发布时间: 2018-05-16 摘要点击次数: 全文下载次数: DOI: 10.11834/jig.170083 2018 | Volume 23 | Number 5 图像分析和识别

 收稿日期: 2017-03-22; 修回日期: 2017-11-14 基金项目: 国家自然科学基金项目（51365052） 第一作者简介: 亚森江·木沙(1972-), 男, 讲师, 2017年于南京理工大学获计算机应用技术博士学位, 主要研究方向为计算机视觉与模式识别、数字图象处理。E-mail:yasin.xjedu@gmail.com. 中图法分类号: TP391 文献标识码: A 文章编号: 1006-8961(2018)05-0674-14

# 关键词

Object tracking algorithm based on matrix low-rank representation
Yasin Musa, Muhtar Kerim
School of Mechanical Engineering, Xinjiang University, Urumqi 830046, China
Supported by: National Natural Science Foundation of China (51365052)

# Abstract

Objective Visual object tracking is a significant computer vision task that can be applied to many domains, such as military, robotics, intelligent visual surveillance, human-computer interaction, and medical diagnosis. A large variety of trackers that have been proposed in the literature in the past decades have delivered satisfactory performances. Despite the success of researching on this topic, visual object tracking still suffers from difficulties in handling complex object appearance changes caused by factors such as illumination, partial occlusion, shape deformation, background clutter, low contrast, specularities, camera motion, and at least seven more aspects. Generally, visual tracking is a search (or classification) problem that continuously infers the state of a target in video sequences, aims to identify the candidate while it matches to the target template accurately, and returns it as a tracking result. Constructing an effective and high-performance tracker has two core issues. The first is the issue of representative feature learning and high-level modeling. The second is the problem of filtering and efficient searching. Given that the target states in every video frame are represented using several online learned feature templates, the modeling capability of the tracker will significantly depend on the generalizability of template data and accurate model representation with error estimation precision because of the complex interference factors caused by the target itself or the scene conditions. In addition, the relationship between each data pixel is significantly damaged while its original data structures are being changed because the sample data are intentionally forced into vector form in most existing algorithms. Moreover, the computational complexity with high data dimensionality must be increased. Therefore, designing an effective model representation mechanism of the 2D appearance of moving objects with the appropriate data expression is the key issue for the success of a visual tracker. Method In this study, the appearance model representation problem of generative-model-based visual object tracking algorithm is investigated in depth. In a prior work, we formulated the observation model via tensor (3D array) nuclear norm regularization. The tracker is called tensor nuclear norm regression-based tracker (TNRT) and has achieved favorable results in many tracking environments. However, the TNRT requires high hardware conditions and graphics processing unit computing demands, which will lead to slow tracking speeds if some practical uses require low hardware conditions. Therefore, we redesign a novel matrix low-rank representation-based observation model and its corresponding likelihood measurement function, as well as maintain several good properties of the TNRT algorithm, such as multitask joint learning, nuclear norm regularization-based model representation, and original data structures of sample signals. In the proposed tracking framework, several critical feature templates (dictionary or subspace) are learned from online data using the incremental principal component analysis algorithm. Then, in accordance with the appearance information of an incoming video frame, the proposed appearance modeling mechanism will use the feature templates to represent the target candidate linearly with independent and identically distributed Gaussian-Laplacian mixture noise by adopting the multitask joint learning strategy. Subsequently, the matrix nuclear norm and weighted ${\rm L}_1$-norm-based joint maximum likelihood function measure the distances between target candidates and feature subspace scrupulously. Given that the intrinsic data structures of samples are guaranteed using the matrix form and the spatial distributions of visual features remain intact, the proposed multitask observation modeling via matrix low-rank regularization-based objective function will construct more accurate and flexible sample signals than ${\rm L}_1$, ${\rm L}_2$, or other hybrid regularization-based model representation methods. Then, in every frame, the identical likelihood measurement function of our algorithm measures each candidate sample with obvious comparability. Finally, the tracker is able to explore the potential characteristics of the sample data fully and further detect the complex appearance changes of the target with some challenging disturbances, such as occlusion or strong illuminations. Meanwhile, the observation model, which formulates matrix-form-based data prototypes, can improve the tracking speed remarkably with its distinctly reduced data dimensionality and low computational complexity. Result Although the pixels of residual data always show similar grayscale intensities and share some spatial information with 2D data prototypes, such as block-shaped linking areas, the conventional observation model using ${\rm L}_1$, ${\rm L}_2$, or other hybrid regularization-based model representation methods cannot fully examine the potential structure of residual data. In comparison to these traditional methods, the matrix low-rank regression model (MLRM) more precisely explores the residual data and further detects the spatial characteristics of reconstruction error. In other words, the MLRM significantly discovers the low-rank characteristics of the residual matrix. In this study, we aim to evaluate our proposed tracking algorithm systematically and experimentally on 10 public video fragments that cover the previously mentioned challenging noisy factors and compare it with several state-of-the-art algorithms commonly cited in influential literature. We indicate that each tracker can be evaluated objectively using survival curves, such as average center point error (ACE), average overlap rate (AOR), and average success rate (ASR). Our tracking algorithm reflects the favorable robustness in these noisy environments and obtains the best results in each video sequence, with ACE, AOR, and ASR of 5.29 pixels, 78%, and 98.28%, respectively. Conclusion In this study, a novel multitask matrix low-rank model representation method and its corresponding maximum likelihood estimation function are designed. The analysis of a large variety of circumstances in several public video sequences provides objective insight into the strengths and weaknesses of each tracker. The appearance modeling mechanism and maximum likelihood estimation function of the proposed MLRM algorithm play critical roles and achieve favorable tracking results in several challenging video sequences. Qualitative and quantitative experimental evaluations of a number of challenging noisy environments indicate that the proposed MLRM algorithm can reflect the best robustness to elevate the model degradation or drifting problem caused by occlusion and strong illumination and can achieve the same or even better results when compared with several state-of-the-art algorithms.

