基于视觉的目标检测与跟踪综述

尹宏鹏; 陈波; 柴毅; 刘兆栋

doi:10.16383/j.aas.2016.c150823

基于视觉的目标检测与跟踪综述

doi: 10.16383/j.aas.2016.c150823

尹宏鹏^1,2, ,,
陈波^2,,
柴毅^2,,
刘兆栋^2,

1.
信息物理社会可信服务计算教育部重点实验室(重庆大学) 重庆 400030
2.
重庆大学自动化学院重庆 400044

基金项目:

重庆市基础科学与前沿研究技术专项重点项目 cstc2015jcyjB0569

中央高校基本科研业务专项基金 106112015CDJXY170003

国家自然科学基金 61203321

重庆市研究生科研创新项目 CYB14023

中央高校基本科研业务专项基金 106112016CDJZR175511

详细信息

作者简介:
陈波  重庆大学自动化学院硕士研究生.2015年获得重庆大学学士学位.主要研究方向为深度学习, 计算机视觉.E-mail:qiurenbieyuan@gmail.com

柴毅  重庆大学自动化学院教授.2001年获得重庆大学博士学位.主要研究方向为信息处理, 融合与控制, 计算机网络与系统控制.E-mail:chaiyi@cqu.edu.cn

刘兆栋  重庆大学自动化学院博士研究生.主要研究方向为稀疏表示, 机器学习.E-mail:liuzhaodong@cqu.edu.cn

通讯作者:
尹宏鹏重庆大学自动化学院副教授.2009年获得重庆大学博士学位.主要研究方向为模式识别, 图像处理与计算机视觉.本文通信作者.E-mail:yinhongpeng@gmail.com

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出版历程
- 收稿日期: 2015-12-14
- 录用日期: 2016-05-16
- 刊出日期: 2016-10-20

Vision-based Object Detection and Tracking: A Review

YIN Hong-Peng^{1,2
, ,},
CHEN Bo^2
,,
CHAI Yi^2
,,
LIU Zhao-Dong^2
,

1.
Key Laboratory of Dependable Service Computing in Cyber Physical Society(Chongqing University), Ministry of Education, Chongqing 400030
2.
College of Automation, Chongqing University, Chongqing 400044

Funds:

Chongqing Nature Science Foundation of Fundamental Science and Frontier Technologies cstc2015jcyjB0569

China Central Universities Foundation 106112015CDJXY170003

National Natural Science Foundation of China 61203321

Chongqing Graduate Student Research Innovation Project CYB14023

China Central Universities Foundation 106112016CDJZR175511

More Information

Author Bio:
Master student at the College of Automation, Chongqing University. He received his bachelor0s degree from Chongqing University in 2015. His research interest covers deep learning and computer vision.E-mail:

Professor at the College of Automation, Chongqing University. He received his Ph. D. degree from Chongqing University in 2001. His research interest covers information processing, integration and control, and computer network and system control.E-mail:

Ph. D. candidate at the College of Automation, Chongqing University. His research interest covers sparse representation and machine learning.E-mail:

Corresponding author: YIN Hong-Peng Associate professor at the College of Automation, Chongqing University. He received his Ph. D. degree from Chongqing University in 2009. His research interest covers pattern recognition, image processing, and computer vision. Corresponding author of this paper.E-mail:yinhongpeng@gmail.com

摘要

摘要: 基于视觉的目标检测与跟踪是图像处理、计算机视觉、模式识别等众多学科的交叉研究课题，在视频监控、虚拟现实、人机交互、自主导航等领域，具有重要的理论研究意义和实际应用价值.本文对目标检测与跟踪的发展历史、研究现状以及典型方法给出了较为全面的梳理和总结.首先，根据所处理的数据对象的不同，将目标检测分为基于背景建模和基于前景建模的方法，并分别对背景建模与特征表达方法进行了归纳总结.其次，根据跟踪过程有无目标检测的参与，将跟踪方法分为生成式与判别式，对基于统计的表观建模方法进行了归纳总结.然后，对典型算法的优缺点进行了梳理与分析，并给出了其在标准数据集上的性能对比.最后，总结了该领域待解决的难点问题，对其未来的发展趋势进行了展望.
- 计算机视觉 /
- 目标检测 /
- 目标跟踪 /
- 背景建模 /
- 表观建模
Abstract: Vision-based object detection and tracking is an active research topic in image processing, computer vision, pattern recognition, etc. It finds wide applications in video surveillance, virtual reality, human-computer interaction, autonomous navigation, etc. This survey gives a detail overview of the history, the state-of-the-art, and typical methods in this domain. Firstly, object detection is divided into background-modeling-based methods and foreground-modeling-based methods according to the different data objects processed. Background modeling and feature representation are further summarized respectively. Then, object tracking is divided into generative and discriminative methods according to whether the detection process is involved. Statistical based appearance modeling is presented. Besides, discussions are presented on the advantages and drawbacks of typical algorithms. The performances of different algorithms on benchmark datasets are given. Finally, the outstanding issues are summarized. The future trends of this field are discussed.
- Computer vision /
- object detection /
- object tracking /
- background modeling /
- appearance modeling

HTML全文

非刚性点阵配准(Non-rigid point set registration)是将某一点阵(称为源点阵)与其发生形变后的点阵(称为目标点阵)进行匹配的过程.该技术在计算机视觉、机器学习、医学图像处理、模式识别以及地理信息系统中扮演着极其重要的角色.基于当前算法的特点,非刚性点阵配准算法大体可以分为两大类:基于迭代或非迭代的算法和基于学习或非学习的算法.由于本文算法主要涉及基于迭代的问题,所以我们主要从基于迭代或非迭代的角度来介绍当前的非刚性点阵配准算法.

在基于非迭代的非刚性点阵配准算法中,两组点阵之间的对应关系是通过使用某种高级结构特征(High level structural features)仅进行一次相似性评估后直接找回两组点阵之间的对应关系. 在基于非迭代的配准模型中,直线^[1]、曲线^[2]、表面结构^[3]、Shape context^[4-5]和图论(Graphs)^[6-7]等特征被用于两个点阵之间相似度的评估.在非迭代算法中,Shape context和Graphs是最受欢迎的两种特征描述法,其核心是通过最小化两个点阵之间的分布差异(使用Shape context时)或者拓扑结构差异(使用Graphs时)来找回点阵之间的对应关系^[4-9].最近,一部分研究人员^[10-14] 在传统的基于Graphs特征算法的基础上加入了学习要素,通过在配准前使用适当的学习样本进行学习来优化算法中的参数设置,从而提高了算法的配准精度.但是这类算法由于使用了Shape context 或Graphs特征,当相邻点较为接近时该类特征则变得非常相似以至于这类算法并不能达到较好的配准效果^{[8, 15-16]}.

基于迭代的算法通常包括两个相互交替的过程:对应关系评估(Correspondence estimation)和空间变换更新(Transformation updating).相对于基于非迭代的算法,基于迭代的算法的优势在于它们在迭代过程中逐步地调整源点阵的初始几何形状和空间位置使得源点阵在几何形状和空间位置上变得越来越接近目标点阵,从而使得通过几何结构特征寻找它们之间的对应关系变得更加容易.TPS-RPM^[17]是第一个利用迭代技术来进行非刚性点阵配准的算法.它通过使用点阵到点阵的距离、Softassign^[18-19]和退火算法^[20-21]来评估点阵之间的对应概率和控制薄板样条函数(Thin plate spline,TPS)^[22]的更新. Myronenko等^[23] 在TPS-RPM算法框架基础上提出了在空间变换更新中增加运动一致性约束条件(Motion coherence constraint)^[24]来提高配准过程中空间变换的稳定性,并利用最大似然法(Maximum likelihood)来评估点阵之间的对应关系. 之后,Myronenko等^[25]在文献^[23]的基础上发表了著名的CPD算法(Coherent points drift algorithm),他们改良了空间变换模型使之既可以适用于刚性和非刚性的点阵配准问题,并可以在配准精度要求相对不高的情况下通过使用快速高斯变换(Fast Gauss transform)^[26]和矩阵低秩逼近(Low-rank matrix approximation)^[27]技术减少计算量来提升算法的配准速度.近期,Jian等^[16]提出了一种基于高斯混合模型(Gaussian mixture model)的非刚性点阵配准算法(称为GMMREG).该算法不直接在几何空间中配准两个点阵,而是把两个点阵先转变成为两个高斯混合模型,然后在这基础上进行对应关系评估,空间变换更新基于最小化两个高斯混合模型的L2距离^[28].最近,国内的Ma等^[29]提出了一种基于Shape context特征和L2E评估^[30]的算法,Wang等^[31]通过使用不对称的高斯模型捕捉空间点阵的不对称分布,并用其作为特征描述进行点阵的非刚性配准.

