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一种用于目标跟踪边界框回归的光滑IoU损失

李功 赵巍 刘鹏 唐降龙

李功, 赵巍, 刘鹏, 唐降龙. 一种用于目标跟踪边界框回归的光滑IoU损失. 自动化学报, 2023, 49(2): 288−306 doi: 10.16383/j.aas.c210525
引用本文: 李功, 赵巍, 刘鹏, 唐降龙. 一种用于目标跟踪边界框回归的光滑IoU损失. 自动化学报, 2023, 49(2): 288−306 doi: 10.16383/j.aas.c210525
Li Gong, Zhao Wei, Liu Peng, Tang Xiang-Long. Smooth-IoU loss for bounding box regression in visual tracking. Acta Automatica Sinica, 2023, 49(2): 288−306 doi: 10.16383/j.aas.c210525
Citation: Li Gong, Zhao Wei, Liu Peng, Tang Xiang-Long. Smooth-IoU loss for bounding box regression in visual tracking. Acta Automatica Sinica, 2023, 49(2): 288−306 doi: 10.16383/j.aas.c210525

一种用于目标跟踪边界框回归的光滑IoU损失

doi: 10.16383/j.aas.c210525
基金项目: 国家自然科学基金(51935005), 基础科研项目(JCKY20200603C010), 空间智能控制技术重点实验室基金(ZDSYS-2018-02)资助
详细信息
    作者简介:

    李功:哈尔滨工业大学模式识别与智能系统研究中心博士研究生. 分别于2015年和2018年获得哈尔滨工业大学学士和硕士学位. 主要研究方向为计算机视觉中的目标跟踪, 模式识别. E-mail: ligong101@126.com

    赵巍:哈尔滨工业大学副教授. 主要研究方向为模式识别, 机器学习和计算机视觉. 本文通信作者.E-mail: zhaowei@hit.edu.cn

    刘鹏:哈尔滨工业大学教授. 2007 年获得哈尔滨工业大学博士学位. 主要研究方向为图像处理, 视频分析, 模式识别和大规模集成电路设计. E-mail: pengliu@hit.edu.cn

    唐降龙:哈尔滨工业大学教授. 1995年获得哈尔滨工业大学博士学位. 主要研究方向为模式识别, 图像处理和机器学习. E-mail: tangxl@hit.edu.cn

Smooth-IoU Loss for Bounding Box Regression in Visual Tracking

Funds: Supported by National Natural Science Foundation of China (51935005), Basic Scientific Research Projects (JCKY20200603C010), and Mutual Fund of Space Intelligent Control Technology Key Laboratory (ZDSYS-2018-02)
More Information
    Author Bio:

    LI Gong Ph.D. candidate at the Pattern Recognition and Intelligent System Research Center, Harbin Institute of Technology. He received his bachelor and master degrees from Harbin Institute of Technology in 2015 and 2018, respectively. His research interest covers target tracking in computer vision and pattern recognition

    ZHAO Wei Associate professor at Harbin Institute of Technology. Her research interest covers pattern recognition, machine learning, and computer vision. Corresponding author of this paper

    LIU Peng Professor at Harbin Institute of Technology. He received his Ph.D. degree from Harbin Institute of Technology in 2007. His research interest covers image processing, video analysis, pattern recognition, and design of large scale integrated circuits

    TANG Xiang-Long Professor at Harbin Institute of Technology. He received his Ph.D. degree from Harbin Institute of Technology in 1995. His research interest covers pattern recognition, image processing, and machine learning

  • 摘要: 边界框回归分支是深度目标跟踪器的关键模块, 其性能直接影响跟踪器的精度. 评价精度的指标之一是交并比(Intersection over union, IoU). 基于IoU的损失函数取代了$ \ell_n $-norm损失成为目前主流的边界框回归损失函数, 然而IoU损失函数存在2个固有缺陷: 1)当预测框与真值框不相交时IoU为常量 0, 无法梯度下降更新边界框的参数; 2)在IoU取得最优值时其梯度不存在, 边界框很难收敛到 IoU 最优处. 揭示了在回归过程中IoU最优的边界框各参数之间蕴含的定量关系, 指出在边界框中心处于特定位置时存在多种尺寸不同的边界框使IoU损失最优的情况, 这增加了边界框尺寸回归的不确定性. 从优化两个统计分布之间散度的视角看待边界框回归问题, 提出了光滑IoU (Smooth-IoU, SIoU)损失, 即构造了在全局上光滑(即连续可微)且极值唯一的损失函数, 该损失函数自然蕴含边界框各参数之间特定的最优关系, 其唯一取极值的边界框可使IoU达到最优. 光滑性确保了在全局上梯度存在使得边界框更容易回归到极值处, 而极值唯一确保了在全局上可梯度下降更新参数, 从而避开了IoU损失的固有缺陷. 提出的光滑损失可以很容易取代IoU损失集成到现有的深度目标跟踪器上训练边界框回归, 在 LaSOT、GOT-10k、TrackingNet、OTB2015和VOT2018测试基准上所取得的结果, 验证了光滑IoU损失的易用性和有效性.
  • 图  1  深度目标跟踪模型的边界框回归示意图

