Similarity Distance-Based Label Assignment for Tiny Object Detection
用于微小物体检测的基于相似度距离的标签分配

Despite the significant progress in object detection achieved with deep learning technology, the detection accuracy will sharply decrease when the objects to be detected are tiny. Small objects are usually defined as objects with sizes less than a certain threshold value. For example, in Microsoft COCO [11], if the area of an object is less than or equal to 1024, it is considered a small object. In many cases, however, the objects of interest are in fact much smaller than the above definition. For example, in the AI-TOD dataset, the average edge length of an object is only 12.8 pixels, far smaller than in other datasets.
尽管深度学习技术在目标检测方面取得了重大进展，但当要检测的物体很小时，检测精度会急剧下降。小对象通常定义为大小小于特定阈值的对象。例如，在 Microsoft COCO [ 11] 中，如果对象的面积小于或等于 1024，则将其视为小对象。然而，在许多情况下，感兴趣的对象实际上比上述定义小得多。例如，在 AI-TOD 数据集中，对象的平均边长仅为 12.8 像素，远小于其他数据集。

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As stated in a previous paper [1], due to the extremely small size of the objects of interest, there are three main challenges in tiny object detection. First, most object detectors use downsampling for feature extraction, which will result in a large amount of information loss for tiny objects. Second, due to the limited amount of valid information they contain, small objects are easily disturbed by noise. Finally, the smaller an object is, the more sensitive it is to changes in the bounding box [2]. Consequently, if we use traditional label assignment metrics, such as the IoU, GIoU [12], DIoU [13], and CIoU [13], for object detection, the number of positive samples obtained for tiny objects will be very small.
正如之前的论文[1]所述，由于感兴趣的物体的尺寸极小，在微小物体检测方面存在三个主要挑战。首先，大多数目标检测器使用下采样进行特征提取，这将导致微小物体的大量信息丢失。其次，由于它们所包含的有效信息量有限，小物体很容易受到噪音的干扰。最后，对象越小，它对边界框的变化就越敏感 [ 2]。因此，如果我们使用传统的标签分配指标，如 IoU、GIoU [ 12]、DIoU [ 13] 和 CIoU [ 13]，用于物体检测，则为微小物体获得的阳性样本数量将非常少。

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Many methods and have been proposed to improve the accuracy and efficiency of tiny object detection. For example, from the perspective of data augmentation, Kisantal et al. [14] proposed increasing the number of training samples by copying tiny objects, randomly transforming the copies and then pasting the results into new positions in an image.
已经提出了许多方法来提高微小物体检测的准确性和效率。例如，从数据增强的角度来看，Kisantal等[14]提出通过复制微小的物体，随机转换副本，然后将结果粘贴到图像中的新位置来增加训练样本的数量。

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The label assignment strategy plays a significant role in object detection. Depending on whether each label is either strictly negative or strictly positive, such strategies can be divided into hard label assignment strategies and soft label assignment strategies. In a soft label assignment strategy, different weights are set for different samples based on the calculation results, examples include GFL [15], VFL [16], TOOD [17] and DW [18]. Hard label assignment strategies can be further divided into static and dynamic strategies depending on whether the thresholds for designating positive and negative samples are fixed. Static label assignment strategies include those based on the IoU and DotD [2] metrics as well as RFLA [4]. Examples of dynamic label assignment strategies include ATSS [19], PAA [20], OTA [21], and DSLA [22]. From another perspective, label assignment strategies can be divided into prediction-based and prediction-free strategies. A prediction-based method assigns a sample a positive/negative label based on the relationship between the ground-truth and predicted bounding boxes, while a prediction-free method assigns labels based only on the anchors or other existing information.
标签分配策略在对象检测中起着重要作用。根据每个标签是严格负数还是严格正数，此类策略可分为硬标签分配策略和软标签分配策略。在软标签分配策略中，根据计算结果为不同的样本设置不同的权重，例如GFL [ 15]、VFL [ 16]、TOOD [ 17] 和 DW [ 18]。硬标签分配策略可进一步分为静态策略和动态策略，具体取决于指定阳性和阴性样本的阈值是否固定。静态标签分配策略包括基于 IoU 和 DotD [ 2] 指标以及 RFLA [ 4] 的策略。动态标签分配策略的例子包括 ATSS [ 19]、PAA [ 20]、OTA [ 21] 和 DSLA [ 22]。从另一个角度来看，标签分配策略可以分为基于预测的策略和无预测的策略。基于预测的方法根据真值和预测边界框之间的关系为样本分配正/负标签，而无预测方法仅根据锚点或其他现有信息分配标签。

