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题名: 基于黎曼流形的目标跟踪和识别
其他题名: Object Tracking and Recognition Based on Riemannian Manifold
作者: 李广伟
导师: 尹健 ; 史泽林
分类号: TP391.4
关键词: 目标跟踪 ; 目标识别 ; 黎曼流形 ; 李群 ; 几何优化
索取号: TP391.4/L31/2010
学位专业: 模式识别与智能系统
学位类别: 博士
答辩日期: 2010-05-31
授予单位: 中国科学院沈阳自动化研究所
学位授予地点: 中国科学院沈阳自动化研究所
作者部门: 光电信息技术研究室
中文摘要: 目标精确跟踪和识别是无人飞行器光电探测与制导的核心技术,正确分析目标发生的几何形变和表征目标的特征数据是构建高性能的目标跟踪和识别算法的关键。当运动变换参数或特征数据分布在非欧空间时,基于欧氏几何和线性代数的优化算法以及分析、处理数据的方法暴露出其固有的未能真实反映参数或数据的几何结构的弱点。本文以流形思想作指导,基于几何优化算法,将以往求取几何变换参数的方法和处理数据的视角,由欧氏空间转换至李群或黎曼流形。由于充分考虑了变换参数或目标特征数据的几何结构,据此所设计的目标跟踪和识别算法的综合性能较前者有明显的提高。 论文以无人飞行器高机动条件下的目标跟踪和识别为研究背景,开展目标在显著透视条件下或目标图像发生其它非线性变形时的识别和跟踪研究。论文重点关注特殊线性群、正定对称流形和Grassmann流形三类特殊流形在目标跟踪和识别中的应用。首先,特殊线性群是投影变换群的正则化。在内蕴几何优化框架下,利用由测地线方程所决定的黎曼指数映射,结合目标跟踪和配准的具体特点,提出了基于黎曼二阶测地优化的投影目标跟踪算法,对比分析了基于三种不同几何优化策略的投影图像配准算法的性能;进一步,通过求取特殊线性群样本的黎曼均值和协方差矩阵,构建了基于黎曼流形的李群正态分布,分析了在平面目标识别中引进李群正态分布的必要性和优越性。其次,正定对称流形是对用于目标建模的特征协方差矩阵集合的正确数学描述。通过研究正定对称流形上的仿射不变黎曼结构和李群结构之异同,提出了一种基于对数-欧几里德度量的特征协方差目标跟踪方法,理论分析和实验验证了算法的有效性。最后,Grassmann流形方法是研究子空间距离度量的有力工具。将目标光照的线性变化融入现有的仿射不变形状识别框架,提出仿射光照不变形状空间概念和基于Grassmann流形的仿射光照不变形状分析算法,理论分析了算法的正确性,实验验证了算法的有效性。 研究具有普适性、精确性、快速性和鲁棒性的跟踪和识别算法,既需要丰富的跟踪和识别技术作为支撑,也需要先进的理论作为引领。本文在通用模式理论(General Pattern Theory)的指导下,利用黎曼几何、李群理论和几何优化算法,发展和丰富了现有的目标跟踪和识别方法,为开拓飞行器光电探测与制导新的基础理论和提供新的算法支持奠定了坚实的基础。
英文摘要: The precise target tracking and recognition is the core technique of the optical-elctronic detection and guidance for the unmanned aerial vehicles. The accurate analysis of the geometric warps and the processing data is the key to build a high-performance target tracking and recognition algorithm. When the motion transformation parameters or the feature data reside in a non-Euclidean space, the methods of optimizing the function and processing data based on Euclidean space and traditional vector algebra expose the intrinsic drawback that they can not exploit the correct geometric structure of the parameters or data. Guided by the manifold principle, this dissertation studies the methods of finding the optimum transformation parameters and analysizing the feature data in Riemannian manifold other than on Euclidean space. Thanks to utilizing their geometric structure correctly, the general performance for the tracking and recognition demonstrate more improvement and superiority than that in Euclidean space. Based on the research background of the target tracking and recognition for the unmanned aerial vehicles under the condition of high-mobility, this dissertation aims at designing algorithms for target tracking and recognition under the remarkable projection transformation or other nonlinear warps or deformation of the objects. The dissertation mainly focuses on the application of three special manifolds in the automatic target tracking and recognition. Firstly, a special linear group results from the normalization of the projection group. Under the intrinisic geometric optimization framework, we work with the Riemannian exponential map which is determined by the optimum geodesic on the special linear group, and propose the Riemannian manifold-based projective image registration algorithm utilizing the specific characteristics of the pratical target tracking and registration application. We compare three different geometric optimization algorithms for target tracking. Based on the Riemannian manifold optimization algorithms, we obtain the samples’ Karcher Riemannian mean and covariance matrix on the special linear group and construct a Lie group norm distribution. Theoritical analysis and comparative experiments under the simple background shows the necessarity and superiority of the statictical distribution on the Lie group. Secondly, the symmetric positive-definite manifold is the correct mathematical representation of the feature covariance matrix which is a popular method of constructing model for tracking now. The recent reaserch indicates that a novel Lie group structure can be endowed on the symmetric positive-definite manifolds, which is different from the affine invariant structure on it. This novel Lie group structure has a bi-invariant Riemannian metric essentially, called the Log-Euclidean metric. We propose a feature convariance target tracking approach based on the Log-Euclidean metric structure. Finally, the Grassmann subspace method is a powerful tool of studying the distance metric problem between substances. The dissertation intergrates the linear illumination variation into the affine invariant shape space framework and proposes the concept of affine illumination invariant shape space. It is a general geometric illumination invariant shape recognition approach. The theoritical analysis and experiments demonstrate the validity and prospects of the proposed concept and algorithms. Designing a universal and accurate algorithm for target tracking and recognition with the high rate and robustness needs not only abound skills and techniques but also an advanced theory which can give a theoretical guidance to understand, design and evaluate the algorithms of target tracking and recognition. Based on the General Pattern Theory, Lie group theory, Riemannian geometry and the geometric optimization algorithms, this dissertation developes and enriches the current approaches for tracking and recognition, laying a solid foundation for exploiting a novel theory and algorithms of the optical-elctronic detection and guidance for the unmanned aerial vehicles.
语种: 中文
产权排序: 1
内容类型: 学位论文
URI标识: http://ir.sia.cn/handle/173321/9234
Appears in Collections:光电信息技术研究室_学位论文

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Recommended Citation:
李广伟.基于黎曼流形的目标跟踪和识别.[博士学位论文].中国科学院沈阳自动化研究所.2010
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