    Fig.  1  The schematic of bounding box regression in deep tracking model

    图  2  边界框类比为正态分布的示意图

    Fig.  2  The schematic of bounding box analogized as Gaussian distribution

    图  3  ${\cal{L}}_{{\rm{IoU}}}$${\cal{L}}_{{\rm{SIoU}}}$在对数坐标下的可视化图像示例

    Fig.  3  A visualized example of ${\cal{L}}_{{\rm{SIoU}}}$and${\cal{L}}_{{\rm{IoU}}}$viewed in the logarithmic scale of horizontal axis

    图  4  $ d_{\cal{H}}>2 $时最优化${\cal{L}}_{{\rm{SIoU}}}$${\cal{L}}_{{\rm{IoU}}}$的边界框示例

    Fig.  4  Illustration of predicted box that minimizes${\cal{L}}_{{\rm{SIoU}}}$ and ${\cal{L}}_{{\rm{IoU}}}$ if $ d_{\cal{H}}>2 $

    图  5  正则项 ${\cal{R}}_{{S}}$ 的图像示例

    Fig.  5  Illustration of regularization ${\cal{R}}_{{S}}$

    图  6  不同参数 $ \lambda $$ |x| $ 的光滑代理函数${\cal A}_\lambda(x)$

    Fig.  6  Plot of smooth surrogate function${\cal A}_\lambda(x)$ for $ |x| $with different$ \lambda $controlling its shape

    图  7  梯度截断后的${\cal{L}}_{{\rm{SIoU}}}$可视化示例

    Fig.  7  A visualized example of ${\cal{L}}_{{\rm{SIoU}}}$ with truncated gradient

    图  8  从两种分布中采样近距离和远距离的初始预测框位置

    Fig.  8  Sample the initial predicted boxes subject to normal distribution with short and longmean-variance

    图  9  各种边界框回归损失比较

    Fig.  9  Comparison among the convergence performance of different bounding box regression losses

    图  10  不同迭代次数的$ {\cal{L}}_{{\rm{GIoU}}} $$ {\cal{L}}_{{\rm{CIoU}}} $$ {\cal{L}}_{{\rm{SIoU}}} $的回归示例

    Fig.  10  Illustration of predicted boxes via $ {\cal{L}}_{{\rm{GIoU}}} $, $ {\cal{L}}_{{\rm{CIoU}}} $ and $ {\cal{L}}_{{\rm{SIoU}}} $ regressing in different iterations

    图  11  在LaSOT测试集上, 分别以 $ {\cal{L}}_{{\rm{IoU}}} $(点线框标出)和$ {\cal{L}}_{{\rm{SIoU}}} $(虚线框标出)训练的模型 SiamFC++ 的可视化结果示例 (实线框为真值标签)

    Fig.  11  Visualized tracking results of SiamFC++trained using $ {\cal{L}}_{{\rm{IoU}}} $ (marked in dotted box) and$ {\cal{L}}_{{\rm{SIoU}}} $ (marked in dashed box) on LaSOT(solid box denotes groundtruth)

    图  12  在LaSOT上评估成功率、精确率和标准化精确率结果

    Fig.  12  Success plot with area under the curve, precision plot and normalized precision plot on LaSOT

    图  13  在GOT-10k 上的成功率图

    Fig.  13  Success plot on GOT-10k

    表  1  在基准 LaSOT 上, 分别以 $ {\cal{L}}_{{\rm{IoU}}} $(原本的)和 $ {\cal{L}}_{{\rm{SIoU}}} $训练的模型 SiamFC++的测试结果(%)

    Table  1  Comparison between the performance of SiamFC++ trained using $ {\cal{L}}_{{\rm{IoU}}} $ (original), $ {\cal{L}}_{{\rm{SIoU}}} $on the test set of LaSOT (%)

    评价指标 成功率 精确度 标准化精确度
    ${\cal{L} }_{{\rm{IoU}}}$ 55.6 55.5 64.8
    ${\cal{L} }_{{\rm{SIoU}}}$ 57.6 58.3 66.9
    相对增益 3.60 5.05 3.24
    下载: 导出CSV