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Although there have been many studies on label assignment strategies for object detection, most such strategies are designed for conventional datasets, with few specifically designed for tiny objects. When these traditional label assignment strategies are directly used for tiny object detection, they suffer a significant decrease in accuracy. To date, the label assignment strategies and metrics designed specifically for tiny objects mainly include $S^{3}$FD [23], DotD [2], NWD-RKA [24] and RFLA [4].
尽管已经有许多关于目标检测的标签分配策略的研究，但大多数此类策略都是为传统数据集设计的，很少有专门为微小对象设计的。当这些传统的标签分配策略直接用于微小物体检测时，它们的准确性会显著降低。迄今为止，专为微小物体设计的标签分配策略和指标主要包括 $S^{3}$ FD [ 23]、DotD [ 2]、NWD-RKA [ 24] 和 RFLA [ 4]。

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In $S^{3}$FD, the threshold value is first reduced (from 0.5 to 0.35) to obtain more positive samples for ground truth and then is further lowered to 0.1 to obtain positive samples for those ground truths that were not addressed with the first threshold reduction. However, $S^{3}$FD also uses the traditional IoU metric to compute the similarity between the ground truth and anchor. To overcome the weakness of the IoU metric, the novel DotD formula was introduced to reduce the sensitivity to the bounding box size. Based on this metric, more positive samples can be obtained for the ground truth. In NWD-RKA, a normalized Wasserstein distance is introduced as a replacement for the IoU, and a ranking-based strategy is used to assign the top-k samples as positive. RFLA explores the relationship between the ground truth and anchor from the perspective of the receptive field, on this basis, the ground truth and anchor are modeled as Gaussian distributions. Then, the distance between these two Gaussian distributions is calculated based on the Kullback–Leibler divergence (KLD), which is used in place of the IoU metric.
在 FD 中 $S^{3}$ ，首先降低阈值（从 0.5 降低到 0.35）以获得更多的地面实况正样本，然后进一步降低到 0.1 以获得那些未通过第一个阈值降低解决的地面实况的正样本。但是， $S^{3}$ FD 还使用传统的 IoU 指标来计算地面实况和锚点之间的相似性。为了克服 IoU 度量的弱点，引入了新颖的 DotD 公式来降低对边界框大小的敏感性。基于该指标，可以获得更多地面实况的正样本。在 NWD-RKA 中，引入了归一化的 Wasserstein 距离作为 IoU 的替代品，并使用基于排序的策略将 top-k 样本分配为正样本。RFLA从感受场的角度探讨了基真值和锚点之间的关系，在此基础上，将基真值和锚点建模为高斯分布。然后，根据 Kullback-Leibler 散度 （KLD） 计算这两个高斯分布之间的距离，该散度用于代替 IoU 度量。

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One of the most important steps in label assignment is to calculate a value that reflects the similarity between different bounding boxes. Specifically, for an anchor-based label assignment strategy, the similarity between the anchors and ground truths must be quantified before assigning labels.
标签分配中最重要的步骤之一是计算反映不同边界框之间相似性的值。具体而言，对于基于锚点的标签分配策略，在分配标签之前，必须量化锚点和基本事实之间的相似性。

