基于李群指数映射的二阶最小化射影目标跟踪  

Projective Target Tracking Using Second-order Minimization Method Based on Lie Group Exponential Map

作　　者：李广伟[1,2,3] 尹健[4] 史泽林[1] 刘云鹏[1,3] 

机构地区：[1]中国科学院沈阳自动化研究所,沈阳110016 [2]青岛大学管理科学与工程系,山东青岛266071 [3]中国科学院研究生院,北京100039 [4]空军装备研究院总体所,北京100076

出　　处：《光电工程》2009年第2期16-22,共7页Opto-Electronic Engineering

基　　金：中国科学院国防科技创新基金项目(CXJJ-65)

摘　　要：基于空间变换模型的目标跟踪问题常归结为非线性最小二乘优化问题,射影变换模型的高度非线性使得基于向量空间的优化算法倍显局限。通过李群指数映射将正则射影变换群局部线性化,在内蕴几何优化理论的框架下,结合目标跟踪的具体特点,提出一种无需计算赫森阵的二阶最小化射影变形目标跟踪算法。与基于向量空间和基于李代数参数化的高斯-牛顿两种优化算法作对比实验,结果证实本文算法的可行性和高效性。Target tracking based on the space transformation model can usually be solved by dealing with the nonlinear least-square optimization problem. The geometric optimization algorithm based on the vector space has more limitation for high nonlinearities of the projective transformation. The mapping between a Lie group and its Lie algebra can make us to utilize the specific properties of the target tracking to propose a second-order minimization tracking method for the projective-based geometric warps within the intrinsic geometric optimization framework. In this approach, the Hessian matrix needs not to be calculated, so the computation complexity is reduced. Comparative experiments with the algorithm based on the vector space and the Gauss-Newton algorithm based on the Lie algebra parameterization validate the feasibility and high effectiveness of our method.

关 键 词：射影变换 目标跟踪 几何优化 李群 指数映射 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]