本文中,我们提出了一种基于混合特征的非刚性点阵配准算法.本算法的主要贡献体现在以下3个方面:

1) 全局结构特征描述算法:我们提出了一种利用和向量来描述点阵中各点的全局结构特征的描述算法.

2) 局部结构特征描述算法:我们提出了一种利用点阵之间的局部区域相邻点的距离和描述点阵中各点的局部结构特征的描述算法.

3) 基于混合特征的点阵对应评估算法:我们通过混合全局和局部结构特征描述算法提出了一种基于混合特征的能量方程,该方程允许使用混合特征进行点阵对应评估,使得在配准过程中所使用的特征不再单一化,使配准精度得到了提高并在大部分实验中超越了当前相关算法.

1. 方法

我们首先定义了全局和局部特征描述法以及混合特征能量优化方程,然后对本文算法的两个核心步骤进行介绍.在本章的后面部分,我们将对本文算法的参数设定以及本文算法与当前相关方法的差异进行说明.假设 $\{{\pmb a}_{i},i=1,2,\cdots,n\}$ 和 $\{{\pmb b}_{j},j=1,2,\cdots,m\}$ 是两组需要进行配准的点阵, ${\pmb a}$ 和 ${\pmb b}$ 分别为源点阵和目标点阵.

1.1 全局和局部结构特征差异

我们首先定义了两种特征描述法,分别被用来评估源点阵 ${\pmb a}$ 与目标点阵 ${\pmb b}$ 之间的全局与局部几何结构特征差异.

1.1.1 全局结构特征差异

全局几何结构特征差异被定义为

\begin {equation} G_{{\pmb a}_{i}{\pmb b}_{j}}= |{\pmb v}_{{\pmb a}_{i}}-{\pmb v}_{{\pmb b}_{j}} |\end {equation}

(1)

其中 $G_{\pmb{ab}}$ 为全局结构差异矩阵,矩阵中的每个元素值为两个向量 ${\pmb v}_{{\pmb a}_{i}}$ 与 ${\pmb v}_{{\pmb b}_{j}}$ 相减后的模. $G_{\pmb{ab}}$ 被用于评估点阵 ${\pmb a}$ 与点阵 ${\pmb b}$ 之间的全局结构特征差异. ${\pmb v}_{{\pmb a}_{i}}$ 与 ${\pmb v}_{{\pmb b}_{j}}$ 则是我们提出的全局结构特征描述法,定义为

\begin {equation} {\pmb v}_{{\pmb a}_{i}}=\sum_{k=1,,kneqi}^{n}\overrightarrow{{\pmb a}_{i}{\pmb a}_{k}}\end {equation}

(2)

\begin {equation} {\pmb v}_{{\pmb b}_{j}}=\sum_{k=1,,kneqj}^{m}\overrightarrow{{\pmb b}_{j}{\pmb b}_{k}}\end {equation}

(3)

其中 $\overrightarrow{{\pmb a}_{i}{\pmb a}_{k}}$ 与 $\overrightarrow{{\pmb b}_{j}{\pmb b}_{k}}$ 分别是点 ${\pmb a}_{i}$ 到点 ${\pmb a}_{k}$ 与点 ${\pmb b}_{j}$ 到 ${\pmb b}_{k}$ 的几何向量. ${\pmb v}_{{\pmb a}_{i}}$ 与 ${\pmb v}_{{\pmb b}_{j}}$ 则是分别用来描述点 ${{\pmb a}_{i}}$ 与点 ${{\pmb b}_{j}}$ 的全局结构特征的和向量.

1.1.2 局部结构特征差异

局部结构特征差异被定义为

\begin {equation}L_{{\pmb a}_{i}{\pmb b}_{j}}=\sum_{k=1}^{K}\parallel T({ N}({\pmb a}_{i})_{k},{\pmb b}_{j})-{N}({\pmb b}_{j})_{k}\parallel^{2}\end {equation}

(4)

其中 $L_{{\pmb a}{\pmb b}}$ 是点阵 ${\pmb a}$ 与点阵 ${\pmb b}$ 之间的局部结构差异矩阵,K 为相邻点的个数. ${N}({\pmb a}_{i})_{k}$ 和 ${N}({\pmb b}_{j})_{k}$ 分别为点 ${\pmb a}_{i}$ 和点 ${\pmb b}_{j}$ 的第 k 个最近点. T 则是平移方程,被定义为

\begin {equation}T({N}({\pmb a}_{i})_{k},{\pmb b}_{j})={N}({\pmb a}_{i})_{k}+({\pmb b}_{j}-{\pmb a}_{i})\end {equation}

(5)

其主要思想为考虑在点阵 ${\pmb a}$ 与 ${\pmb b}$ 中的每一个点与其相邻点( ${N}({\pmb a}_{i})_{k=1,\cdots,K}$ 或 $N{{({{a}_{i}})}_{k=1,\cdots ,K}}$ )构成了一个局部小段,评估点阵 ${\pmb a}$ 与 ${\pmb b}$ 之间的对应关系就可以转化为评估局部小段的相似度. 例如,首先将 ${\pmb a}_{i}$ 以及它的 K个相邻点 ${N}({\pmb a}_{i})_{k=1,\cdots,K}$ 根据平移向量 $\overrightarrow{{\pmb a}_{i}{\pmb b}_{j}}$ 移动到点 ${\pmb b}_{j}$ . 然后把点 ${\pmb a}_{i}$ 的相邻点 ${N}({\pmb a}_{i})_{k=1,\cdots,K}$ 与点 ${\pmb b}_{j}$ 的相邻点 ${N}({\pmb b}_{j=1,2,\cdots,m})$ 之间的几何距离进行累加.最后,点 ${\pmb a}_{i}$ 在点阵 ${\pmb b}$ 中的对应点被确定为拥有最小距离和的点 ${N}({\pmb b}_{j})$ .其中,局部结构特征差异主要决定于相邻点个数 K,同时 K也决定了两个点阵之间局部结构相似度的评估.

在这里,我们使用Linear assignment技术来最小化全局结构特征差异矩阵 $G_{\pmb{ab}}$ 与局部结构特征差异矩阵 $L_{{\pmb{ab}}}$ ,我们将会获得两种对应关系,它们分别是基于最小化的全局结构特征差异和局部结构特征差异计算而来的.