# Key words

data prototypes; matrix low-rank representation; multi-task; observation modeling; likelihood estimation; object tracking

# 0 引言

1) 将观测建模常见的样本数据向量化表示机制转化为2维矩阵，使得观测信号与候选样本的原始数据结构保持一致。这比三阶张量的数据结构简单，且还能简化算法复杂度和资源开销；

2) 设计一种矩阵低秩回归观测模型及其相应的目标似然度估计函数，完美保留TNRM模型优秀的多任务观测建模特性；

# 1.1 基于矩阵低秩回归的观测模型

 $\mathit{\boldsymbol{\bar y}} = ts\left( {\mathit{\boldsymbol{UX}}} \right) + {\varepsilon _1} + {\varepsilon _2}$ (1)

 $\begin{array}{*{20}{c}} {\mathop {\min }\limits_{{\varepsilon _1},{\varepsilon _2},\mathit{\boldsymbol{X}}} {{\left\| {{\mathit{\boldsymbol{\varepsilon }}_1}} \right\|}_ * } + {\lambda _1}{{\left\| {{\mathit{\boldsymbol{\varepsilon }}_2}} \right\|}_1} + {\lambda _2}{{\left\| \mathit{\boldsymbol{X}} \right\|}_{2,1}}}\\ {{\rm{s}}.\;{\rm{t}}.\;\mathit{\boldsymbol{\bar y}} = ts\left( {\mathit{\boldsymbol{UX}}} \right) + {\mathit{\boldsymbol{\varepsilon }}_1} + {\mathit{\boldsymbol{\varepsilon }}_2}} \end{array}$ (2)

 ${{\mathit{\boldsymbol{\bar Z}}}_i} = mat\left( {\mathit{\boldsymbol{Ux}}} \right) + \mathit{\boldsymbol{E}}_1^i + \mathit{\boldsymbol{E}}_2^i$ (3)

 $\begin{array}{*{20}{c}} {\mathop {\min }\limits_{{\mathit{\boldsymbol{E}}_1},{\mathit{\boldsymbol{E}}_2},\mathit{\boldsymbol{x}}} {{\left\| {{\mathit{\boldsymbol{E}}_1}} \right\|}_ * } + {\lambda _1}{{\left\| {{\mathit{\boldsymbol{E}}_2}} \right\|}_1} + \frac{{{\lambda _2}}}{2}{{\left\| \mathit{\boldsymbol{x}} \right\|}_2^2}}\\ {{\rm{s}}.\;{\rm{t}}.\;\mathit{\boldsymbol{\bar Z}} = mat\left( {\mathit{\boldsymbol{Ux}}} \right) + {\mathit{\boldsymbol{E}}_1} + {\mathit{\boldsymbol{E}}_2}} \end{array}$ (4)

