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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, 2021, 47(x): 1−19 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, 2021, 47(x): 1−19 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, 2021, 47(x): 1−19 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, 2021, 47(x): 1−19 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: 国家自然科学基金重点项目 (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生. 分别在2015年和2018年获得哈尔滨工业大学的学士学位和硕士学位. 主要研究方向为计算机视觉中的目标跟踪和模式识别. E-mail: ligong101@126.com

    赵巍:哈尔滨工业大学计算机科学与技术学院副教授. 曾获黑龙江省科学技术进步一等奖. 主要研究领域包括模式识别,机器学习和计算机视觉. E-mail: zhaowei@hit.edu.cn

    刘鹏:哈尔滨工业大学计算机科学与技术学院教授. 2007 年获得哈尔滨工业大学微电子和固体电子学博士学位. 主要研究方向包括图像处理,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:哈尔滨工业大学计算机科学与技术学院教授. 在~1995 年获得哈尔滨工业大学计算机应用技术博士学位. 主要研究方向包括模式识别,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: Partially supported by the National Natural Science Foundation of China under Grants (No. 51935005), the Basic Scientific Research Projects (No. JCKY20200603C010), and the Mutual Fund of Space Intelligent Control Technology Key Laboratory (No. ZDSYS-2018-02)
More Information
    Author Bio:

    LI Gong is currently working toward a Ph.D. at the Pattern Recognition and Intelligent System Research Center, Harbin Institute of Technology. He received B.S. and M.S. degrees from Harbin Institute of Technology, Harbin, China, in 2015 and in 2018, respectively. His research interest covers computer vision and pattern recognition

    ZHAO Wei is an associate professor at the School of Computer Science and Technology, Harbin Institute of Technology. She won a First Prize of Heilongjiang Province Science and Technology Progress. Her research fields include pattern recognition, machine learning, and computer vision

    LIU Peng is aprofessor at the School of Computer Science and Technology, Harbin Institute of Technology. He received his Ph.D. in microelectronics and solid-state electronics from Harbin Institute of Technology in 2007. His research interests cover image processing, video analysis, pattern recognition, and the design of large scale integrated circuits

    TANG Xiang-Long is a professor at the School of Computer Science and Technology, Harbin Institute of Technology. He received his Ph.D. in computer application technology from Harbin Institute of Technology in 1995. His research interset 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 损失函数存在两个固有缺陷: 一个是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; 另一个是在 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. 本文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. 本文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 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 IoU 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 和 OTB2015 等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.
    1)  收稿日期 2021-06-11 录用日期 2021-09-17 Manuscript received June 11, 2021; accepted September 17, 2021 国家自然科学基金重点项目 (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 Partially supported by the National Natural Science Foundation of China under Grants (No. 51935005), the Basic Scientific Research Projects (No. JCKY20200603C010), and the Mutual
    2)  Fund of Space Intelligent Control Technology Key Laboratory (No. ZDSYS-2018-02) 本文责任编委 桑农 Recommended by Associate Editor SANG Nong 1. 哈尔滨工业大学计算学部模式识别与智能系统研究中心 哈尔滨 150001 1. Pattern Recognition and Intelligence System Research Center, Faculty of Computing, Harbin Institute of Technology, Harbin 150001
    3)  1 对于不同的研究对象, 光滑的含义也有所区别, 在本文中称在开集 $ X\in \mathbb{R}^n $ 上的函数 $ f:X\to\mathbb{R} $ 是光滑的, 如果 $ f $$ C^1 $类的. $ C^1 $类的函数必然是可微的. 在本文的定义下光滑性也可以称作连续可微性
  • 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

    图  2  从边界框映射到正态分布的示意图

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

    图  3  ${\cal{L}}_{{\rm{IoU}}}$${\cal{L}}_{{\rm{SIoU}}}$可视化图象示例

    Fig.  3  An visualized example of ${\cal{L}}_{{\rm{SIoU}}}$ loss LsIou and IoU loss ${\cal{L}}_{IoU} = 1-{\rm{IoU}}$. Better 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 minimize ${\cal{L}}_{{\rm{SIoU}}}$ and ${\cal{L}}_{{\rm{IoU}}}$ if $ d_{\cal{H}}>2 $.

