Smooth-IoU Loss for Bounding Box Regression in Visual Tracking
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
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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.-
关键词:
- 光滑IoU 损失 /
- $ \ell_n $-norm 损失 /
- 边界框回归 /
- 目标跟踪
Abstract: The branch of bounding box regression is a critical module in visual object trackers, and its performance directly affects accuracy of a tracker. One of evaluation metrics used to measure accuracy is Intersection over Union (IoU). The IoU loss which was proposed to replace$ \ell_n $ -norm loss for bounding box regression is increasingly popular. However, there are two inherent issues in IoU loss: one is that the parameters of bounding box can not be updated via gradient descent if the predicted box does not intersect with ground-truth box; the other is the gradient of the optimal IoU does not exist, so that it is difficult to make the predicted box regressed to the IoU optimum. We reveal the explicit relationship among the parameters of IoU optimal bounding box in regression process, and point out that the size of a predicted box which make IoU loss optimal is not unique when its center is in specific areas, increasing the uncertainty of bounding box regression. From the perspective of optimizing divergence between two distributions, we propose a Smooth-IoU loss, which is a globally smooth (i.e., continuously differentiable) loss function with unique extremum. The Smooth-IoU loss naturally implicates a specific optimal relationship among the parameters of bounding box, and its gradient over the global domain exists, making it easier to regress the predicted box to the extremal bounding box, and the unique extremum ensures that the parameters can be updated via gradient descent. In addition, the proposed smooth-IoU loss can be easily incorporated into existing trackers by replacing the IoU-based loss to train bounding box regression. Extensive experiments on visual tracking benchmarks including OTB2015, TrackingNet, GOT-10k, and LaSOT demonstrate that Smooth-IoU loss achieves state-of-the-art performance, confirming its effectiveness and efficiency.-
Key words:
- Smooth-IoU loss /
- $ \ell_n $-norm loss /
- bounding box regression /
- visual tracking
1) 收稿日期 2021-06-11 录用日期 2021-09-17 Manuscript received June 11, 2021; accepted September 17, 2021 国家自然科学基金重点项目 (51935005), 基础科研项目(JCKY20200603C010), 空间智能控制技术重点实验室基金 (ZDSYS-2018-02) 资助 Partially supported by the National Natural Science Foundation of China under Grants (No. 51935005), the Basic Scientific Research Projects (No. JCKY20200603C010), and the Mutual2) Fund of Space Intelligent Control Technology Key Laboratory (No. ZDSYS-2018-02) 本文责任编委 桑农 Recommended by Associate Editor SANG Nong 1. 哈尔滨工业大学计算学部模式识别与智能系统研究中心 哈尔滨 150001 1. Pattern Recognition and Intelligence System Research Center, Faculty of Computing, Harbin Institute of Technology, Harbin 1500013) 1 对于不同的研究对象, 光滑的含义也有所区别, 在本文中称在开集$ X\in \mathbb{R}^n $ 上的函数$ f:X\to\mathbb{R} $ 是光滑的, 如果$ f $ 是$ 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 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
${\cal{L}}_{{\rm{IoU}}}$ 和${\cal{L}}_{{\rm{SIoU}}}$ 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 当
$ d_{\cal{H}}>2 $ 时最优化${\cal{L}}_{{\rm{SIoU}}}$ 和${\cal{L}}_{{\rm{IoU}}}$ 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 $ 下$ |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}}} $ 和$ {\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}}} $ 和$ {\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
表 1 分别以
$ {\cal{L}}_{{\rm{IoU}}} $ 和$ {\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 LaSOTLoss $ \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% 
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表 2 分别以
$ {\cal{L}}_{{\rm{IoU}}} $ 和$ {\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 LaSOTLoss $ \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%
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表 3 分别以
$ {\cal{L}}_{{\rm{IoU}}} $ 和$ {\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 LaSOTLoss $ \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 %
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表 4 分别以
$ {\cal{L}}_{{\rm{IoU}}} $ 和$ {\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-10kLoss $ \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%
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表 5 分别以
$ {\cal{L}}_{{\rm{IoU}}} $ 和$ {\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-10kLoss $ \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%
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表 6 分别以
$ {\cal{L}}_{{\rm{IoU}}} $ 和$ {\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%
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表 7 分别以
$ {\cal{L}}_{{\rm{IoU}}} $ 和$ {\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%
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表 8 分别以
$ {\cal{L}}_{{\rm{IoU}}} $ 和$ {\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%
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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
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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
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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
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表 12 分别以
$ {\cal{L}}_{{\rm{IoU}}} $ 和$ {\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 VOT2018Loss$ \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
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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
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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
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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%
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