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Common label assignment metrics, such as the IoU, GIoU [12], DIoU [13] and CIoU [13], are usually based on the overlap between the anchor and the ground truth. These metrics have the serious problem that if the overlap is zero, which is often the case for tiny objects, these metrics may become invalid. Some more suitable methods use distance-based evaluation metrics or even use Gaussian distributions to model the ground truth and anchor, such as the DotD [2], NWD [3] and RFLA [4]. We present a simple comparison between the existing metrics and our SimD metric from three perspectives in Table I. For example, DotD only considers location similarity and may not adapt different object sizes in a dataset, so it is not comprehensive or adaptive. NWD and RFLA are not adaptive because they respectively have a hyperparameter $C$ and $\beta$ need to set. Following the existing approaches, we consider proposing an adaptive method without any hyperparameters.
常见的标签分配指标，如 IoU、GIoU [ 12]、DIoU [ 13] 和 CIoU [ 13]，通常基于锚点和地面实况之间的重叠。这些指标存在一个严重的问题，即如果重叠为零（通常适用于微小对象），则这些指标可能会变得无效。一些更合适的方法使用基于距离的评估度量，甚至使用高斯分布来模拟地面实况和锚点，例如 DotD [ 2]、NWD [ 3] 和 RFLA [ 4]。我们在表中从三个角度对现有指标和我们的 SimD 指标进行了简单的比较。例如，DotD 仅考虑位置相似性，可能不会适应数据集中的不同对象大小，因此它不全面或自适应。NWD 和 RFLA 不是自适应的，因为它们分别具有超参数 $C$ 并且 $\beta$ 需要设置。根据现有方法，我们考虑提出一种没有任何超参数的自适应方法。

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In this paper, we introduce a novel metric named Similarity Distance (SimD) to better reflect the similarity between different bounding boxes. The Similarity Distance is defined as follows:
在本文中，我们引入了一种名为相似度距离（SimD）的新度量，以更好地反映不同边界框之间的相似性。相似距离定义如下：

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$$SimD=e^{-\left(sim_{location}+sim_{shape}\right)}$$

(1)

$$sim_{location}=\sqrt{\left(\cfrac{x_{g}-x_{a}}{\frac{1}{m}\times\left(w_{g}+w_{a}\right)}\right)^{2}+\left(\cfrac{y_{g}-y_{a}}{\frac{1}{n}\times\left(h_{g}+h_{a}\right)}\right)^{2}}$$

(2)

$$sim_{shape}=\sqrt{\left(\cfrac{w_{g}-w_{a}}{\frac{1}{m}\times\left(w_{g}+w_{a}\right)}\right)^{2}+\left(\cfrac{h_{g}-h_{a}}{\frac{1}{n}\times\left(h_{g}+h_{a}\right)}\right)^{2}}$$

(3)

where $m$ and $n$ are shown below:
其中 $m$ 和 $n$ 如下所示：

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$$m=\cfrac{{\sum_{i=1}^{M}}{\sum_{j=1}^{N_{i}}{\sum_{k=1}^{Q_{i}}\cfrac{\left|x_{ij}-x_{ik}\right|}{w_{ij}+w_{ik}}}}}{{\sum_{i=1}^{M}}N_{i}\times Q_{i}}$$

(4)

$$n=\cfrac{{\sum_{i=1}^{M}}{\sum_{j=1}^{N_{i}}{\sum_{k=1}^{Q_{i}}\cfrac{\left|y_{ij}-y_{ik}\right|}{h_{ij}+h_{ik}}}}}{{\sum_{i=1}^{M}}N_{i}\times Q_{i}}$$

(5)