    图  5  正则项 $ {\cal{R}}_{\bf{S}} $ 的图象示例(阴影区域满足$ d_{\cal{H}}<2 $, 箭头代表某一梯度轨迹)

    Fig.  5  Illustration of regularization $ {\cal{R}}_{\bf{S}} $ (the filled areas satisfy $ d_{\cal{H}}<2 $, arrows stand for a trail of gradients)

    图  6  不同参数 $ \lambda $$ |x| $ 的光滑代理函数$ A_\lambda(x) $

    Fig.  6  Plot of smooth surrogate function $ A_\lambda(x) $ for $ |x| $, where $ \lambda $ control its shape

    图  7  梯度截断后的 ${\cal{L}}_{{\rm{SIoU}}}$ 损失

    Fig.  7  An 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 low and high mean-variance

    图  9  比较各种边界框回归损失i.e. $ {\cal{L}}_{{\rm{IoU}}} $, $ {\cal{L}}_{{\rm{GIoU}}} $, $ {\cal{L}}_{{\rm{DIoU}}} $, $ {\cal{L}}_{{\rm{CIoU}}} $ 和提出的 $ {\cal{L}}_{{\rm{SIoU}}} $)的收敛能力

    Fig.  9  Comparison among the convergence performance of different bounding box regression losses(i.e. $ {\cal{L}}_{{\rm{IoU}}} $, $ {\cal{L}}_{{\rm{GIoU}}} $, $ {\cal{L}}_{{\rm{DIoU}}} $, $ {\cal{L}}_{{\rm{CIoU}}} $, and proposed $ {\cal{L}}_{{\rm{SIoU}}} $)

    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  分别以 $ {\cal{L}}_{{\rm{IoU}}} $$ {\cal{L}}_{{\rm{SIoU}}} $ 训练的模型 SiamFC++ 在 LaSOT 测试集上的可视化结果示例

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

    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 AUC, 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  分别以 $ {\cal{L}}_{{\rm{IoU}}} $$ {\cal{L}}_{{\rm{SIoU}}} $ 训练的模型 SiamFC++在基准 LaSOT 上的测试结果

    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

    Loss $ \backslash $ Metric $ Succ. $ $ Prec. $ $ P_{norm} $
    ${\cal{L} }_{{\rm{IoU}}}$ 55.6 55.5 64.8
    ${\cal{L} }_{{\rm{SIoU}}}$ 57.6 58.3 66.9
    Rel. Improv. (%) 3.60% 5.05% 3.24%
    下载: 导出CSV

    表  2  分别以 $ {\cal{L}}_{{\rm{IoU}}} $$ {\cal{L}}_{{\rm{SIoU}}} $ 训练的模型 SiamBAN 在基准 LaSOT 上的测试结果

    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

    Loss $ \backslash $ Metric $ Succ. $ $ Prec. $ $ P_{norm} $
    ${\cal{L} }_{{\rm{IoU}}}$ 51.4 52.1 59.8
    ${\cal{L} }_{{\rm{SIoU}}}$ 54.3 53.9 63.3
    Rel. Improv. (%) 5.64% 3.45% 4.85%
    下载: 导出CSV

    表  3  分别以 $ {\cal{L}}_{{\rm{IoU}}} $$ {\cal{L}}_{{\rm{SIoU}}} $ 训练的模型 SiamCAR 在基准 LaSOT 上的测试结果

    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

    Loss $ \backslash $ Metric $ Succ. $ $ Prec. $ $ P_{norm} $
    ${\cal{L} }_{{\rm{IoU}}}$ 51.6 52.4 61.0
    ${\cal{L} }_{{\rm{SIoU}}}$ 54.9 54.8 63.1
    Rel. Improv. (%) 6.39 % 4.58% 3.44 %
    下载: 导出CSV