    表  2  在基准LaSOT上, 分别以$ {\cal{L}}_{{\rm{IoU}}} $(原本的)和$ {\cal{L}}_{{\rm{SIoU}}} $训练的模型SiamBAN的测试对比(%)

    Table  2  Comparison between the performance of SiamBAN trained using $ {\cal{L}}_{{\rm{IoU}}} $ (original), $ {\cal{L}}_{{\rm{SIoU}}} $on the test set of LaSOT (%)

    评价指标 成功率 精确度 标准化精确度
    ${\cal{L} }_{{\rm{IoU}}}$ 51.4 52.1 59.8
    ${\cal{L} }_{{\rm{SIoU}}}$ 54.3 53.9 63.3
    相对增益 5.64 3.45 4.85
    下载: 导出CSV

    表  3  在基准LaSOT上, 分别以$ {\cal{L}}_{{\rm{IoU}}} $(原本的)和 $ {\cal{L}}_{{\rm{SIoU}}} $训练模型SiamCAR的测试对比(%)

    Table  3  Comparison between the performance of SiamCAR trained using $ {\cal{L}}_{{\rm{IoU}}} $ (original), $ {\cal{L}}_{{\rm{SIoU}}} $ on the test set of LaSOT (%)

    评价指标 成功率 精确率 标准化精确率
    ${\cal{L} }_{{\rm{IoU}}}$ 51.6 52.4 61.0
    ${\cal{L} }_{{\rm{SIoU}}}$ 54.9 54.8 63.1
    相对增益 6.39 4.58 3.44
    下载: 导出CSV

    表  4  在基准LaSOT上, 与先进方法的性能评估对比

    Table  4  Performance evaluation for state-of-the-artalgorithms on LaSOT

    方法 成功率 精确率 标准化精确率
    SiamBAN 51.4 52.1 59.8
    ATOM 51.5 50.5 57.6
    SiamCAR 51.6 52.4 61.0
    SiamRPN++ 49.6 49.1 56.9
    Ocean-online 56.0 56.6 65.1
    SiamFC++ 55.6 55.5 64.8
    DiMP 56.8 56.4 64.3
    SiamBAN (SIoU) 54.3 53.9 63.3
    SiamCAR (SIoU) 54.2 53.7 63.1
    SiamFC++ (SIoU) 57.6 58.3 66.9
    下载: 导出CSV

    表  5  在GOT-10k上, 分别以$ {\cal{L}}_{{\rm{IoU}}} $(原本的)和$ {\cal{L}}_{{\rm{SIoU}}} $训练的模型SiamFC++ 测试对比(%)

    Table  5  Comparison between the performance of SiamFC++ trained using $ {\cal{L}}_{{\rm{IoU}}} $ (original), $ {\cal{L}}_{{\rm{SIoU}}} $on the test set of GOT-10k (%)

    评价指标 $ {\rm{AO}} $ ${\rm{SR} }_{0.50}$ ${\rm{SR} }_{0.75}$
    ${\cal{L} }_{{\rm{IoU}}}$ 59.5 69.5 47.9
    ${\cal{L} }_{{\rm{SIoU}}}$ 61.7 74.7 46.8
    相对增益 3.69 7.48 −2.29
    下载: 导出CSV

    表  6  在GOT-10k上, 分别以$ {\cal{L}}_{{\rm{IoU}}} $(原本的)和$ {\cal{L}}_{{\rm{SIoU}}} $训练的模型SiamCAR测试结果(%)

    Table  6  Comparison between the performance of SiamCAR trained using $ {\cal{L}}_{{\rm{IoU}}} $ (original), $ {\cal{L}}_{{\rm{SIoU}}} $on the test set of GOT-10k (%)

    评价指标 $ {\rm{AO}} $ ${\rm{SR} }_{0.50}$ ${\rm{SR} }_{0.75}$
    ${\cal{L} }_{{\rm{IoU}}}$ 58.1 68.3 44.1
    ${\cal{L} }_{{\rm{SIoU}}}$ 60.2 72.6 46.4
    相对增益 3.61 6.29 5.22
    下载: 导出CSV

    表  7  在基准GOT-10k上, 与先进方法的性能评估对比 (%)

    Table  7  Performance evaluation for state-of-the-artalgorithms on GOT-10k (%)

    方法 $ {\rm{AO}} $ ${\rm{SR} }_{0.50}$
    MDNet 29.9 30.3
    SPM 51.3 59.3
    ATOM 55.6 63.4
    SiamCAR 56.9 67.0
    SiamRPN++ 51.7 61.8
    Ocean-online 61.1 72.1
    D3S 59.7 67.6
    SiamFC++ 59.5 69.5
    DiMP-50 61.1 71.2
    SiamCAR (SIoU) 60.2 72.6
    SiamFC++ (SIoU) 61.7 74.7
    下载: 导出CSV