# 1.2 目标函数参数的优化

 $\begin{array}{*{20}{c}} {{L_\mu }\left( {{\mathit{\boldsymbol{E}}_1},{\mathit{\boldsymbol{E}}_2},\mathit{\boldsymbol{x}},\mathit{\boldsymbol{\varphi }}} \right) = }\\ {{{\left\| {{\mathit{\boldsymbol{E}}_1}} \right\|}_ * } + {\lambda _1}{{\left\| {{\mathit{\boldsymbol{E}}_2}} \right\|}_1} + \frac{{{\lambda _2}}}{2}\left\| \mathit{\boldsymbol{x}} \right\|_2^2 + }\\ {{\rm{tr}}\left[ {{\mathit{\boldsymbol{\varphi }}^{\rm{T}}}\left( {\mathit{\boldsymbol{\bar Z}} - {\rm{mat}}\left( {\mathit{\boldsymbol{Ux}}} \right) - {\mathit{\boldsymbol{E}}_1} - {\mathit{\boldsymbol{E}}_2}} \right)} \right] + }\\ {\frac{{\rm{ \mathsf{ μ} }}}{2}\left\| {\mathit{\boldsymbol{\bar Z}} - {\rm{mat}}\left( {\mathit{\boldsymbol{Ux}}} \right) - {\mathit{\boldsymbol{E}}_1} - {\mathit{\boldsymbol{E}}_2}} \right\|_{\rm{F}}^2} \end{array}$ (5)

 $\begin{array}{*{20}{c}} {{L_\mu }\left( {{\mathit{\boldsymbol{E}}_1},{\mathit{\boldsymbol{E}}_2},\mathit{\boldsymbol{x}},\mathit{\boldsymbol{\varphi }}} \right) = {{\left\| {{\mathit{\boldsymbol{E}}_1}} \right\|}_ * } + {\lambda _1}{{\left\| {{\mathit{\boldsymbol{E}}_2}} \right\|}_1} + \frac{{{\lambda _2}}}{2}\left\| \mathit{\boldsymbol{x}} \right\|_2^2 + }\\ {\frac{\mu}{2}\left\| {\mathit{\boldsymbol{\bar Z}} - {\rm{mat}}\left( {\mathit{\boldsymbol{Ux}}} \right) - {\mathit{\boldsymbol{E}}_1} - {\mathit{\boldsymbol{E}}_2} + \frac{\mathit{\boldsymbol{\varphi }}}{\mu }} \right\|_{\rm{F}}^2 - \frac{{\left\| \mathit{\boldsymbol{\varphi }} \right\|_{\rm{F}}^2}}{{2\mu }}} \end{array}$ (6)

 $\mathop {\min }\limits_{{\mathit{\boldsymbol{E}}_1},{\mathit{\boldsymbol{E}}_2},\mathit{\boldsymbol{x}},\mathit{\boldsymbol{\varphi }}} {L_\mu }\left( {{\mathit{\boldsymbol{E}}_1},{\mathit{\boldsymbol{E}}_2},\mathit{\boldsymbol{x}},\mathit{\boldsymbol{\varphi }}} \right)$ (7)

 $\mathit{\boldsymbol{X}} * = {D_\mu }\left( \mathit{\boldsymbol{Q}} \right) = \mathit{\boldsymbol{U}}\left[ {\max \left( {\mathit{\boldsymbol{S}} - \mu \mathit{\boldsymbol{I}},0} \right)} \right]{\mathit{\boldsymbol{V}}^{\rm{T}}}$ (8)

1) 初始化：${{\mathit{\boldsymbol{x}}}^{\rm{0}}}\rm{=0, }{{\mathit{\boldsymbol{ \varphi}} }^{\rm{0}}}\rm{=0, }\mathit{\boldsymbol{E}}_{1}^{\rm{0}}\rm{=0, }\mathit{\boldsymbol{E}}_{2}^{\rm{0}}\rm{=0, \mathsf{ μ}} \rm{ =0}\rm{.1}, {{\mathit{\mu }}_{\rm{max}}}\rm{=1}{{\rm{0}}^{\rm{6}}}\rm{, }\mathit{\rho }\rm{=10, }\mathit{k}\rm{=0}$