    表  4  分别以 $ {\cal{L}}_{{\rm{IoU}}} $$ {\cal{L}}_{{\rm{SIoU}}} $ 训练的模型 SiamFC++ 在 GOT-10k 上测试结果

    Table  4  Comparison between the performance of SiamFC++ trained using $ {\cal{L}}_{{\rm{IoU}}} $ (original), $ {\cal{L}}_{{\rm{SIoU}}} $ on the test set of GOT-10k

    Loss $ \backslash $ Metric $ {\rm{AO}} $ $ {\rm{SR}}_{.50} $ $ {\rm{SR}}_{.75} $
    ${\cal{L} }_{{\rm{IoU}}}$ 59.5 69.5 47.9
    ${\cal{L} }_{{\rm{SIoU}}}$ 61.7 74.7 46.8
    Rel. Improv. (%) 3.69% 7.48% −2.29%
    下载: 导出CSV

    表  5  分别以 $ {\cal{L}}_{{\rm{IoU}}} $$ {\cal{L}}_{{\rm{SIoU}}} $ 训练的模型 SiamCAR 在 GOT-10k 上测试结果

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

    Loss $ \backslash $ Metric $ {\rm{AO}} $ $ {\rm{SR}}_{.50} $ $ {\rm{SR}}_{.75} $
    ${\cal{L} }_{{\rm{IoU}}}$ 58.1 68.3 44.1
    ${\cal{L} }_{{\rm{SIoU}}}$ 60.2 72.6 46.4
    Rel. Improv. (%) 3.61% 6.29% 5.22%
    下载: 导出CSV

    表  6  分别以 $ {\cal{L}}_{{\rm{IoU}}} $$ {\cal{L}}_{{\rm{SIoU}}} $ 训练的模型 SiamFC++ 在TrackingNet上测试结果

    Table  6  Comparison between the performance of SiamFC++ trained using $ {\cal{L}}_{{\rm{IoU}}} $ (original), $ {\cal{L}}_{{\rm{SIoU}}} $ on the test of TrackingNet.

    Loss$ \backslash $Metric $ Prec. $ $ P_{norm} $ $ Succ. $
    ${\cal{L} }_{\rm{{IoU}}}$ 70.5 80.0 75.4
    ${\cal{L} }_{{\rm{SIoU}}}$ 72.1 81.9 76.2
    Rel. Improv. (%) 2.27% 2.37% 1.06%
    下载: 导出CSV

    表  7  分别以 $ {\cal{L}}_{{\rm{IoU}}} $$ {\cal{L}}_{{\rm{SIoU}}} $ 训练的模型 SiamFC++ 在OTB2015上测试结果

    Table  7  Comparison between the performance of SiamFC++ trained using $ {\cal{L}}_{{\rm{IoU}}} $ (original), $ {\cal{L}}_{{\rm{SIoU}}} $ on OTB2015.

    Loss $ \backslash $ Metric $ Succ. $ $ Prec. $
    ${\cal{L} }_{{\rm{IoU}}}$ 68.2 89.5
    ${\cal{L} }_{{\rm{SIoU}}}$ 68.7 89.8
    Rel. Improv. (%) 0.74% 0.34%
    下载: 导出CSV

    表  8  分别以 $ {\cal{L}}_{{\rm{IoU}}} $$ {\cal{L}}_{{\rm{SIoU}}} $ 训练的模型 SiamBAN 在OTB2015上测试结果

    Table  8  Comparison between the performance of SiamBAN trained using $ {\cal{L}}_{{\rm{IoU}}} $ (original), $ {\cal{L}}_{{\rm{SIoU}}} $ on OTB2015.