The SimD contains two parts, location similarity, $sim_{location}$ and shape similarity, $sim_{shape}$. As shown in (2), ($x_{g}$, $y_{g}$) and ($x_{a}$, $y_{a}$) respectively represent the center coordinate of ground truth and anchor, $w_{g}$, $w_{a}$, $h_{g}$, $h_{a}$ represent the width and height of ground truth and anchor, the main part of the formula is the distance between the center point of ground truth and anchor, similar to the DotD formula [2]. The difference is that we use the widths and heights of the two bounding boxes multiplied by corresponding parameters to eliminate the differences between bounding boxes of different sizes. This process is similar to the idea of normalization. This is also why our metric can easily adapt to different object sizes in a dataset. The shape similarity in (3) is similar to (2).
SimD 包含两个部分，位置相似度和 $sim_{location}$ 形状相似度。 $sim_{shape}$ 如（2）所示，（ $x_{g}$ ， $y_{g}$ ） 和 （ $x_{a}$ ， $y_{a}$ ） 分别表示地实值和锚点的中心坐标， $w_{g}$ 、 $w_{a}$ 、 $h_{g}$ $h_{a}$ 表示地实值和锚点的宽度和高度，公式的主要部分是地实值和锚点中心点之间的距离，类似于 DotD 公式 [ 2]。不同之处在于，我们使用两个边界框的宽度和高度乘以相应的参数来消除不同大小的边界框之间的差异。这个过程类似于规范化的想法。这也是为什么我们的指标可以轻松适应数据集中不同的对象大小。（3）中的形状相似性与（2）相似。

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The definitions of the two normalization parameters are shown in (4) and (5). Because they are quite similar, we take the parameter $m$ in (4) as an example for further discussion. $m$ is the average ratio of the distance in the $x$-direction to the sum of the two widths for all ground truths and anchors in each image in the whole train set. $M$ represents the number of images in the train set, $N_{i}$ and $Q_{i}$ represent the number of ground truths and anchors, respectively, in the $i$-th image. $x_{ij}$ and $x_{ik}$ respectively represent the $x$-coordinate of the center point of $j$-th ground truth and $k$-th anchor in $i$-th image. $w_{ij}$ and $w_{ik}$ respectively represent the width of $j$-th ground truth and $k$-th anchor in $i$-th image. Because the two normalization parameters are computed based on the train set, our metric can also automatically adapt to different datasets.
两个归一化参数的定义如（4）和（5）所示。由于它们非常相似，我们以（4） $m$ 中的参数为例进行进一步讨论。 $m$ 是整个训练集中每个图像中所有地面真值和锚点的 $x$ -direction 距离与两个宽度之和的平均比率。 $M$ 表示训练集中的图像数， $N_{i}$ 并 $Q_{i}$ 分别表示 $i$ 第 -th 个图像中的地面真值数和锚点数。 $x_{ij}$ 并 $x_{ik}$ 分别表示 -th 地图和 $k$ -th 锚点的中心 $i$ 点 $x$ $j$ 的 -坐标。 $w_{ij}$ 并 $w_{ik}$ 分别表示 -th 图像中 $j$ $i$ -th ground truth 和 $k$ -th 锚点的宽度。由于这两个归一化参数是基于训练集计算的，因此我们的指标也可以自动适应不同的数据集。

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To facilitate label assignment, we use an exponential function to scale the value of SimD to the range between zero and one. If the two bounding boxes are the same, the value below the root sign will be zero, so SimD will be equal to one. If the two bounding boxes greatly differ, this value will be very large, so SimD will approach zero.
为了便于标签分配，我们使用指数函数将 SimD 的值缩放到 0 到 1 之间的范围。如果两个边界框相同，则根号下方的值将为零，因此 SimD 将等于 1。如果两个边界框相差很大，则此值将非常大，因此 SimD 将接近于零。

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The novel SimD metric defined in (1) can well reflect the relationship between two bounding boxes and is easy to compute. Therefore, it can be used in place of the IoU in scenarios where the similarity between two bounding boxes needs to be calculated.
（1）中定义的新颖的SimD度量可以很好地反映两个边界框之间的关系，并且易于计算。因此，在需要计算两个边界框之间的相似度的场景中，它可以代替 IoU 使用。