2) 迭代开始：

While not converged and $k<k_{\rm max}$ do

3) 令其他变量固定不变，求解$\mathit{\boldsymbol{x}}$

 ${\mathit{\boldsymbol{x}}^{k + 1}} = \frac{1}{{1 + \frac{{{\lambda _2}}}{\mu }}}{\mathit{\boldsymbol{U}}^{\rm{T}}} \cdot vec\left( {{{\mathit{\boldsymbol{\bar Z}}}_i} - \mathit{\boldsymbol{E}}_1^{\rm{k}} - \mathit{\boldsymbol{E}}_2^{\rm{k}} + \frac{{{\mathit{\boldsymbol{\varphi }}^{\rm{k}}}}}{\mu }} \right)$

4) 令其他变量固定不变，求解$\mathit{\boldsymbol{E}}_1$

 $\begin{array}{*{20}{c}} {\mathit{\boldsymbol{E}}_1^{{\rm{k}} + 1} = \mathop {\min }\limits_{{\mathit{\boldsymbol{E}}_1}} \frac{1}{\mu }{{\left\| {\mathit{\boldsymbol{E}}_1^{\rm{k}}} \right\|}_ * } + }\\ {\frac{1}{2}\left\| {\mathit{\boldsymbol{E}}_2^{\rm{k}} - \left[ {{{\mathit{\boldsymbol{\bar Z}}}_i} - mat\left( {\mathit{\boldsymbol{U}}{\mathit{\boldsymbol{x}}^{{\rm{k}} + 1}}} \right)} \right] - \mathit{\boldsymbol{E}}_1^{\rm{k}} + \frac{{{\mathit{\boldsymbol{\varphi }}^{\rm{k}}}}}{\mu }} \right\|_{\rm{F}}^2} \end{array}$

5) 令其他变量固定不变，对$\mathit{\boldsymbol{E}}_2$求解

 $\begin{array}{*{20}{c}} {\mathit{\boldsymbol{E}}_2^{{\rm{k}} + 1} = \mathop {\min }\limits_{{\mathit{\boldsymbol{E}}_2}} \frac{{{\lambda _1}}}{\mu }{{\left\| {\mathit{\boldsymbol{E}}_2^{\rm{k}}} \right\|}_1} + }\\ {\frac{1}{2}\left\| {\mathit{\boldsymbol{E}}_2^{\rm{k}} - \left[ {{{\mathit{\boldsymbol{\bar Z}}}_i} - mat\left( {\mathit{\boldsymbol{U}}{\mathit{\boldsymbol{x}}^{{\rm{k}} + 1}}} \right)} \right] - \mathit{\boldsymbol{E}}_1^{\rm{k}} + \frac{{{\mathit{\boldsymbol{\varphi }}^{\rm{k}}}}}{\mu }} \right\|_{\rm{F}}^2} \end{array}$

6) 令其他变量固定不变，求解拉格朗日乘子

 ${\mathit{\boldsymbol{\varphi }}^{{\rm{k + 1}}}} = {\mathit{\boldsymbol{\varphi }}^{\rm{k}}} + \mu \left[ {\left( {{{\mathit{\boldsymbol{\bar Z}}}_i} - \mathit{\boldsymbol{U}}{\mathit{\boldsymbol{x}}^{{\rm{k}} + 1}}} \right) - \mathit{\boldsymbol{E}}_1^{{\rm{k + 1}}} - \mathit{\boldsymbol{E}}_2^{{\rm{k + 1}}}} \right]$

7) 更新参数$\mathit{\mu }\ \rm{:}\ \mathit{\mu }\rm{=min(}\mathit{\rho \mu }\rm{, }{{\mathit{\mu }}_{\rm{max}}}\rm{)}$

8) 检查收敛条件

 ${\left\| {{{\mathit{\boldsymbol{\bar Z}}}_i} - mat\left( {\mathit{\boldsymbol{U}}{\mathit{\boldsymbol{x}}^{{\rm{k}} + 1}}} \right) - \mathit{\boldsymbol{E}}_1^{k + 1} - \mathit{\boldsymbol{E}}_2^{k + 2}} \right\|_\infty } < \xi$