1.2 基于混合特征的能量优化方程

本文中提出的基于混合特征的能量优化方程被定义为

\begin {equation}E(M)=\sum_{i=1}^n\sum_{j=1}^m G_{{\pmb a}_{i}{\pmb b}_{j}}M_{ij}+\alpha \sum_{i=1}^n\sum_{j=1}^m L_{{\pmb a}_{i}{\pmb b}_{j}}M_{ij}\end {equation}

(6)

其中 $\sum_{i=1}^n \sum_{j=1}^m G_{{\pmb a}_{i}{\pmb b}_{j}}M_{ij}$ 和 $\sum_{i=1}^n\sum_{j=1}^m L_{{\pmb a}_{i}{\pmb b}_{j}}M_{ij}$ 分别描述了基于最小化全局和局部结构特征差异计算的能量,可以被考虑为Linear assignment问题. $G_{{\pmb a}{\pmb b}}$ 和 $L_{{\pmb a}{\pmb b}}$ 分别正规化至[0,1]区间. n 和 m分别代表了点阵 ${\pmb a}$ 与 ${\pmb b}$ 中的序列长度. M_ij是对应矩阵,表示了点阵 ${\pmb a}$ 与点阵 ${\pmb b}$ 之间的对应关系,当点 ${\pmb a}_{i}$ 与点 ${\pmb b}_{j}$ 相对应时赋值为1,反之则赋值为0. M_ij 始终满足 ${\sum_{j=1}^m}M_{ij}=1$ 和 ${\sum_{i=1}^n}M_{ij}=1$ . $\alpha$ 为权重参数用于调节能量优化时 $\sum_{i=1}^n\sum_{j=1}^m G_{{\pmb a}_{i}{\pmb b}_{j}}M_{ij}$ 与 $\sum_{i=1}^n\sum_{j=1}^m L_{{\pmb a}_{i}{\pmb b}_{j}}M_{ij}$ 的比重. 在配准过程中,能量调节参数 $\alpha$ 通过退火算法在每次迭代中逐渐减小,最后趋近为0.

1.3 配准过程

首先我们创建一个可变形的代理点阵 ${{\pmb a}^{w}}$ ,并使其在配准开始时满足 ${\pmb a}^{w}={\pmb a}$ .本文算法的主要过程是:1) 首先利用前述基于混合特征的能量优化方程在每次迭代中评估 ${{\pmb a}^{w}}$ 和 ${\pmb b}$ 的对应关系(前述式(1) $\thicksim$ (6) 中的 ${{\pmb a}_{i}}$ 应使用 ${{\pmb a}^{w}}$ ); 2) 随后使用TPS空间变换更新 ${{\pmb a}^{w}}$ 的空间位置及几何形状,该TPS空间变换由步骤1) 中获取的对应关系建立而来.这两个步骤1) 和2) 相互交替迭代以至于代理点阵 ${{\pmb a}^{w}}$ 能逐渐在空间位置和几何形状上越来越接近其目标点阵 ${\pmb b}$ ,最终准确地匹配上它在点阵 ${\pmb b}$ 中的真实对应点.使用代理点阵 ${\pmb a}^{w}$ 评估获得的对应点即为点阵 ${\pmb a}$ 的对应关系.

1.3.1 步骤1:对应关系评估

在每一次迭代中,点阵 ${{\pmb a}^{w}}$ 与 ${\pmb b}$ 的对应关系通过最小化基于混合特征的能量优化方程(6) 获得.基于混合特征的能量优化在本文中被看作一个线性分配问题,所以式(6) 可以使用Jonker-Volgenant算法^[32]求解.Jonker-Volgenant算法已被广泛用于解决线性分配问题,它可以提供最短广增路(Shortest augmenting path)并拥有O $(N^3) $ 的计算复杂度.

对于线性分配中的Integer cost问题,在配准前我们首先将需要配准的点阵坐标缩放至[0,1]之间,然后在每一次迭代中把计算出的全局与局部结构特征差异矩阵通过使用 $\lfloor{G_{{\pmb a}^{w}{\pmb b}}}× R \rceil$ 和 $\lfloor {L_{{\pmb a}^{w}{\pmb b}}}× R \rceil$ 进行数值处理,其中R被设为 $10^{6}$ .对于非方形矩阵问题(点阵 ${\pmb b}$ 包含冗余点),非方形矩阵 ${{ G}_{{\pmb a}^{w}{\pmb b}}}$ 和 ${L_{{\pmb a}^{w}{\pmb b}}}$ 可以通过分配虚拟项(Dummy entries)^[33]来转换为方形矩阵,而且不会影响整体能量优化.转换后 $E(M)$ 则可以使用通常手段求解,并且仍然给出最优解.虽然我们提供了一种针对目标点阵包含冗余点的配准解决方案,但是本文算法并不能很好地处理包含冗余点的配准问题.原因是用于描述各点全局结构特征的和向量 ${\pmb v}_{{\pmb a}_{i}}$ 和 ${\pmb v}_{{\pmb b}_{j}}$ 容易受冗余点的影响.

通过使用Jonker-Volgenant算法求解的对应关系矩阵M确保了从点阵 ${{\pmb a}^{w}}$ 到点阵 ${\pmb b}$ 的一一对应关系. 当前迭代的对应点集 ${\pmb b}^{c}$ 由式(7) 进行更新

\begin{equation}{\pmb b}^{c}= M \cdot {\pmb b}\end{equation}

(7)

本文提出的基于混合特征的能量优化方程为使用混合特征来评估对应关系提供了一个灵活方法.例如,当 $\alpha$ 非常大时,最小化E等于最小化局部结构特征差异 ${L_{{\pmb a}^{w}{\pmb b}}}$ ,求出的点对点的对应关系是基于最小化两个点阵之间的局部结构特征差异.当 $\alpha$ 逐渐变小时,对应关系评估开始转向使用最小化全局结构特征差异,求出的点对点的对应关系是基于最小化两个点阵之间的全局结构特征差异.

1.3.2 步骤 2:空间变换更新

当更新完当前对应点集 ${\pmb b}^{c}$ 后,空间变换通过使用 ${\pmb b}^{c}$ 和源点阵 ${\pmb a}$ 的对应关系进行更新(由于 ${\pmb a}$ 和 ${{\pmb a}^{w}}$ 拥有相同的点阵序列,所以 ${\pmb b}^{c}$ 也是源点阵 ${\pmb a}$ 的对应点集).本文中,我们使用TPS空间变换来建立从 ${\pmb a}$ 到 ${\pmb b}^{c}$ 的映射关系

\begin{equation}f({\pmb a},{\pmb d},{ w})={\pmb a}\cdot {d} + \phi({\pmb a})\cdot{ w}\end{equation}

(8)

其中 ${d}$ 为一个仿射系数矩阵, ${ w}$ 为一个非刚性形变系数矩阵. $\phi({\pmb a})$ 称为TPS内核方程(TPS kernel function),分别在二维和三维映射中被定义为 $\phi({\pmb a})=\|{\pmb a}-{{\pmb a}_{c}}\|^{2}\log \|{\pmb a}-{{\pmb a}_{c}}\|$ 和 $\phi({\pmb a})=\|{\pmb a}-{{\pmb a}_{c}}\|$ . ${{\pmb a}_{c}}$ 是从点阵 ${\pmb a}$ 中选取的一组控制点.

为了使用适当的仿射系数 ${ d}$ 和非刚性形变系数 ${ w}$ 来建立从 ${\pmb a}$ 到它的对应点集 ${\pmb b}^{c}$ 的映射关系,TPS能量方程被定义为

\begin{equation}E_{\textrm{TPS}}({ d},{w})=\|{\pmb b}^{c}-{\pmb a} {d}- \Phi {w}\|^{2}+λ \textrm{tr}({w}^{\rm T} \Phi { w})\end{equation}

(9)

其中正规化参数λ用于调节非刚性形变系数 ${w}$ ,同时它也被前述使用在式(6) 中用来控制权重参数 $\alpha$ 的能量权重调节所控制. ${\Phi}$ 是TPS内核矩阵,由前述TPS内核方程 $\phi({\pmb a})$ 计算而来.

