed method in this paper is better than that of conventional linear regression (direct least squares regression) and nonlinear regression (generic artificial neural network). The proposed method contributes to enhance the total accuracy of a gaze tracking system.  
This work is supported by Program for Changjiang Scholars and Innovation Research Team in University under Grant No. IRT1208, Basic Research Fund of Beijing Institute of Technology under Grant (No. 20130242015) and Autonomous Program of State Key Laboratory of Explosion Science and Technology under Grant No. YBKT15-09. The authors would like to thank the editor and all anonymous reviewers for their constructive suggestions.  
Figure 11: Comparison of gaze estimation accuracy results between proposed method and other methods considering error compensation.  
**Author Contributions:** All authors made significant contributions to this article. [PERSON] was mainly responsible for deployment of the system and revision of the paper; [PERSON] was responsible for developing gaze estimation method, performing the experiments, and writing the paper; [PERSON], the corresponding author, was responsible for conceiving and designing the experiments.  
**Conflicts of Interest:** The authors declare no conflict of interest.  
**Appendix**