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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2018, Vol. 35 ›› Issue (6): 635-647.doi: 10.3969/j.issn.1005-3085.2018.06.003

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视线跟踪系统角膜曲率中心模型优化算法及鲁棒性

薛小娜,   高淑萍,   黄柳玉,   张宝玉   

  1. 西安电子科技大学数学与统计学院，西安  710071
  • 收稿日期:2016-11-10 接受日期:2017-07-10 出版日期:2018-12-15 发布日期:2019-02-15

Optimization Algorithm and Robustness for the Models of the Center of Corneal Curvature in Gaze Tracking System

XUE Xiao-na,   GAO Shu-ping,   HUANG Liu-yu,   ZHANG Bao-yu   

  1. School of Mathematics and Statistics, Xidian University, Xi'an 710071
  • Received:2016-11-10 Accepted:2017-07-10 Online:2018-12-15 Published:2019-02-15

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摘要： 为了高效获取3D视线跟踪技术中的角膜曲率中心，使系统满足实时准确及稳定性需求，本文构建了两类角膜曲率中心模型及其求解方法．首先，利用光学原理及眼球特征建立了两种求解该中心的模型，即非线性方程组模型和改进的模型．其次，针对模型特点构造了一种基于遗传算法与LM算法的新型混合算法（GA-LM），以快速求解所建模型．最后，多组数值实验结果表明本文所建立的模型及GA-LM算法是有效的，其能快速准确求出3D视线跟踪系统中的角膜曲率中心．

关键词: 角膜曲率中心, 非线性方程组模型, 优化模型, GA-LM算法, 鲁棒性

Abstract: To efficiently obtain the corneal curvature center of the three-dimentional (3D) gaze tracking technology and make the system satisfy the requirements of real-time accuracy and stability, two kinds of corneal curvature center models and the solution method are proposed in this paper. Firstly, two models, nonlinear equations model and the improved model, are established to solve the center by using optic theory and the characteristics of eyeballs. Secondly, in order to quickly solve these two models, a new hybrid algorithm (GA-LM) based on genetic algorithm and LM algorithm is constructed. Finally, numerical experiments show that the proposed models and GA-LM are effective, which can quickly and accurately obtain the corneal curvature center in the 3D gaze tracking system.

Key words: the center of corneal curvature, nonlinear equations model, optimization model, GA-LM algorithm, robustness

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