为了计算 ${d}$ 和 ${w}$ 的最小二乘解,矩阵的QR分解技术^[34]被用于分离点阵的仿射和非刚性形变空间

\begin{equation}{\pmb a}=QR=[Q_{1}|Q_{2}] \left(\begin{array}{c}{R}_{1} \\0 \\\end{array} \right)\end{equation}

(10)

其中,Q₁ $\in {\bf R}^{N× D}$ , ${ Q}_{2}$ $\in {\bf R}^{N×(N-D)}$ , ${R}_{1}$ $\in {\bf R}^{D× D}$ . 此外,Q₁与Q₂拥有相同的正交列. 所以式(9) 可以转换为

\begin{equation}\begin{aligned}E_{\textrm{TPS}}(\boldsymbol{\gamma},{d})=\|Q^{\rm T}_{2}{\pmb b}^{c}-Q^{\rm T}_{2} \Phi Q_{2} \boldsymbol{\gamma}\|^{2}+ \|Q^{\rm T}_{1}{\pmb b}^{c}-\\{ R}_{1}{ d}-Q^{\rm T}_{1}\Phi Q_{2}\boldsymbol{\gamma}\|^{2} +λ\boldsymbol{\gamma}^{\rm T}Q^{\rm T}_{2} \Phi Q_{2}\boldsymbol{\gamma}\end{aligned}\end{equation}

(11)

其中 ${ w}=Q_{2}\boldsymbol{\gamma}$ , $\boldsymbol{\gamma}$ $\in{\bf R}^{(N-D-1) × (D+1) }$ .式(11) 的最小二乘解可以通过先最小化 $\boldsymbol{\gamma}$ ,然后最小化 ${d}$ 来求解. ${ w}$ 和 ${ d}$ 的解为

\begin{equation}\hat{{ w}}=Q_{2}\boldsymbol{\gamma}=Q_{2}(Q^{\rm T}_{2} \Phi Q_{2}+λ I_{N-D-1})^{-1}Q^{\rm T}_{2}{\pmb b}^{c}\end{equation}

(12)

\begin{equation}\hat{{ d}}={R}^{-1}(Q^{\rm T}_{1}{\pmb b}^{c}-\Phi {w})\end{equation}

(13)

代理点阵 ${\pmb a}^{w}$ 的空间位置与几何形状被更新为

\begin{equation}{\pmb a}^{w}={\pmb a}\cdot {d} + \Phi \cdot { w}\end{equation}

(14)

代理点阵 ${\pmb a}^{w}$ 的空间位置与几何形状更新后,本文算法重新回到步骤1(第1.3.1节)进行对应关系评估,两个步骤交替进行直到能量权重调节中的T达到终止设置(T_final).

1.4 算法伪代码及参数设置

算法 1给出了本文算法的伪代码.

算法 1. 基于混合特征的非刚性配准算法

输入. 点阵 ${\pmb a}$ , ${{\pmb a}^{w}}$ 和 ${\pmb b}$ .

预处理. 初始化参数T_init,T_final,r, $λ_{init}$ 和 $\alpha_{init}$ . 设定 K并且确定点阵 ${{\pmb a}^{w}}$ 和 ${\pmb b}$ 的相邻点集 ${N}({\pmb a}_{i})$ 和 ${ N}({\pmb b}_{j})$ .

开始 . 能量权重调节计划.

步骤 1. 使用式(6) 和(7) 评估当前对应关系 ${\pmb b}^{c}$ .

步骤 2. 使用式(12) 和(13) 更新TPS空间变换.

使用式(14) 更新 ${{\pmb a}^{w}}$ .

通过调节减小T,然后更新参数 $\alpha$ 和λ.

结束. 直至满足 $T\leq T_{final}$ .

输出. 代理点阵 ${{\pmb a}^{w}}$ }.\vskip2

本文提出的基于混合特征的非刚性点阵配准算法包含四组重要参数:调节参数T_init,T_final 和 r,权重参数 $\alpha$ ,正规化参数λ 以及相邻点个数参数K.每组参数的详细设定如下

1) 调节参数:能量权重调节中所使用的T^[20-21]在配准开始前被设定为一个较高的值T_init,随后在每次迭代中利用一个线性调节计划 $T=T × r$ 使得T值在配准过程中被逐步降低,其中 r为调节率.当到达一个较低的设定值 T_init 时,调节计划停止.本文中设计该线性调节计划的目的主要有2方面: 首先利用T来逐步减小式(6) 中的权重参数 $\alpha$ ,使得式(6) 的能量优化问题可以从首先最小化局部结构特征差异逐步过度到最小化全局结构特征差异;其次利用T来逐步减小式(9) 和(12) 中的正规化参数λ,使得TPS空间变换可以从更加刚性的形变更新逐渐转化为更加非刚性的形变更新.由于调节参数从根本上决定了算法迭代的次数,所以T_init,T_final 和r 的参数设定原则为满足配准所需的足够迭代次数.基于前期使用Fish 1点阵^[17]进行的试错实验(Trial-and-error experiment),起始T_init值被设为点阵 ${\pmb a}$ 到 ${\pmb b}$ 最大距离平方的 $1/10$ ,终止T_final 值被设为点阵 ${\pmb a}$ 中各点到其最近点平均距离平方的 $1/8$ ,调节率r 通常被设为0.7.

2) 权重参数:权重参数 $\alpha$ 在每次迭代中,通过使用 $\alpha=\alpha_{init} × T$ 被逐渐减小, $\alpha$ 的初始值设定原则为能够保证在配准前期整个算法可以集中在利用最小化局部结构特征差异来评估点阵的对应关系.初始值 $\alpha_{init}$ 被设为相邻点个数的平方 $K^{2}$ .

3) 正规化参数:正规化参数λ在每次迭代中,通过使用 $λ=λ_{init}× T$ 被逐渐减小,由于λ主要用来控制TPS变换中的刚性和非刚性形变(λ较大时,TPS呈现出刚性变换; λ较小时,TPS转为呈现非刚性形变),所以λ的初始值设定原则为能够确保在配准前期TPS处于刚性变换.初始值 $λ_{init}$ 被设为点阵 ${\pmb a}$ 中点的数量.

4) 相邻点数量参数:参数K的默认值设定是基于用于区别局部结构差异所需的最少相邻点数.例如,当我们需要区别角(Corner,其中包含2个相邻点)和十字(Cross,其中包含4个相邻点)时,我们至少需要借助4个相邻点来判断.基于上述考虑,我们将参数K在二维和三维配准情况下的默认值设为5.

2. 相关研究

当前主要有TPS-RPM^[17],CPD^[25],GMMREG (L2 +TPS)^[16],Ma等^[29]和Wang等^[31]5种算法与本文算法相似,表 1详细列举了本文算法与上述5种算法之间存在的差异.

表 1 本文算法与相关算法的不同

Table 1 Methodological differences between our method and the current methods

算法	对应关系评估			空间变换更新
	使用的特征	对应关系	约束条件	空间变换方程
本文算法	混合特征	B	TPS 能量方程 1	TPS
TPS-RPM	高斯概率密度	F	TPS 能量方程 2	TPS
CPD	高斯概率密度	F	MCC-NLL	GRBF
GMMREG	高斯概率密度	F	最小化 L2 距离	TPS
Ma 等^[29]	Shape context	B	L2E 评估子^[30]	RKHS
Wang 等^[31]	MoAG	F	最小化 L2 距离	RKHS
注: B: 二值对应; F: 模糊对应; GRBF (Gaussian radial basis function): 高斯径向基函数; TPS: 薄板样条函数; MCC-NLL(Motion coherence constraint based negative log-likelihod):基于运动一致性的负对数似然; RKHS (Reproducing kernel Hilbert space): 再生核Hilbert空间; MoAG (Mixture of asymmetric Gaussian model): 混合非对称高斯模型; 在TPS能量方程 2中, $λ_{2}\textrm{tr}(d-I)^{\rm T}(d-I)$ 被加到了式(7) (TPS能量方程 1) 来控制仿射变换.

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1) 对应关系评估:与上述基于单一特征配准的5种算法不同,本文算法是一种基于混合特征的能量优化问题,且允许使用混合特征进行点阵之间的对应关系评估.因为本文算法与Ma等使用了线性分配技术求解对应关系,所以我们都提供了一个二值对应关系,即在对应关系矩阵M_ij中仅使用0和1来描述对应关系.在TPS-RPM,CPD,GMMREG和Wang等^[31]算法中,空间变换方程是建立在模糊对应(Fuzzy correspondences,即对应概率)关系基础上的,所以在指导代理点阵 ${{\pmb a}^{w}}$ 改变其空间位置和几何形状时会发生模糊更新,同时也会需要更多的迭代次数才能完成配准.在本文算法中,建立在最小化全局或局部结构特征差异的二值对应关系可以为代理点阵 ${{\pmb a}^{w}}$ 提供一个正确且清晰的空间位置与几何形状的更新指导.