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SimD-based label assignment. In traditional object detectors, such as Faster R-CNN [8], Cascade R-CNN [25] and DetectoRS [26], the label assignment strategy for the RPN and R-CNN models is MaxIoUAssigner. MaxIoUAssigner considers three threshold values: a positive threshold, a negative threshold and a minimum positive threshold. Anchors for which the IoU with respect to the ground truth is higher than the positive threshold are positive samples, those for which the IoU is lower than the negative threshold are negative samples, and those for which the IoU is between the positive threshold and the negative threshold are ignored. For tiny object detection, Xu et al. introduced the RKA [24] and HLA [4] label assignment strategies, which do not use fixed thresholds to divide positive and negative samples. In RKA, the top-k anchors associated with a ground truth are simply selected as positive samples, this strategy can increase the number of positive samples because the assignment of positive labels is not limited by a positive threshold. However, introducing too many low-quality positive samples may cause the detection accuracy to degrade.
基于 SimD 的标签分配。在传统的目标检测器中，如Faster R-CNN [ 8]、Cascade R-CNN [ 25]和DetectoRS [ 26]，RPN和R-CNN模型的标签分配策略是MaxIoUAssigner。MaxIoUAssigner 考虑三个阈值：正阈值、负阈值和最小正阈值。IoU 相对于真值高于正阈值的锚点为正样本，IoU 低于负阈值的锚点为负样本，IoU 介于正阈值和负阈值之间的锚点被忽略。对于微小目标检测，Xu等人引入了RKA[24]和HLA[4]标签分配策略，它们不使用固定的阈值来划分阳性和阴性样本。在 RKA 中，与地面实况相关的 top-k 锚点被简单地选择为正样本，这种策略可以增加正样本的数量，因为正标签的分配不受正阈值的限制。然而，引入过多的低质量阳性样品可能会导致检测精度下降。

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In this paper, we follow the traditional MaxIoUAssigner strategy and simply use SimD in place of the IoU. The positive threshold, negative threshold, and minimum positive threshold are set to 0.7, 0.3, and 0.3, respectively. Our label assignment strategy is named MaxSimDAssigner.
在本文中，我们遵循传统的 MaxIoUAssigner 策略，简单地使用 SimD 代替 IoU。阳性阈值、负阈值和最小阳性阈值分别设置为 0.7、0.3 和 0.3。我们的标签分配策略被命名为 MaxSimDAssigner。

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SimD-based NMS. Non Maximum Suppression (NMS) is one of the most important components of postprocessing. Its purpose is to eliminate predicted bounding boxes that are repeatedly detected by preserving only the best detection result. In the traditional NMS procedure, first, the IoUs between the bounding box with the highest score and all other bounding boxes are computed. Then, bounding boxes with an IoU higher than a certain threshold will be eliminated. Considering the advantages of SimD, we can simply use it as the metric for NMS in place of the traditional IoU metric.
基于 SimD 的 NMS。非最大抑制 （NMS） 是后处理中最重要的组件之一。其目的是通过仅保留最佳检测结果来消除重复检测的预测边界框。在传统的 NMS 过程中，首先计算得分最高的边界框与所有其他边界框之间的 IoU。然后，将消除 IoU 高于特定阈值的边界框。考虑到 SimD 的优势，我们可以简单地将其用作 NMS 的指标，而不是传统的 IoU 指标。

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There are two main types of tiny object detection datasets: one contains only small objects, such as AI-TOD [27], AI-TODv2 [24], and SODA-D [1], the other contains both small and medium-sized objects, such as VisDrone2019 [28] and TinyPerson [29].
微小目标检测数据集主要有两种类型：一种只包含小对象，如AI-TOD [ 27]、AI-TODv2 [ 24]和SODA-D [ 1]，另一种同时包含中小型对象，如VisDrone2019 [ 28]和TinyPerson [ 29]。

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AI-TOD. AI-TOD (Tiny Object Detection in Aerial Images) is an aerial remote sensing small object detection dataset collected to address the shortage of available datasets for aerial image object detection tasks. It contains 28,036 images and 700,621 object instances divided into eight categories with accurate annotations. Due to the extremely small size of its object instances (the mean size is only 12.8 pixels), it can be effectively used to test the capabilities of tiny object detectors.
人工智能TOD。AI-TOD（Tiny Object Detection in Aerial Images）是航空遥感小目标检测数据集，旨在解决航空影像目标检测任务可用数据集的短缺问题。它包含 28,036 张图像和 700,621 个对象实例，分为 8 个类别，并具有准确的注释。由于其物体实例的尺寸极小（平均尺寸仅为 12.8 像素），因此可以有效地用于测试微小物体检测器的能力。

