3D视线跟踪系统中的非线性方程组算法与鲁棒性分析

发布时间：2018-04-13 10:41

本文选题：角膜曲率中心 + 瞳孔中心　；参考：《西安电子科技大学》2015年硕士论文

【摘要】：视线跟踪技术是通过采集实时眼动信息来实现对用户眼睛注视方向的估计,进而得到其视线落点的一种方法。随着科学技术的不断发展,视线跟踪系统作为一种新型的人机交互设备,广泛应用于生物工程、道路交通、广告设计、心理分析等领域。目前,3D桌面式视线跟踪系统具有不需要用户佩戴任何设备且允许用户有较大的头动范围等优点而受到广泛关注,成为视线跟踪技术中的一个主要研究方向。3D视线跟踪技术虽然发展迅速,但还有许多尚未解决的问题,本文主要对3D视线跟踪系统中的数学模型与算法进行了研究,具体工作如下:1.求解角膜曲率中心的混合智能算法。本文首先将角膜曲率中心的非线性方程组模型转化为无约束优化模型(CCCUO)及改进的优化模型(MCCCUO),然后结合遗传算法和LM算法,提出了一种混合智能算法(GALM算法),即先用遗传算法进行全局搜索求出一个近似解,再将此解作为初始值,用LM算法进一步求得更高精度的解。运用GALM算法分别求解两种优化模型,并与遗传算法进行了比较。实验结果表明了GALM算法优于遗传算法,提高了解的精度,减少了计算时间。2.瞳孔中心非线性方程组模型的求解。首先求出角膜表面折射点的坐标,然后针对瞳孔中心的非线性方程组模型对解的约束不强导致存在4个解的缺陷问题,对模型进行了改进,增加了两个不等式约束条件,最后根据瞳孔中心和角膜曲率中心的位置关系设置初始值,运用LM算法求出瞳孔中心的准确位置。3.角膜曲率中心模型的鲁棒性分析。首先将其非线性方程组线性化,通过近似线性方程组的条件数来衡量病态性,结果表明非线性方程组模型对参数变化非常敏感。然后对角膜曲率中心模型的两种优化模型采用相同的参数扰动进行测试。数值实验表明无约束优化模型(CCCUO)鲁棒性差,而改进的优化模型(MCCCUO)受参数扰动的影响较小,鲁棒性较好。
[Abstract]:Line of sight tracking technology is a method to estimate the gaze direction of the user by collecting real-time eye movement information, and then to get the location of the eye sight.With the development of science and technology, line of sight tracking system, as a new type of human-computer interactive equipment, is widely used in bioengineering, road traffic, advertising design, psychological analysis and other fields.At present, 3D desktop line of sight tracking system has the advantages of not requiring the user to wear any device and allowing the user to have a large head-moving range and so on.Although it has developed rapidly, there are still many unsolved problems. In this paper, the mathematical model and algorithm of 3D line of sight tracking system are studied.The work is as follows: 1.A hybrid intelligent algorithm for solving corneal curvature centers.In this paper, the nonlinear equations model of corneal curvature center is first transformed into an unconstrained optimization model (CCCUO) and an improved optimization model (MCCCUOO), which is then combined with genetic algorithm and LM algorithm.In this paper, a hybrid intelligent algorithm (GALM) is proposed, in which an approximate solution is obtained by global search with genetic algorithm, then the solution is taken as the initial value, and a higher precision solution is obtained by using LM algorithm.Two optimization models are solved by GALM algorithm and compared with genetic algorithm.The experimental results show that the GALM algorithm is superior to the genetic algorithm, improves the accuracy of the solution, and reduces the computing time. 2.The solution of the nonlinear equations of pupil center.The coordinate of refraction point on corneal surface is obtained first, and then two inequality constraints are added to improve the model for the defect of four solutions caused by the constraint of the nonlinear equations model in the center of pupil.Finally, according to the relationship between the center of pupil and the center of corneal curvature, the initial value is set, and the exact position of pupil center is calculated by LM algorithm.Robustness analysis of corneal curvature center model.Firstly, the nonlinear equations are linearized, and the ill-condition is measured by approximating the condition number of linear equations. The results show that the nonlinear equations model is very sensitive to the change of parameters.Then the two optimization models of corneal curvature center model were tested with the same parameter disturbance.Numerical experiments show that the unconstrained optimization model (CCCUO) has poor robustness, while the improved optimization model (MCCCUO) is less affected by parameter disturbances and has better robustness.
【学位授予单位】：西安电子科技大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TP391.41;O241.7;TP18

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