2) 空间变换更新: 本文算法使用的是标准TPS能量方程.TPS-RPM在式(6) 中增加了 $λ_{2} \textrm{tr} [d-I]^{\rm T}[d-I]$ 项用于控制仿射参数.由于本文算法在每次迭代中提供了一个较为精确的二值对应关系给TPS空间变换,所以我们仅需要使用λ来控制 ${w}$ 系数在刚性和非刚性变换上的作用.同时一个自由的仿射变换(也就是不受控制的仿射系数 ${d}$ )可以帮助代理点阵 ${{\pmb a}^{w}}$ 快速(使用更少的迭代次数)地找到更加接近目标点阵 ${\pmb b}$ 的空间位置和几何形状来完成接下来的非刚性配准.此外,与CPD中强制相邻点集保持运动一致性不同,本文算法通过在整个配准过程中固定相邻点集 ${N}({\pmb a}_{i}^{w})$ 和 ${N}({\pmb b}_{j})$ ,来保护代理点阵 ${{\pmb a}^{w}}$ 的拓扑结构特征.

3. 实验

我们使用Matlab实现了本文算法的主要过程,其中Jonker-Volgenant算法使用C++编写并利用Matlab mex function调用Jonker-Volgenant算法的C++函数.我们首先基于以下四种配准模式测试了本文算法的各项性能,

1) 轮廓配准 (2D synthetic point set);

2) 3D 轮廓配准 (3D face point set);

3) 序列图像 (CMU house and CMU hotel sequence);

4) 真实图像特征点配准 (Pascal 2007 challenge datasets).

而且,本文算法还与下列当前典型的8种算法进行了性能比较实验,

1) 基于迭代的算法: TPS-RPM^[17],CPD^[25],GMMREG(L2 + TPS)^[16],Wang等^[31];

2) 基于Graph的学习算法: Caetano等^[10],Leordeanu等^[13],Torresani等^[14];

3) 基于Graph的非学习算法: Zhou等^[9].

最后,我们评估了本文算法的计算复杂度并且讨论了如何降低本文算法的计算复杂度.

3.1 实验设计

Line^[17]、Fish 1^[17]、Fish 2^[25]、Chinese character^[17]和3D face^[25]是非刚性点阵算法在轮廓点阵配准测试中普遍使用的几个流行点阵,它们分别来自TPS-RPM^[17]和CPD^[25].本文首先使用这5个点阵作为源点阵,并使用下面人工合成的方法创建了一系列丰富的目标点阵与TPS-RPM,CPD和GMMREG进行了性能对比实验.为了达到公平的实验对比,在目标点阵的生成、误差测量和性能评估上我们遵循了TPS-RPM^[17]和CPD^[25]中所用的方法.由于本文中提出的全局特征描述法(见第1.1.1节)是由和向量设计而来,当配准目标点阵中包含冗余点时,本文算法并不能很好地处理包含冗余点的配准问题,所以在本实验中我们不进行包含冗余点的配准模式性能测试.

目标点阵:

1) 形变级别: 我们设置8个控制点(三维配准情况是为6个控制点)在每组轮廓点阵边缘.为了创建一系列不同形变级别且适合的目标点阵,每个控制点拥有上、下、左、右4个方向的自由移动以及0.2的移动步长.8个(或6个)控制点的移动循序以及方向被随机设定. 在本实验中,TPS空间变换被用于使用这8个(或6个)控制点使前述源点阵发生形变创建新目标点阵.因为被移动的控制点数量反映了点阵的形变大小,所以本实验中形变级别被定义为移动控制点的数量(二维和三维情况下的最大形变级别分别为8和6) .

2) 噪音比:我们通过利用均值为0且标准偏差从0.01至0.05的高斯白噪声(Gaussian white noise)创建了5个噪音级别的目标点阵.

3) 旋转角度:我们认为在适当旋转下的配准性能测试是必要的,因为通常形变发生时都会伴随着旋转.但是过大旋转会导致相关算法产生不稳定或无价值的配准结果,所以我们主要专注于在以 $15^{\circ}$ 为间隔,旋转 $-30^{\circ}$ 到 $30^{\circ}$ 的情况下的配准性能测试.在三维配准实验中,源点阵被沿Z轴旋转来创建新目标点阵.

误差测量: 在误差测量中,通常可以选择的测量方法很多.例如,正确匹配百分比、配准后点阵之间的平均距离等.为了保证直接和公平的比较,我们遵循了TPS-RPM与CPD中的误差测量法,即代理点阵 ${{\pmb a}^{w}}$ 与目标点阵 ${\pmb b}$ 之间平均距离的平方.

性能评估:平均误差(即100次测试中的平均距离平方与标准偏差)在本实验中被用来比较不同算法之间的配准性能.对于每组点阵,在每种形变级别、噪音比、旋转角度下执行了100次的随机实验.

3.2 二维轮廓点阵的配准结果

在第一系列的实验中,我们在不同的二维人造轮廓点阵上评估了本文算法的性能.与后面的序列图像(CMU sequences and Pascal 2007challenge)以及真实图像特征点(Pascal 2007challenge)配准相比,这些二维轮廓点阵拥有更多的点数以及较密的点阵分布.在这类点阵配准中,由于相邻点彼此靠近且拥有相似的局部结构特征,所以在评价各点的局部特征结构相似度时变得更加困难.本文算法与相关算法的比较结果如下.

3.2.1 Line

在点阵Line的配准测试中,本文算法仅与TPS-RPM进行对比测试.因为其他算法并没有在该点阵上进行测试并公布相关的参数设定.性能测试统计数据(平均误差与标准偏差)展示在图 1的第1 行.本文算法在所有的实验中展现了准确的配准结果,并且在所有形变级别、噪音比、旋转角度的测试中,给出了最优的配准结果.图 2给出了本文算法的一个配准实例.

图 1 二维轮廓点阵配准下的性能对比(误差线表示了100次随机测试中平均误差的标准偏差值.从第1行至第4行分别为点阵Line,Fish 1,Chinese character以及Fish2的实验结果.

Fig. 1 Comparison of our results against CPD,TPS-RPM and GMMREG on 2D contour point set registration (The error bars indicate the standard deviations of the mean errors in100 random experiments. From the top row to bottom row are: Line,Fish 1,Chinese character and Fish 2,respectively.

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图 2 本文算法的配准实例: Line

Fig. 2 Registration examples on Line point set

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3.2.2 Fish 1

在点阵Fish 1的配准测试中,我们测试了本文算法与CPD,TPS-RPM 和GMMREG的性能,图 1的第2行展示了测试结果.这4种算法均给出了准确的配准结果,本文算法在所有的形变级别和所有旋转角度的测试中展现了最优的性能结果.在目标点阵含有噪音的配准测试中,这四种算法均展现了准确的配准结果,GMMREG 表现得更好. 图 3给出了本文算法的一个配准实例.

图 3 本文算法的配准实例: Fish 1

Fig. 3 Registration examples on Fish 1 point set

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3.2.3 Chinese character

在点阵Chinese character的配准测试中,本文算法仅与TPS-RPM进行对比实验.因为CPD与GMMREG并未在非刚性配准中测试过该点阵(GMMREG仅在刚性配准中测试过该点阵).本文算法在所有形变级别、噪音比从0.01至0.03、所有旋转角度的测试中给出了最优的配准结果.图 4给出了一个本文算法的配准实例.

图 4 本文算法的配准实例: Chinese character

Fig. 4 Registration examples on Chinese character point set

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3.2.4 Fish 2

本文算法与CPD的性能测试结果展示在图 1的第4行.本文算法在所有的实验中展现了准确的配准结果,并且在所有形变级别、噪音比以及旋转角度的测试中给出了最优的配准性能.图 5给出了本文算法的一个配准实例.