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SODA-D. The SODA (Small Object Detection dAtasets) series includes two datasets: SODA-A and SODA-D. SODA-D was collected from MVD [30], which consists of images captured from streets, highways and other similar scenes. There are 25,834 extremely small objects (with areas ranging from 0 to 144) in SODA-D [1], making it an excellent benchmark for tiny object detection tasks.
苏打水-D。SODA（Small Object Detection dAtasets）系列包括两个数据集：SODA-A和SODA-D。SODA-D是从MVD [ 30]收集的，MVD由从街道、高速公路和其他类似场景中捕获的图像组成。SODA-D [ 1] 中有 25,834 个极小物体（面积范围从 0 到 144），使其成为微小物体检测任务的绝佳基准。

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VisDrone2019. VisDrone2019 is a dataset from the VisDrone Object Detection in Images Challenge. For this competition, 10,209 static images were captured by an unmanned drone in different locations at different heights and angles. VisDrone2019 is also an excellent dataset for evaluating tiny object detectors because it contains not only extremely small objects but also normally sized objects.
VisDrone2019年。VisDrone2019 是 VisDrone 图像对象检测挑战赛的数据集。在本次比赛中，无人驾驶无人机在不同位置、不同高度和角度拍摄了10,209张静态图像。VisDrone2019 也是评估微小物体探测器的优秀数据集，因为它不仅包含极小的物体，还包含正常大小的物体。

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In the following series of experiments, we use a computer with one NVIDIA RTX A6000 GPU and implement various models based on the object detection framework MMDetection [31] and PyTorch [32]. We use general object detectors such as Faster R-CNN, Cascade R-CNN and DetectoRS as the base models and simply replace the MaxIoUAssigner module with our SimD assignment module. Our method can effectively adaptive to any backbone networks and anchor-based detectors. Following the main stream settings, for all of the models, ResNet-50-FPN pretrained on ImageNet is used as the backbone, and stochastic gradient descent (SGD) is used as the optimizer, with a momentum of 0.9 and a weight decay of 0.0001. The batch size is set to 2, and the initial learning rate is 0.005. The number of RPN proposals is 3000 in both the training and testing stages. For the VisDrone2019 dataset, the number of epochs for training is set to 12, and the learning rate decays at the 8th and 11th epochs. For AI-TOD, AI-TODv2 and SODA-D, the number of training epochs is 24, and the learning rate decays in the 20th and 23rd epochs. For NMS, we use the IoU metric, and the IoU threshold is set to 0.7 for RPN and 0.5 for R-CNN. Other aspects of the configuration, such as the data preprocessing and pipeline, follow the defaults in MMDetection.
在下面的一系列实验中，我们使用一台带有一个 NVIDIA RTX A6000 GPU 的计算机，并基于对象检测框架 MMDetection [ 31] 和 PyTorch [ 32] 实现各种模型。我们使用 Faster R-CNN、Cascade R-CNN 和 DetectoRS 等通用目标检测器作为基本模型，只需将 MaxIoUAssigner 模块替换为我们的 SimD 分配模块即可。我们的方法可以有效地适应任何骨干网络和基于锚点的检测器。按照主流设置，对于所有模型，使用在 ImageNet 上预训练的 ResNet-50-FPN 作为主干，使用随机梯度下降 （SGD） 作为优化器，动量为 0.9，权重衰减为 0.0001。批处理大小设置为 2，初始学习率为 0.005。在训练和测试阶段，RPN 提案的数量为 3000 个。对于 VisDrone2019 数据集，训练的 epoch 数设置为 12，学习率在第 8 和第 11 个 epoch 衰减。对于 AI-TOD、AI-TODv2 和 SODA-D，训练周期数为 24，学习率在第 20 和第 23 周期衰减。对于 NMS，我们使用 IoU 指标，RPN 的 IoU 阈值设置为 0.7，R-CNN 的 IoU 阈值设置为 0.5。配置的其他方面（如数据预处理和管道）遵循 MMDetection 中的默认值。

