摘 要

工学 硕士学位论文

基于流形的粒子滤波研究及其

在人脸跟踪中的应用

学生姓名 指导教师

江苏科技大学 二OO九年三月

摘 要

本文系统介绍了适用于解决非线性非高斯系统问题的粒子滤波的基本原理和关键技术，针对标准粒子滤波（PF）中存在的粒子退化及算法实时性问题，把流形、权值选择和线性优化重采样等思想引入到PF中进行算法改进，提出了基于施蒂费尔流形和权值选择的粒子滤波（SM-WS-PF）、基于施蒂费尔流形和线性优化重采样的粒子滤波（SM-LOCR-PF），并将改进算法应用到非线性、非高斯系统状态估计中，与UPF进行了性能仿真对比分析，仿真结果表明改进算法不仅能增加粒子多样性，有效防止粒子退化现象，改善滤波精度，而且能提高算法的实时性和鲁棒性。同时本文还总结了粒子

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ABSTRACT

滤波主要收敛性结果及其分析证明，考虑到硬件资源的承载能力，本文还设计了一种结合似然分布自调整和样本自适应调整两种方法的改进自适应粒子滤波，最后采用捷联惯导误差模型对设计的自适应算法进行仿真分析。

人脸跟踪是属于计算机视觉研究领域的一个重要分支，它作为人脸信息处理中的一项关键技术，在基于内容的图像与视频检索、视频监控与跟踪、视频会议以及智能人机交互等方面都有着重要的应用价值。实际研究表明将粒子滤波引入人脸跟踪领域能很好的保证跟踪精度和鲁棒性，但是却丧失了实时性；而且当目标所在环境中存在多个人脸时，通常的粒子滤波算法会导致发散，所以本文又加入了Isomap学习方法。实验分析表明，本文提出的SM-PF和Isomap-SM-PF算法，尤其是后者，能大大提高算法实时性，在人脸姿态变化、旋转、遮挡、背景等发生变化时也能很好的进行跟踪，表现出一定的优越性。

关键字 粒子滤波；收敛性证明；流形；自适应；人脸跟踪

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摘 要

ABSTRACT

This paper systematically introduced the basic principles and the key technologies of the particle filter which is properly used to solve the problems of the non-linear and non-Gaussian systems. To solve the problem of particle degeneracy and overload calculation in particle filter (PF), we applied manifold learning, weight selected and linear optimizing resampling method to PF, which replaced the traditional resampling method, and proposed the improved particle filter based on Stiefel Manifold , which combines weight selected method and linear optimizing resampling method respectively together, called SM-WS-PF and SM-LOCR-PF.We adopted improved PF to non-linear and non-Gaussian system state estimation, and analyzed the tracking performance of SM-WS-PF, SM-LOCR-PF and UPF. Simulation results show that improved algorithms can effectively solve the problem of particle degeneracy, increase particle diversity, and improve filter accuracy and real-time performance of the algorithm. In addition, We analysis and prove the main convergence results of particle filter. Considering the capacity of hardware resources, we also design a new adaptive particle filter in view of the algorithmic limitations caused by configuration of hardware,and adopt the SINS error model to testify the performance of the new adaptive algorithm.

Face tracking is an important branch of computer vision research filed, as information processing in the face of a key technology in content-based image and video search, video surveillance and tracking, video conferencing, as well as intelligent human-computer interaction, and so on. Nowsdays, more experiment results indicate that Particle filter can show very good performance in this area to ensure the accuracy of tracking and robustness, but the loss of real-time. Further, it is still some problems that we should concern, the common PF algorithm will lead to divergence when we track face among several persons. In the paper, the proposed SM-PF and Isomap-SM-PF algorithm are used to solve this shortcomings. Simulator experimental results showed the algorithm's robustness to the agile motion of face, the change of il- lumination and partial occlusion in the presence of complex background, especially the Isomap-SM-PF's performance.

Keywords: Particle filter; Convergence Proof; Manifold; Adaptive particle filter; Face

tracking

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目 录

目 录

摘 要 .................................................................................................................................... I ABSTRACT ......................................................................................................................... III 第1章 绪 论 ....................................................................................................................... 1 1.1 选题的意义和实用价值............................................................................................... 1 1.2 国内外研究现状和发展趋势....................................................................................... 2 1.2.1粒子滤波的发展与应用 ......................................................................................... 2 1.2.2 粒子滤波的缺陷和现有的解决方法 .................................................................... 2 1.2.3 需要深入研究的问题 ............................................................................................ 4 1.3 课题研究内容和主要章节安排................................................................................... 5 1.3.1课题研究内容 ......................................................................................................... 5 1.3.2 课题主要章节安排 ................................................................................................ 6 第2章 粒子滤波技术及其收敛性分析证明 ....................................................................... 7 2.1滤波问题常用框架........................................................................................................ 7 2.1.1 滤波常用框架 ........................................................................................................ 7 2.1.2 动态空间模型 ........................................................................................................ 8 2.1.3 递推贝叶斯估计 .................................................................................................... 8 2.2 粒子滤波理论............................................................................................................... 9 2.2.1 标准粒子滤波算法 ................................................................................................ 9 2.2.2 粒子集的退化和重采样 ...................................................................................... 10 2.2.3 标准粒子滤波伪代码 .......................................................................................... 11 2.3 粒子滤波主要收敛性结果分析................................................................................. 13 2.3.1 基本问题描述 ...................................................................................................... 13 2.3.2 粒子滤波引入 ...................................................................................................... 14 2.3.3 主要的结论 .......................................................................................................... 15 2.3.4 修正粒子滤波 ...................................................................................................... 18 2.3.5命题1的证明 ....................................................................................................... 20 2.4 本章小结..................................................................................................................... 28 第3章 基于流形分布的改进粒子滤波研究 ..................................................................... 29 3.1标准粒子滤波的缺点.................................................................................................. 29 3.1.1选取好的重要性密度函数 ................................................................................... 29 3.1.2 重采样 .................................................................................................................. 30 3.2 改进粒子滤波研究..................................................................................................... 31 3.2.1改进重要性密度函数的粒子滤波 ....................................................................... 31 3.2.2改进重采样环节处理的粒子滤波 ....................................................................... 31 3.3 基于施蒂费尔流形的粒子滤波研究......................................................................... 31 3.3.1施蒂费尔流形 ....................................................................................................... 31 3.3.2 矩阵变量分布 ...................................................................................................... 32 3.3.3 流形上的状态空间模型 ...................................................................................... 32

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