图 5 本文算法的配准实例: Fish 2

Fig. 5 Registration examples on Fish 2 point set

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在二维轮廓点阵配准测试中,所有的算法均给出了准确的配准结果,但是本文算法在形变与旋转测试中明显地超越了相关算法.

3.3 三维人脸点阵的配准结果

在第二系列的实验中,我们评估了本文算法在三维配准中的性能.本实验中使用的3D face点阵已被CPD和GMMREG等算法用于测试其在三维配准中的性能. 图 6 给出了本文算法与CPD、GMMREG算法的性能测试结果.本文算法在所有实验中给出了准确的配准结果,同时在所有形变级别、噪音比从0.01至0.04以及所有旋转角度的实验中给出了最优的性能结果.图 7给出了一个本文算法的配准实例.

图 6 三维Face轮廓点阵配准下的性能对比 (误差线表示了100次随机测试中平均误差的标准偏差值.)

Fig. 6 Comparison of our results against CPD and GMMREG on3D face contour point set registration (The error bars indicate the standard deviations of the mean errors in 100 random experiments.)

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图 7 3D face点阵配准实例

Fig. 7 Registration examples on 3D face point set

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3.4 序列图像的配准结果

在第三系列的实验中,我们测试了本文算法在序列图像特征点配准问题上的性能.与二维和三维人造点阵相比,序列图像拥有更少的特征点,这些点稀疏地分布在图像中.CMU house和CMU hotel序列图像是目前用于测试基于Graph的学习算法最流行的实验数据.两个序列图像分别由111和101幅图组成,每幅图拥有30个标记的特征点.在本实验中,我们使用正确配准点数的百分比(称为配准率)为误差测量法.

本文算法与三种基于Graph的学习算法{^{[10, 13-14]},一种基于Graph的非学习算法^[9],和三种基于迭代的算法^{[16, 25, 31]}分别在这两组序列图像的所有配准可能中进行了性能对比实验.

表 2展示了实验结果.在House序列图像的配准中,对于Caetano等^[10]与Zhou等^[9],我们报告了他们公布的配准率的上限值,对于Leordeanu等^[13]、Torresani等^[14]和Wang等^[31],我们给出了他们公布的配准率. 本文算法,Wang等^[31]和Torresani等^[14]给出了完美的配准结果,也超越了其他算法.但是从算法运行时间角度来看,本文算法的运行时间(平均0.049秒)比Torresani等公布的平均运行时间4.8秒^[14]快了很多(该对比也考虑了使用电脑的性能问题).在CMU hotel序列图像的配准中,Wang等^{[14, 31]}与Zhou等^[9]没有提供他们的实验结果. 与CPD,GMMREG,Leordeanu等^[13]和Caetano等^[10]相比较,本文算法展现了更好的配准精度. 图 8给出了本文算法的两个配准实例.

表 2 CMU house和CMU hotel序列图像中所有可能的图像配准结果 (%)

Table 2 Matching rates on the CMU house and CMU hotel for all possible image pairs (%)

算法	CMU house	CMU hotel
本文算法	100.0	99.3
CPD	99.6	98.9
GMMREG	99.5	97.1
Wang 等^[31]	100.0	无
Torresani 等^[14]	100.0	无
Zhou 等^[9]	≈ 100.0	无
Leordeanu 等^[13]	99.8	94.8
Caetano 等^[10]	＜ 96.0	＜ 90.0

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图 8 CMU house与CMU hotel配准实例

Fig. 8 Registration examples on CMU house and CMU hotel

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3.5 图像特征点的配准结果

在第四系列的实验中,我们使用Leordeanu等^[13]的测试数据测试了本文算法的性能.这套测试数据集从Pascal 2007 challenge数据库中挑选出来的,包含30对汽车图像与20对摩托车图像. 每对图像中包含 $30\sim60$ 个特征点.本文算法与CPD,GMMREG,Zhou等^[9]和Leordeanu等^[13]进行了性能对比,其结果在表 3中列出,对于Zhou等^[9] (A)和 Leordeanu等^[13] (B),我们报告了他们公布的实验结果. 本文算法给出了最优的配准率.图 9给出了本文算法的两个配准实例.

图 9 Pascal 2007 challenge 配准实例

Fig. 9 Registration examples on Pascal 2007 challenge

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表 3 汽车与摩托车图像库的配准结果 (%)

Table 3 Matching rates on cars and motorbikes (%)

本文算法	CPD	GMMREG	A	B
93	80	82	80	80

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3.6 计算复杂度

本文算法的计算复杂度主要与两个方面相关:1) 决定收敛性的能量权重调节参数 T_init,T_final 与 r;2) 用于求解基于混合特征的能量优化方程的线性分配算法.

3.6.1 收敛范围

收敛范围主要与形变级别和能量权重调节参数设定相关.在其他相关算法中,TPS-RPM的收敛范围由退火算法决定,CPD和GMMREG则分别由容差停止准则(Tolerance stopping criterion)以及最大迭代次数所决定.我们调查了上述这四种算法在点阵Chinese character形变实验中的收敛范围.本文算法、TPS-RPM、CPD与GMMREG的参数设定值遵循前述Fish1实验中的设定值.CPD和TPS-RPM分别平均需要43次与85次迭代来完成整个配准过程,而GMMREG则需要最大迭代次数(100次)才能完成配准. 原因是由于容差停止准则被设定为 $10^{-10}$ ,GMMREG在配准中最小化后的L2距离很难达到该标准.本文算法仅需要17次迭代就可以完成配准.

此外,我们也调查了本文算法在不同能量权重调节参数设定下的收敛范围.图 10给出了在Chinese character点阵形变实验中的例子.对于每一个能量权重调节参数设定值,我们在每一个形变级别下运行了100次随机实验.基于图 10展示的实验结果,随着调节初始值T_init降低为默认值的 $1/10$ 时,本文算法的性能发生了轻微的退化,配准所需迭代次数减少了 $41%$ (平均迭代次数从17次减少至10次);随着最终值T_final增加为默认值的10倍时,本文算法的性能发生了退化,配准所需迭代次数减少了 $41%$ (平均迭代次数从17次减少到10 次);随着调节速率r减少为默认值的 $1/2$ ,本文算法的性能轻微退化,配准所需迭代次数减少了 $65%$ (从17次减少至仅需6 次).即便能量权重调节参数被显著地改变了,所有的实验依旧展现了非常高的配准精度(也就是误差低于0.0013且标准偏差在 $\pm 0.0015$ 之内).基于这些结果,本文算法的计算复杂度可以通过调整能量权重调节参数设定大幅降低,同时算法依旧维持了很高的配准精度.

图 10 不同能量权重调节参数设定下的配准性能

Fig. 10 Relationships between performances and different energy tradeoff adjustment parameter settings

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3.6.2 Jonker-Volgenant算法性能

为了使用线性分配技术求解二值对应矩阵M,本文算法使用了Jonker-Volgenant算法^[32],该算法提供了O $(N^{3})$ 的计算复杂度. 我们在一台4GB内存和2.67GHz Intel(R)Xeon(R) CPU的电脑上使用Matlab mex function功能测试了C++代码的Jonker-Volgenant算法性能. 表 4给出了使用Jonker-Volgenant 算法求解不同大小的二值对应矩阵所需时间.Jonker-Volgenant算法展现了快速的求解能力,同时也为本文算法实现快速非刚性点阵配准提供了支撑.

表 4 Jonker-Volgenant 算法性能 (测试矩阵由 Matlab 的 rand 函数自动生成.)

Table 4 Performance of Jonker-Volgenant algorithm (The cost matrices were generated by Matlab rand function.)

矩阵大小	200	500	1 000	2 000	3 000
所需时间 (秒)	0.002	0.016	0.100	0.316	0.588

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4. 结论

我们已经介绍了一种基于混合特征的非刚性点阵配准算法:1) 设计出了一种基于和向量特征的全局结构特征描述算法;2) 提出了一种利用点阵之间的局部区域相邻点的距离和描述点阵中各点的局部结构特征的描述算法;3) 提出一种基于混合特征的能量方程并设计了该方程的能量权重调节,该方程允许使用混合特征进行点阵对应评估.最后将本文算法与8种当前典型算法进行了性能对比测试,本文算法在绝大多数的形变和旋转配准情况中展现了最好的配准结果.