9) 更新$k:k=k+1$

end while

10)迭代结束。

# 1.3 计算复杂度及参数影响分析

 $d\left( {\mathit{\boldsymbol{\bar Z}};{\mathit{\boldsymbol{E}}_1},{\mathit{\boldsymbol{E}}_2}} \right) = {\left\| {{\mathit{\boldsymbol{E}}_1}} \right\|_ * } + {\lambda _1}{\left\| {{\mathit{\boldsymbol{E}}_2}} \right\|_1}$ (12)

 $p\left( {{\mathit{\boldsymbol{Z}}_t}\left| {{\mathit{\boldsymbol{S}}_t}} \right.} \right) = \max \ {{\rm{e}}^{ - \gamma d\left( {\mathit{\boldsymbol{\bar Z}};{\mathit{\boldsymbol{E}}_1},{\mathit{\boldsymbol{E}}_2}} \right)}}$ (13)

# 3 实验与分析

Table 2 Testing video sequences and it's challenging factors

 视频名称 干扰因素 目标遮挡 光照变化 尺度变化 姿态变化 旋转变化 视角变化 画面晃动 运动模糊 运动突变 相似目标 背景杂乱 Occlusion2 重 轻 轻 中 轻 Caviar3 重 中 微 有 Deer 轻 轻 轻 重 重 有 重 Jumping 重 重 重 轻 DavidIndoorNew 轻 重 中 重 中 轻 轻 轻 DavidOutdoor 重 中 轻 轻 Owl 重 重 重 重 Face 中 轻 中 重 Car4 重 中 轻 轻 轻 Football 重 轻 中 中 中 有 重

# 3.1 实验条件及评估准则

1) 假设某一测试视频的总长为$T$，其每一帧的索引号用$t$表示($t=1, 2, \cdots , T$)，测试视频某一帧中目标区域实际中心点为$\mathit{G}_{\mathit{x}, \mathit{y}}^{\mathit{t}}$，跟踪中心点为$\mathit{O}_{\mathit{x}, \mathit{y}}^{\mathit{t}}$，那么在t时刻的跟踪中心点误差(CE)可以用这两点之间的欧氏距离来度量，即

 $C{E_t} = {\left\| {O_{x,y}^t - G_{x,y}^t} \right\|_2}$ (14)

 $ACE = \frac{1}{T}\sum\limits_{t = 1}^T {C{E_t}}$ (15)

2) 假设$R_t^O$是某一视频帧中t时刻所跟踪到的目标像素区域，$R_t^G$是目标在此帧中的实际像素区域，那么t时刻的跟踪重叠率为

 $O{R_t} = \frac{{\mathit{\boldsymbol{R}}_t^G \cap \mathit{\boldsymbol{R}}_t^O}}{{\mathit{\boldsymbol{R}}_t^G \cap \mathit{\boldsymbol{R}}_t^O}}$ (16)

 $AOR = \frac{1}{T}\sum\limits_{t = 1}^T {O{R_t}}$ (17)

3) 假设跟踪算法在长度为$T$的某一测试视频中成功跟踪到的总帧数记为$M$，那么算法在此视频的平均跟踪成功率计算公式为

 $ASR = M/T$ (18)

# 3.2 实验结果定量分析

Table 3 Average center point error of each algorithms in some video sequences

 视频 IVT[1] SCM[3] MTT[4] OSPT[14] ASLAS[13] LSST[2] TNRM[9] 本文 Occlusion2 5.14 4.54 7.79 4.04 3.06 3.3 3.17 3.05 Caviar3 62.75 62.15 66.92 4.36 2.17 3.07 3.00 4.03 DavidOutdoor 50.66 77.12 376.12 5.76 87.51 6.44 5.27 4.67 DavidIndoorNew 2.83 30.44 12.48 3.21 2.81 3.15 4.27 2.78 Car4 2.99 78.29 8.82 3.03 5.80 2.87 2.77 2.68 Owl 126.66 6.81 179.2 47.44 7.96 6.2 6.49 5.64 Jumping 10.61 3.88 53.76 5.01 6.02 4.77 4.38 4.48 Face 13.67 11.88 150.18 24.11 11.58 12.34 9.37 12.07 Deer 16.46 10.41 9.80 8.60 6.35 10.03 7.93 8.23 Football 5.76 11.06 6.87 33.71 17.24 7.57 4.95 5.31 总平均值 29.75 29.66 87.19 13.93 15.05 5.97 5.16 5.29 注：加粗字体为最优结果。