    表  8  在TrackingNet上, 分别以$ {\cal{L}}_{{\rm{IoU}}} $(原本的)和$ {\cal{L}}_{{\rm{SIoU}}} $训练的模型SiamFC++的测试结果(%)

    Table  8  Comparison between the performance of SiamFC++ trained using $ {\cal{L}}_{{\rm{IoU}}} $ (original), $ {\cal{L}}_{{\rm{SIoU}}} $on the test of TrackingNet (%)

    评价指标 精确率 标准化精确率 成功率
    ${\cal{L} }_{\rm{{IoU}}}$ 70.5 80.0 75.4
    ${\cal{L} }_{{\rm{SIoU}}}$ 72.1 81.9 76.2
    相对增益 2.27 2.37 1.06
    下载: 导出CSV

    表  9  在基准TrackingNet上, 与先进方法的性能评估对比 (%)

    Table  9  Performance evaluation for state-of-the-artalgorithms on TrackingNet (%)

    方法 成功率 标准化精确率
    MDNet 60.6 70.5
    ATOM 70.3 77.1
    DaSiamRPN 63.8 73.3
    SiamRPN++ 73.3 80.0
    UpdateNet 67.7 75.2
    SPM 71.2 77.8
    SiamFC++ 75.4 80.0
    DiMP 74.0 80.1
    SiamFC++ (SIoU) 76.2 81.9
    下载: 导出CSV

    表  10  在OTB2015上, 分别以$ {\cal{L}}_{{\rm{IoU}}} $(原本的)和$ {\cal{L}}_{{\rm{SIoU}}} $训练的模型SiamFC++ 的测试结果 (%)

    Table  10  Comparison between the performance of SiamFC++ trained using $ {\cal{L}}_{{\rm{IoU}}} $(original),$ {\cal{L}}_{{\rm{SIoU}}} $on the test of OTB2015 (%)

    评价指标 成功率 标准化精确率
    ${\cal{L} }_{ {\rm{IoU} } }$ 68.2 89.5
    ${\cal{L} }_{{\rm{SIoU}}}$ 68.7 89.8
    相对增益 0.74 0.34
    下载: 导出CSV

    表  11  在OTB2015上, 分别以$ {\cal{L}}_{{\rm{IoU}}} $(原本的)和$ {\cal{L}}_{{\rm{SIoU}}} $训练的模型SiamBAN测试结果 (%)

    Table  11  Comparison between the performance of SiamBAN trained using $ {\cal{L}}_{{\rm{IoU}}} $ (original), $ {\cal{L}}_{{\rm{SIoU}}} $on on the test of OTB2015 (%)

    评价指标 成功率 标准化精确率
    ${\cal{L} }_{ {\rm{IoU} } }$ 69.6 91.0
    ${\cal{L} }_{{\rm{SIoU}}}$ 69.9 91.5
    相对增益 0.43 0.55
    下载: 导出CSV

    表  12  在VOT2018上, 分别以$ {\cal{L}}_{{\rm{IoU}}} $(原本的)和$ {\cal{L}}_{{\rm{SIoU}}} $训练的模型SiamFC++ 测试结果(%)

    Table  12  Comparison between the performance of SiamFC++ trained using $ {\cal{L}}_{{\rm{IoU}}} $ (original),$ {\cal{L}}_{{\rm{SIoU}}} $on on the test of VOT2018 (%)

    评价指标 ${\rm{准确率} }$ ${\rm{鲁棒性} }$ ${ {\rm{EAO} } }$
    ${\cal{L} }_{{\rm{IoU}}}$ 0.586 0.201 0.427
    ${\cal{L} }_{{\rm{SIoU}}}$ 0.582 0.196 0.400
    下载: 导出CSV

    表  13  在基准LaSOT 上, 与其他基于IoU损失训练得到的满足不同IoU阈值的测试集图像帧数占比的对比结果 (%)

    Table  13  Comparison results with other IoU-based loss for the ratio of frames exceeding different IoU thresholdson the test set of LaSOT (%)

