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基于李群理论的图像跟踪与识别
Alternative TitleImage Tracking and Recognition based on Lie Group
刘云鹏1,2
Department光电信息技术研究室
Thesis Advisor史泽林
ClassificationTP391.4
Keyword图像跟踪 图像识别 李群 几何优化 流形统计
Call NumberTP391.4/L76/2010
Pages121页
Degree Discipline模式识别与智能系统
Degree Name博士
2010-11-30
Degree Grantor中国科学院沈阳自动化研究所
Place of Conferral沈阳
Abstract图像跟踪与识别是无人飞行器光电探测与制导的关键核心技术,动态几何形变是图像跟踪与识别技术面临的突出难题之一。基于欧氏空间的图像跟踪与识别理论,采用线性或线性逼近的方法处理成像几何变换和图像特征数据分布问题,暴露出其固有的未能真实反映变换参数或特征数据的内在几何结构的弱点,已很难取得突破。事实上,用来描述成像几何变换的仿射变换或射影变换模型的参数空间不是平直的,而是李群。此外,在自动目标跟踪与识别领域涉及到的大量基于图像的特征数据具有李群或其拓展流形结构。因此,正确分析目标成像几何变换和表征目标的特征数据是构建高性能图像跟踪与识别算法的关键。论文以无人飞行器的自动目标跟踪与识别为研究背景,在通用模式理论指导下,开展李群理论在图像跟踪与识别中的应用研究:在分析变换参数或目标特征数据的几何结构基础上,将求取几何变换参数的策略、处理特征数据的视角由欧氏空间转换至李群及其拓展流形。据此所设计的图像跟踪与识别算法的综合性能较欧氏空间算法或现有算法有显著性提高或突破。论文重点关注四种特殊李群及其拓展流形,即仿射群 GA(2,R)、特殊线形群SL(3,R)、正定对称流形和Grassmann流形Gr(k,n),在图像目标跟踪与识别中的应用。研究内容分为两部分。第一部分研究基于李群理论的图像目标跟踪方法,从理论上分析目标跟踪过程中几何变换的实质,并给出物理解释,构建目标成像急速变形下稳定跟踪算法。这一部分包括三章,第3章选择仿射李群GA(2,R)刻画目标的变形,建立定义在李群上的内蕴几何优化算法,然后利用李群和李代数之间的关系求取变换参数。由于考虑了参数变换的几何结构,所设计的图像跟踪算法的综合性能较欧式空间算法有了显著性提高和突破;特殊线性群SL(3,R)是投影变换群的正则化,第4章分析了SL(3,R)群的黎曼几何结构,运用黎曼优化的思想求解最优图像投影变换参数。对比分析了三种不同几何优化策略的图像投影配准算法的性能;第5章针对仿射变换群GA(2,R)下的目标跟踪进行研究,与第3、4章采用几何优化来处理跟踪问题的思路不同的是,本章以流形上的统计为数学工具,构建几何粒子滤波算法,理论分析和实验验证了所提出算法的有效性。Grassmann 流形作为特殊正交群SO(n,R)的商流形,是研究子空间距离度量的有力工具。论文第二部分以Grassmann流形上的统计学为工具,研究基于Grassmann流形统计的仿射不变形状识别方法。这一部分内容集中在第6章,克服传统Kendall形状空间理论只适用于相似变换的局限性, 分析了仿射不变形状空间的几何结构,给出仿射不变形状空间构成Grassmann流形的理论依据;构建目标形状空间的正态分布,从统计推理的角度理解和研究形状识别问题;实验结果表明,所提出的识别算法比基于传统kendall形状空间理论的识别算法具有更优的性能。  本文研究成果丰富和扩展了现有图像跟踪与识别理论和方法,为突破图像跟踪与识别的动态几何形变瓶颈提供了科学依据,为开拓光电探测与制导新的基础理论和算法支持奠定坚实的基础。
Other AbstractImage tracking and recognition is the core technique of the optical-electronic detection and guidance, and dynamic geometric deformation of object image is one of the prominent problems in image tracking and recognition. The image tracking and recognition methods based on Euclidean space handle the parameters of geometric transform and image data by linear or approximately linear fitting, and accordingly possess some intrinsic drawbacks that they fail in utilizing the correct geometric structure of the parameters or data. Therefore, those methods based on Euclidean space are hard in making a breakthrough. In fact, the parameter spaces of the affine transform and projective transform are Lie groups. Additionally, mass feature data captured from image sensor have a Lie groups or their expand manifold structures. Therefore, accurately analyzing geometric transform and effectively representing feature structures of objects is the key to build a high-performance algorithm for image tracking and recognition. According to the above research background,and guided by General Pattern Theory, this dissertation studies Lie Group theory and its application to image tracking and recognition, first studying geometric structure of transform parameters and the feature data is studied, and then studying methods for finding the optimum parameters and analyzing the feature on Lie groups or heir extension manifold other than on Euclidean space. The general performance for the tracking and recognition demonstrates that our methods outperform that in Euclidean space or existing algorithms. The dissertation mainly focuses on the application of four special Lie groups or their extensive manifold in the image tracking and recognition and its content consists simply of two parts as follows: The first part focuses on the image tracking methods based on Lie group, we build stable tracking algorithms with rapid changes in the geometric appearance by analyzing the essence of geometric transform in the tracking,while giving a physical interpretation of methods based on Lie group. This part includes three chapters. In the third chapter, we chose affine Lie group as geometric transform, and then build geometric optimization algorithm on affine Lie group, which can be solved by exponential mapping between Lie Group and its Lie algebra. Thanks to utilizing the geometric structure of geometric transform , the general performance for the image tracking and recognition demonstrates that our methods work better than that in Euclidean space. Additionally, a special linear group results from the normalization of the projective group, In the fourth chapter , we exploit the geometric structure of the underlying space and got the geodesics on through variation method, then , we develop a new image projective registration algorithm based on Riemannian analysis on .we compare three different algorithms for image registration and image tracking. Different to the geometric optimization method for image tracking, the fifth chapter expands the geometric particle filter for visual tracking by an introduction of manifold statics method, which drawing state samples while moving on the low dimension manifold: affine lie group. Theoretic analysis and experimental evaluations demonstrate the promise and effectiveness of the proposed tracking method Grassmann manifold, thought as the quotient space of , is a powerful tool for studying the distance metric between substances. The second part focuses on affine invariant shape recognition methods utilizing on Grassmann manifold statistics. This part corresponds to the sixth chapter. Traditional Kendall shape space theory is only applied to similar transform. However, we utilize the Grassmann manifold structure of the affine shape space. We construct the norm probability models of affine invariant shapes, and then recognize the shape by Bayesian classification. Experiment results show that our recognition algorithm outperforms the algorithm based on Procrustean metric in traditional Kendall shape space theory Our research develops and enriches the current approaches for image tracking and recognition, provide a theoretical basis to overcome the bottlenecks of image tracking and recognition, and laying a solid foundation for an application of a novel theories and algorithms to the optical-electronic detection and guidance.
Language中文
Contribution Rank1
Document Type学位论文
Identifierhttp://ir.sia.cn/handle/173321/9235
Collection光电信息技术研究室
Affiliation1.中国科学院沈阳自动化研究所
2.中国科学院研究生院
Recommended Citation
GB/T 7714
刘云鹏. 基于李群理论的图像跟踪与识别[D]. 沈阳. 中国科学院沈阳自动化研究所,2010.
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