Algorithms And Robustness Analysis For Solving Nonlinear Equations In 3D Gaze Tracking System

Gaze tracking technology is a method which can estimate users gaze direction and obtain the point-of-gaze(POG) by collecting real-time information of eye movement. With the rapid development of science and technology, as a new human-computer interaction device, gaze tracking system can be widely used in biological engineering, road transport, advertisement design, psychological analysis and other fields. At present, 3D desktop gaze tracking system does not require users to wear any devices and allows a larger head movement range, which attracts attention and becomes a major research direction. Although 3D gaze tracking technology develop rapidly, there are still many problems unresolved. In this paper, the mathematical models and algorithms in the 3D gaze tracking system are discussed. The main work is summarized as follows:1. A hybrid intelligent algorithm for solving the corneal curvature center. The nonlinear equations of corneal curvature center is turned to the unconstrained optimization model(CCCUO) and modified optimization model(MCCCUO) in this paper. The genetic algorithm(GA) and Levenberg Marquardt method are combined, and a hybrid intelligent algorithm(GALM algorithm) is proposed. GA is used to find initial value by global searching, and then a more accurate solution is obtained by LM method. GALM algorithm is used for solving two optimization models respectively and compared with the GA. The results show that GALM algorithm is superior to the GA, which not only improves the accuracy of solutions but also reduces computing time.2. Solving nonlinear equations of the pupil center. Firstly, the coordinate of the point of corneal surface refraction is found. Secondly, considering that the existence of four solutions, therefore the nonlinear equations of the pupil center is improved by adding two inequality constraints. Finally, a more exact location of the pupil center is obtained, according to the position relationship between the pupil center and corneal curvature center to set appropriate initial value.3. Robustness analysis for the corneal curvature center models. The nonlinear equations of corneal curvature center is linearized, and then its ill-condition is measured by the condition number of linear equations. The results show that the nonlinear equations is very sensitive to the parameters variations. By same parameters perturbations, the robustness of corneal curvature center optimization models is discussed, and the examples illustrate the robustness of CCCUO is poor and MCCCUO is better.