致谢: 感谢Chui Hai-Li,Rangarajan Anand,Myronenko Andriy,Song Xu-Bo,Jian Bing,Vemuri Baba,Zhou Feng,De la Torre Fernando,Leordeanu Marius,Torresani Lorenzo 和 Caetano Tiberio 提供了他们的算法源代码和测试数据. 这极大地促进了对比实验.我们无偿提供本文算法的Matlab源代码供学术研究.

图 1 基于视觉的目标检测与跟踪框架

Fig. 1 General framework of vision-based object detection and tracking

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图 2 基于背景建模的目标检测流程图

Fig. 2 Flow chart of object detection based on background modeling

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图 3 基于目标建模的目标检测流程图

Fig. 3 Flow chart of object detection based on object modeling

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图 4 限制玻尔兹曼机

Fig. 4 Restricted Boltzmann machine

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图 5 基于自编码机的特征表达

Fig. 5 Feature representation based on auto-encoder

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图 6 单层卷积神经网络

Fig. 6 Single layer convolutional neural network

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图 7 基于单层卷积神经网络的特征表达

Fig. 7 Feature representation based on single layer CNN

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图 8 运动目标跟踪一般流程

Fig. 8 Flow chart of moving object tracking

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表 1 基于视觉的目标检测与跟踪应用领域

Table 1 Applications of vision-based object detection and tracking

应用领域	具体应用
智能监控	公共安全监控(犯罪预防、人流密度检测)、停车场、超市、百货公司、自动售货机、ATM、小区(外来人员访问控制)、交通场景、家庭环境(老幼看护)等
虚拟现实	交互式虚拟世界、游戏控制、虚拟工作室、角色动画、远程会议等
高级人机交互	手语翻译、基于手势的控制、高噪声环境(机场、工厂等)下的信息传递等
动作分析	基于内容的运动视频检索, 高尔夫、网球等的个性化训练, 舞蹈等的编排, 骨科患者的临床研究等
自主导航	车辆导航、机器人导航、太空探测器的导航等
机器人视觉	工业机器人、家庭服务机器人、餐厅服务机器人、太空探测器等

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表 2 目标检测与跟踪相关综述文献

Table 2 Related surveys about object detection and tracking

文献	题目	主要内容	讨论主题	发表年限	不足之处
[8]	Vision based hand gesture recognition for human computer interaction: a survey	从检测、跟踪与识别三方面对手势识别的发展现状进行了梳理与总结	检测、跟踪、识别	2015	只进行了某些具体应用方向上的梳理
[9]	A survey on recent object detection techniques useful for monocular vision-based planetary terrain classification	对行星地形分类中的目标检测技术进行了总结	目标检测	2014	只进行了某些具体应用方向上的梳理
[10]	Sparse coding based visual tracking: review and experimental comparison	对基于稀疏编码的目标跟踪进行了全面的梳理与总结, 给出了实验对比与分析	表观建模	2013	只讨论了目标检测与跟踪的组成部分
[11]	A survey of appearance models in visual object tracking	从全局与局部信息描述的角度探讨了目标跟踪中的视觉表达问题	表观建模	2013
[12]	面向目标检测的稀疏表示方法研究进展	综述了稀疏表示方法在目标检测领域中的国内外重要研究进展	表观建模	2015
[13]	Background subtraction techniques: a review	对几种常用的背景减除方法进行了总结	背景建模	2004
[14]	Traditional and recent approaches in background modeling for foreground detection: an overview	对目标检测中背景建模方法进行了详细讨论	背景建模	2014
[15]	Visual tracking: an experimental survey	对19种先进的跟踪器在315段视频序列上进行了对比实验与性能评估	目标跟踪	2014
[16]	Automated human behavior analysis from surveillance videos: a survey	在人体行为理解的底层处理部分, 对目标检测、分类及其跟踪进行了详细阐述	人体行为理解	2014	没有展开讨论检测跟踪问题
[17]	智能视频监控技术综述	在智能视频监控的底层部分, 对目标检测与跟踪进行了讨论	智能监控	2015	没有展开讨论检测跟踪问题
[18]	Object tracking: a survey	对目标跟踪中的目标表达、特征或运动模型选取等问题进行了分类归纳	目标跟踪	2006	发表年限比较久远, 不断更新的理论和方法亟需梳理总结
[19]	视觉跟踪技术综述	分类归纳了视觉跟踪, 并论述了其在视频监控、图像压缩和三维重构等的应用	目标跟踪	2006
[20]	运动目标检测算法的探讨	对2007年以前的主流运动目标检测方法进行了分类讨论	目标检测	2006
[21]	运动目标跟踪算法研究综述	将运动目标跟踪问题分为运动检测与目标跟踪, 并对跟踪算法进行了综述工作	目标跟踪	2009
[22]	微弱运动目标的检测与跟踪识别算法研究	对强噪声背景下的微弱运动目标检测与跟踪算法进行了探讨	目标检测与跟踪	2010

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表 3 基于人工设计的特征表达方法

Table 3 Human-engineering-based feature representation methods

序号	文献	典型算法	主要思想	提出年限	方法类别
1	[4]	SIFT	通过获取特定关键点附近的梯度信息来描述运动目标, 具有旋转、尺度不变等优良特性, 其改进特征主要有PCA-SIFT^[49]、GLOH^[50]、SURF^[51]、DAISY^[52]等	2004	梯度特征
2	[5]	HOG	通过计算空间分布区域的梯度强度及其方向信息来描述运动目标, 其改进特征主要有v-HOG^[53]、CoHOG^[54]、GIST^[55]等	2005	梯度特征
3	[56]	Gabor	利用Gabor滤波器对图像卷积得到, 在一定程度上模拟了人类视觉的细胞感受野机制	1997	模式特征
4	[57]	LBP	通过计算像素点与周围像素的对比信息, 获得的一种对光照不变的局部描述, 其改进特征主要有CS-LBP^[58]、NR-LBP^[59]等	2004
5	[60]	Haar-like	通过计算相邻矩形区域的像素和之差来描述线性、边缘、中心点以及对角线特征, 其改进特征主要有LAB^[66]等	2001
6	[6]	DPM	其实质是一种弹性形状模型, 是通过将梯度直方图(HOG)特征与Latent SVM相结合而训练得到的一种目标形状描述模型	2010	形状特征
7	[69]	Shape context	通过获取形状上某一参考点与其余点的距离分布来描述目标轮廓	2002
8	[71]	kAS	使用一组近似线性的线段对目标形状进行描述, 具有平移、尺度等不变特性	2008
9	[77]	Color names	通过将图像像素值映射至相应的语义属性来对目标进行描述, 该特征通常包含11种语义属性, 一般需要结合梯度特征一起使用	2009	颜色特征
10	[88]	基于熵的显著性特征	通过计算图像像素的灰度概率分布来获取目标的感兴趣区域	2004	颜色特征

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表 4 基于学习的特征表达方法

Table 4 Learning-based feature representation methods

类别	方法名称
基于深度学习的特征表达	CDBN^[102], SBM^[104], DeCAF^[112], R-CNN^[113], SPPNet^[114], Fast R-CNN^[115], Faster R-CNN^[116], segDeepM^[117], MatchNet^[118], OverFe-at^[121], NIN^[122], GoogLeNet^[123], VGGNet^[124], DeepID Net^[125], Vox-Net^[126], SuperCNN^[127], MDNet^[128], DeepSRDCF^[129], SODLT^[130]