    IoU阈值 ≥ 0.95 ≥ 0.90 ≥ 0.85 ≥ 0.80 ≥ 0.75 ≥ 0.70 ≥ 0.65 ≥ 0.60 ≥ 0.55 ≥ 0.50
    SiamFC++ (SIoU) 2.75 15.93 31.83 44.05 52.33 57.71 61.71 64.41 66.52 68.14
    SiamFC++ (DIoU) 1.60 13.19 29.72 42.84 51.48 57.09 61.28 64.17 66.31 67.95
    SiamFC++ (GIoU) 2.45 16.18 31.10 42.26 50.39 55.81 59.56 62.37 64.58 66.34
    SiamFC++ 1.52 12.73 29.10 41.90 50.20 55.63 59.72 62.51 64.68 66.31
    SiamBAN (SIoU) 1.18 10.79 24.86 36.64 45.50 51.87 56.45 60.03 62.77 64.84
    SiamBAN (GIoU) 1.49 11.77 24.71 35.15 44.77 50.79 54.93 57.76 60.70 63.98
    SiamBAN 1.98 12.89 25.40 35.57 43.46 49.29 53.38 56.53 58.92 60.78
    SiamCAR (SIoU) 1.20 10.80 24.81 36.74 45.75 52.29 56.97 60.71 63.53 65.66
    SiamCAR (DIoU) 1.20 10.91 25.10 36.62 45.04 51.47 56.18 59.89 62.70 64.83
    SiamCAR 1.27 10.62 23.90 35.98 44.93 50.87 55.08 57.86 59.94 61.61
    下载: 导出CSV

    表  14  在基准GOT-10k上, 与其他基于IoU损失训练得到的满足不同IoU阈值的测试集图像帧数占比的对比结果 (%)

    Table  14  Comparison results with other IoU-based loss for the ratio of frames exceeding different IoU thresholdson the test set of GOT-10k (%)

    IoU阈值 ≥ 0.95 ≥ 0.90 ≥ 0.85 ≥ 0.80 ≥ 0.75 ≥ 0.70 ≥ 0.65 ≥ 0.60 ≥ 0.55 ≥ 0.50
    SiamFC++ (SIoU) 0.94 8.18 22.01 35.76 46.83 55.71 62.16 67.40 71.39 74.68
    SiamFC++ (DIoU) 0.72 7.56 21.10 35.11 46.86 55.45 61.68 66.82 70.74 73.86
    SiamFC++ (GIoU) 0.97 7.20 21.80 34.19 45.85 54.50 59.24 63.48 66.02 69.49
    SiamCAR (SIoU) 0.94 8.58 22.20 35.83 46.46 54.74 60.66 65.49 69.30 72.62
    SiamCAR (GIoU) 1.13 6.72 19.23 34.78 45.37 53.73 59.98 64.96 68.95 71.96
    SiamCAR (DIoU) 0.92 6.19 18.85 32.54 43.73 52.51 58.86 64.04 68.09 71.33
    SiamCAR 0.81 8.02 20.76 33.88 44.07 51.87 57.21 61.35 64.99 68.31
    下载: 导出CSV

    表  15  在GOT-10k上, 对${\cal{L}}_{{\rm{SIoU}}}$的正则项和代理函数的消融实验(%)

    Table  15  Ablation studies about the regulariztion and surrogate function on GOT-10k (%)

    评价指标 $ {\rm{AO}} $ ${\rm{SR} }_{0.50}$ ${\rm{SR} }_{0.75}$
    ${\cal{L} }_{ {\rm{SIoU} } }\;({\rm{w/o} } \, {\cal {AR} })$ 59.9 72.1 46.3
    ${\cal{L} }_{ {\rm{SIoU} } }\; ({\rm{w/} } \;{ \cal{AR} })$ 61.7 74.7 46.8
    相对增益 3.01 3.61 1.08
    ${\cal{L} }_{ {\rm{SIoU} } }\;({\rm{w/} } \;{\cal {R} })$ 61.4 74.5 46.7
    相对增益 2.51 3.33 0.86
    ${\cal{L} }_{ {\rm{SIoU} } } \;({\rm{w/} } \;{ {\cal A} }_2)$ 60.3 72.6 46.5
    相对增益 0.67 0.69 0.43
    ${\cal{L} }_{ {\rm{SIoU} } }\; ({\rm{w/} } \;{ {\cal A} }_4)$ 60.6 73.4 46.3
    相对增益 1.17 1.80 0
    ${\cal{L} }_{ {\rm{SIoU} } }\; ({\rm{w/} } \;{ {\cal A} }_8)$ 60.4 73.4 46.0
    相对增益 0.83 1.80 −0.65
    ${\cal{L} }_{ {\rm{SIoU} } }\; ({\rm{w/} } \;{ {\cal A} }_1)$ 58.9 71.3 43.7
    相对增益 −1.17 −1.11 −5.62
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-06-11
  • 录用日期:  2021-09-17
  • 网络出版日期:  2021-11-15
  • 刊出日期:  2023-02-20

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