    Loss $ \backslash $ Metric $ Succ. $ $ Prec. $
    ${\cal{L} }_{{\rm{IoU}}}$ 69.6 91.0
    ${\cal{L} }_{{\rm{SIoU}}}$ 69.9 91.5
    Rel. Improv. (%) 0.43% 0.55%
    下载: 导出CSV

    表  9  与先进方法在基准 LaSOT 上的性能评估对比

    Table  9  Performance evaluation for state-of-the-art algorithms on LaSOT. The best three results are marked in bold, italics and underline fonts, respectively

    Metric$ \backslash $Method SiamBAN ATOM SiamCAR SiamRPN++ Ocean-online SiamFC++ DiMP SiamBAN
    (SIoU)
    SiamCAR
    (SIoU)
    SiamFC++
    (SIoU)
    $ Succ. $ 51.4 51.5 51.6 49.6 56.0 55.6 56.8 54.3 54.2 57.6
    $ Prec. $ 52.1 50.5 52.4 49.1 56.6 55.5 56.4 53.9 53.7 58.3
    $ P_{norm} $ 59.8 57.6 61.0 56.9 65.1 64.8 64.3 63.3 63.1 66.9
    下载: 导出CSV

    表  10  与先进方法在基准 GOT-10k 上的性能评估对比

    Table  10  Performance evaluation for state-of-the-art algorithms on GOT-10k. The best three results are marked in bold, italics and underline fonts, respectively

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

    表  11  与先进方法在基准 TrackingNet 上的性能评估对比

    Table  11  Performance evaluation for state-of-the-art algorithms on TrackingNet. The best three results are marked in bold, italics and underline fonts, respectively

    Metric$ \backslash $Method MDNet ATOM DaSiamRPN SiamRPN++ UpdateNet SPM SiamFC++ DiMP SiamFC++(SIoU)
    $ Succ. $ 60.6 70.3 63.8 73.3 67.7 71.2 75.4 74.0 76.2
    $ P_{norm} $ 70.5 77.1 73.3 80.0 75.2 77.8 80.0 80.1 81.9
    下载: 导出CSV

    表  12  分别以 $ {\cal{L}}_{{\rm{IoU}}} $$ {\cal{L}}_{{\rm{SIoU}}} $ 训练的模型 SiamFC++ 在VOT2018上测试结果

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

    Loss$ \backslash $Metric $ \mathbf{A}\uparrow $ $ \mathbf{R}\downarrow $ $ \mathbf{EAO}\uparrow $
    ${\cal{L} }_{{\rm{IoU}}}$ 0.586 0.201 0.427
    ${\cal{L} }_{{\rm{SIoU}}}$ 0.582 0.196 0.400
    下载: 导出CSV

    表  13  与其它基于 IoU 损失在基准 LaSOT 上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 thresholds on the test set of LaSOT. The best result is marked in bold

    Ratio of Method (%) $ \backslash $IoU ≥ 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  与其它基于 IoU 损失在基准 GOT-10k 上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 thresholds on the test set of GOT-10k. The best result is marked in bold

    Ratio of Method (%) $ \backslash $IoU ≥ 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消融实验

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

    Loss $ \backslash $ Metric $ {\rm{AO}} $ $ {\rm{SR}}_{.50} $ $ {\rm{SR}}_{.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
    Rel. Improv. (%) 3.01% 3.61% 1.08%
    $ {\cal{L}}_{{\rm{SIoU}}}({\rm{w/}} \;{\cal{R}}) $ 61.4 74.5 46.7
    Rel. Improv. (%) 2.51% 3.33% 0.86%
    $ {\cal{L}}_{{\rm{SIoU}}} ({\rm{w/}} \;{\cal{A}}_2) $ 60.3 72.6 46.5
    Rel. Improv. (%) 0.67% 0.69% 0.43%
    $ {\cal{L}}_{{\rm{SIoU}}} ({\rm{w/}} \;{\cal{A}}_4) $ 60.6 73.4 46.3
    Rel. Improv. (%) 1.17 % 1.80% 0.0 %
    $ {\cal{L}}_{{\rm{SIoU}}} ({\rm{w/}} \;{\cal{A}}_8) $ 60.4 73.4 46.0
    Rel. Improv. (%) 0.83 % 1.80 % −0.65 %
    $ {\cal{L}}_{{\rm{SIoU}}} ({\rm{w/}} \;{\cal{A}}_1) $ 58.9 71.3 43.7
    Rel. Improv. (%) −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

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