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表 5 目标检测典型数据集

Table 5 Typical data sets for object detection

序号	参考文献	数据集名字	数据规模	是否标注	特点及描述	主页链接	发布时间
1	[139]	MIT CBCL Pedestrian Database	共924张图片, 64 × 128, PPM格式	否	人体目标处于图像正中间, 且图像视角限定为正向或背向	http://cbcl.mit.edu/software-datasets/PedestrianData.html	2000
2	[140-141]	USC Pedestrian Detection Test Set	共359张图片, 816个人	是	包含单视角下无遮挡、部分遮挡以及多视角下无遮挡的行人检测数据	http://iris.usc.edu/Vision-Users/OldUsers/bowu/DatasetWebpage/dataset.html	2005 / 2007
3	[5]	INRIA Person Dataset	共1 805张图片, 64 × 128	是	包含了各种各样的应用背景, 对行人的姿势没有特别的要求	http://pascal.inrialpes.fr/data/human/	2005
4	[45, 142]	ChangeDetection.Net	共51段视频, 约140 000帧图片	是	包含了动态背景、目标运动、夜晚及阴影影响等多种挑战	http://changedetection.net/	2012/2014
5	[143]	Caltech Pedestrian Dataset	10小时视频, 640 × 480	是	视频为城市交通环境下驱车拍摄所得, 行人之间存在一定的遮挡	http://www.vision.caltech.edu/Image_Datasets/CaltechPedestrians/	2009
6	[144]	CVC Datasets	共9个数据集	部分标注	提供了多种应用场景, 如城市、红外等场景, 行人间存在部分遮挡	http://www.cvc.uab.es/adas/site/?q=node/7	2007/2010/2013～2015
7	[119]	PASCAL VOC Datasets	共11540张图, 含20个类	是	该比赛包括分类、检测、分割、动作分类以及人体布局检测等任务	http://host.robots.ox.ac.uk/pascal/VOC/	2005～2012
8	[120]	ImageNet	共14197122张图片	是	大规模目标识别比赛, 包括目标检测、定位以及场景分类等任务	http://image-net.org/	2010～2015
9	[145]	Microsoft COCO	约328000张图片, 含91个类	是	自然场景下的图像分类、检测、场景理解等, 不仅标注了不同的类别, 还对类中个例进行了标注	http://mscoco.org/	2014

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表 6 目标跟踪典型数据集

Table 6 Typical data sets for object tracking

序号	参考文献	数据集	数据规模	是否标注	特点及描述	主页链接	发布时间
1	[209-210]	Visual Tracker Benchmark	100段序列	是	来源于现有文献, 包括了光照及尺度变化、遮挡、形变等9种挑战	http://www.visual-tracking.net	2013
2	[211]	VIVID	9段序列	是	主要任务为航拍视角下的车辆目标跟踪, 具有表观微小、相似等特点	http://vision.cse.psu.edu/data/vividEval/datasets/datasets.html	2005
3	[212]	CAVIAR	28段序列	是	主要用于人体目标跟踪, 视频内容包含行走、会面、进出场景等行为	http://homepages.inf.ed.ac.uk/rbf/CAVIARDATA1/	2003 / 2004
4	[213]	BIWI Walking Pedestrians Dataset	1段序列	是	主要任务为鸟瞰视角下的行人跟踪, 可用于评测多目标跟踪算法	http://www.vision.ee.ethz.ch/datasets/	2009
5	[214]	“Central” Pedestrian Crossing Sequences	3段序列	是	行人过街序列, 每4帧标定一次	http://www.vision.ee.ethz.ch/datasets/	2007
6	[215]	MOT16	14段序列	是	无约束环境的多目标跟踪, 有不同视角、相机运动、天气影响等挑战	http://motchallenge.net/	2016
7	[216]	PETS2015	7段序列	是	关于停车场中车辆旁边不同活动序列, 可用于目标检测与跟踪、动作识别、场景分析等	http://www.pets2015.net/	2015
8	[217]	VOT Challenge	60段序列(2015年)	是	主要用于短视频跟踪算法的评测, 该比赛从2013年开始举办	http://votchallenge.net/	2013～2015

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表 7 典型跟踪算法的性能对比

Table 7 Performance comparison of typical tracking algorithms

序号	参考文献	跟踪器	准确度	平均失败数	平均覆盖率	速度(EFO)	时间	方法类别
1	[128]	MDNet	0.60	0.69	0.38	0.87	2015	CNN
2	[129]	DeepSRDCF	0.56	1.05	0.32	0.38	2015
3	[130]	SODLT	0.56	1.78	0.23	0.83	2015
4	[218]	SumShift	0.52	1.68	0.23	*16.78*	2011	核学习
5	[219]	ASMS	0.51	1.85	0.21	115.09	2013
6	[217]	S3Tracker	0.52	1.77	0.24	14.27	2015
7	[161]	IVT	0.44	4.33	0.12	8.38	2008	子空间学习
8	[220]	CT	0.39	4.09	0.11	12.90	2012	子空间学习
9	[221]	L1APG	0.47	4.65	0.13	1.51	2012	稀疏表示
10	[222]	OAB	0.45	4.19	0.13	8.00	2014	Online Boosting
11	[223]	MCT	0.47	1.76	0.22	2.77	2011
12	[224]	CMIL	0.43	2.47	0.19	5.14	2010
13	[225]	Struck	0.47	1.61	0.25	2.44	2014	SVM
14	[217]	RobStruck	0.48	1.47	0.22	1.89	2015	SVM
15	[226]	MIL	0.42	3.11	0.17	5.99	2011	随机学习

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参考文献(227)

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1. 方法
1.1 全局和局部结构特征差异
1.2 基于混合特征的能量优化方程
1.3 配准过程
1.4 算法伪代码及参数设置
2. 相关研究
3. 实验
3.1 实验设计
3.2 二维轮廓点阵的配准结果
3.3 三维人脸点阵的配准结果
3.4 序列图像的配准结果
3.5 图像特征点的配准结果
3.6 计算复杂度
4. 结论

1. 方法
1.1 全局和局部结构特征差异
1.2 基于混合特征的能量优化方程
1.3 配准过程
1.4 算法伪代码及参数设置
2. 相关研究
3. 实验
3.1 实验设计
3.2 二维轮廓点阵的配准结果
3.3 三维人脸点阵的配准结果
3.4 序列图像的配准结果
3.5 图像特征点的配准结果
3.6 计算复杂度
4. 结论

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基于视觉的目标检测与跟踪综述

doi: 10.16383/j.aas.2016.c150823

通讯作者: 尹宏鹏 重庆大学自动化学院副教授.2009年获得重庆大学博士学位.主要研究方向为模式识别, 图像处理与计算机视觉.本文通信作者.E-mail:yinhongpeng@gmail.com

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出版历程

Vision-based Object Detection and Tracking: A Review

1. 方法

1.1 全局和局部结构特征差异

1.1.1 全局结构特征差异

1.1.2 局部结构特征差异

1.2 基于混合特征的能量优化方程

1.3 配准过程

1.3.1 步骤1:对应关系评估

1.3.2 步骤 2:空间变换更新

1.4 算法伪代码及参数设置

2. 相关研究

3. 实验

3.1 实验设计

3.2 二维轮廓点阵的配准结果

3.2.1 Line

3.2.2 Fish 1

3.2.3 Chinese character

3.2.4 Fish 2

3.3 三维人脸点阵的配准结果

3.4 序列图像的配准结果

3.5 图像特征点的配准结果

3.6 计算复杂度

3.6.1 收敛范围

3.6.2 Jonker-Volgenant算法性能

4. 结论

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目录

1. 方法

1.1 全局和局部结构特征差异

1.2 基于混合特征的能量优化方程

1.3 配准过程

1.4 算法伪代码及参数设置

2. 相关研究

3. 实验

3.1 实验设计

3.2 二维轮廓点阵的配准结果

3.3 三维人脸点阵的配准结果

3.4 序列图像的配准结果

3.5 图像特征点的配准结果

3.6 计算复杂度

4. 结论

通讯作者:
尹宏鹏重庆大学自动化学院副教授.2009年获得重庆大学博士学位.主要研究方向为模式识别, 图像处理与计算机视觉.本文通信作者.E-mail:yinhongpeng@gmail.com