Table 4 Average overlap rate of each algorithms in some video sequences

 视频 IVT[1] SCM[3] MTT[4] OSPT[14] ASLAS[13] LSST[2] TNRM[9] 本文 Occlusion2 0.80 0.82 0.72 0.84 0.82 0.84 0.86 0.86 Caviar3 0.14 0.15 0.14 0.81 0.85 0.85 0.85 0.84 DavidOutdoor 0.56 0.51 0.10 0.77 0.45 0.76 0.77 0.78 DavidIndoorNew 0.76 0.45 0.54 0.76 0.75 0.72 0.74 0.77 Car4 0.92 0.36 0.63 0.92 0.87 0.92 0.92 0.93 Owl 0.22 0.80 0.09 0.48 0.76 0.81 0.80 0.82 Jumping 0.57 0.72 0.07 0.69 0.69 0.65 0.67 0.70 Face 0.74 0.77 0.24 0.68 0.75 0.76 0.80 0.78 Deer 0.54 0.60 0.61 0.61 0.66 0.57 0.62 0.60 Football 0.74 0.69 0.73 0.62 0.60 0.69 0.77 0.75 总平均值 0.60 0.59 0.39 0.72 0.72 0.76 0.78 0.78 注：加粗字体为最优结果。

Table 5 Averagesuccess rate of each algorithms in some video sequences

 视频 IVT[1] SCM[3] MTT[4] OSPT[14] ASLAS[13] LSST[2] TNRM[9] 本文 Occlusion2 98.79 98.79 92.12 99.7 98.23 98.79 100 100 Caviar3 15.80 15.80 15.20 99.60 99 99.80 98.87 99.80 DavidOutdoor 71.83 65.08 10.71 97.22 51.19 95.63 98.43 96.43 DavidIndoorNew 96.86 51.87 58.74 96.86 96.86 96.41 97.71 96.71 Car4 100 40.15 65.15 100 100 100 100 100 Owl 27.62 97.62 9.21 57.46 97.78 99.52 99.52 99.72 Jumping 82.75 98.72 5.11 95.53 94.25 93.93 98.72 98.40 Face 100 100 26.22 91.87 100 99.80 99.80 100 Deer 66.20 88.73 85.92 84.51 90.14 80.28 92.51 91.73 Football 97.51 83.15 97.24 76.52 75.69 88.12 100 100 总平均值 75.74 73.99 46.56 89.93 90.31 95.23 98.56 98.28 注：加粗字体为最优结果。

# 3.3 实验结果定性分析

1) 局部或完全遮挡。遮挡对跟踪算法性能的影响非常严重，所以在此挑选如图 6所示的富有挑战性测试视频，并展示目标在经历局部或完全遮挡时的跟踪结果。其中，目标除了遭受不同程度的遮挡干扰，还会遇到目标旋转、轻微光照变化、尺度变化、姿态变化、视角变化，以及小尺寸目标等多种干扰。

2) 姿态和光照变化。图 7展示了目标在几款测试视频中受到光照变化或姿态变化时的跟踪结果。光照变化是跟踪建模中影响跟踪性能的第二大干扰噪声。由于其有时候严重破坏目标图像区域的原有机理，从中学习具有代表意义的特征显得十分困难，这对目标外观的有效观测建模带来极大的挑战。这3种测试视频除了包含不同程度的光照噪声干扰外，还有目标旋转、尺度及姿态变化等噪声。其中，DavidIndoorNew主要考核跟踪算法对光照变化、姿态及旋转等变化的适应性，而Car4则考察跟踪算法在室外环境下对光照和尺度变化的鲁棒性。

3) 背景混乱与相似目标。图 8展示了目标在几款测试视频中受到背景混乱等噪声干扰时的跟踪结果。

4) 运动突变与运动模糊。图 9展示了目标在几款测试视频中受到快速运动、摄影机晃动及运动模糊等噪声干扰时的跟踪结果。这些测试视频中，目标自身快速运动或摄影机晃动等原因目标图像区域普遍产生十分模糊的情况。由于这种噪声往往严重破坏目标的有用特征，这使得跟踪中在线学习良好的目标特征并对不断变化的目标外观有效建模变得十分困难。

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