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To facilitate comparison with previous research results, during the testing stage, we use the AI-TOD benchmark
为了便于与以前的研究结果进行比较，在测试阶段，我们使用了AI-TOD基准测试

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evaluation metrics, which comprise the Average Precision (AP), AP_0.5, AP_0.75, AP_vt, AP_t, AP_s and AP_m, for AI-TOD, AI-TODv2 and VisDrone2019. For the SODA-D dataset, we use the COCO evaluation metrics.
评估指标，包括 AI-TOD、AI-TODv2 和 VisDrone2019 的平均精度 （AP）、AP _0.5 、AP _{0.75 vt} 、AP、AP、AP _s 和 AP _m 。对于 SODA-D 数据集，我们使用 COCO 评估指标。

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We design four groups of experiments on the AI-TOD, AI-TODv2, VisDrone2019 and SODA-D datasets. In each group, we replace the IoU metric with our SimD metric in the RPN module and then apply this module in combination with traditional object detection models, including Faster R-CNN, Cascade R-CNN and DetectoRS.
我们在 AI-TOD、AI-TODv2、VisDrone2019 和 SODA-D 数据集上设计了四组实验。在每个组中，我们在 RPN 模块中将 IoU 指标替换为 SimD 指标，然后将该模块与传统的对象检测模型（包括 Faster R-CNN、Cascade R-CNN 和 DetectoRS）结合应用。

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The results on AI-TOD are shown in Table II, where we compare our method to several typical object detection methods. The detectors in the first seven rows are two-stage anchor-based detectors, those in the next three and four rows are one-stage anchor-based and anchor-free detectors, respectively, and the last three rows show the results of our method. Compared with Faster R-CNN, Cascade R-CNN and DetectoRS, we achieve AP improvements of 12.8, 11.2 and 11.8 points, respectively, by using SimD in place of the IoU in RPN. We also compare our method with some specialized detectors for tiny objects, namely, DotD, NWD and RFLA, relative to which our method improves the AP by 10.5, 5.8 and 1.8 points, respectively.
AI-TOD的结果如表II所示，我们将我们的方法与几种典型的目标检测方法进行了比较。前七行的探测器是两级基于锚的探测器，接下来的三行和第四行的探测器分别是一级锚和无锚探测器，最后三行显示了我们的方法结果。与Faster R-CNN、Cascade R-CNN和DetectoRS相比，通过使用SimD代替RPN中的IoU，我们分别实现了12.8、11.2和11.8点的AP改进。我们还将我们的方法与一些专门用于微小物体的探测器（即 DotD、NWD 和 RFLA）进行了比较，相对于这些探测器，我们的方法分别将 AP 提高了 10.5、5.8 和 1.8 点。

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The performance of our method on tiny objects is worthy of special attention. Because of the extremely small size of these objects (very tiny refers to a size range from 2 to 8 pixels), the AP_vt of general object detectors is 0, whereas with the use of SimD, the AP_vt values of Faster R-CNN, Cascade R-CNN and DetectoRS are increased from 0 to 11.9, 13.2 and 13.4 points, respectively.
我们的方法在微小物体上的表现值得特别关注。由于这些物体的尺寸非常小（非常小是指 2 到 8 像素的大小范围），一般物体检测器的 AP _vt 为 0，而使用 SimD 时，Faster R-CNN、Cascade R-CNN 和 DetectoRS 的 AP _vt 值分别从 0 增加到 11.9、13.2 和 13.4 点。

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In addition to AI-TOD, our method also achieves the best performance on AI-TODv2, VisDrone2019 and SODA-D, as shown in Table III, Table IV and Table V, respectively. On AI-TODv2 and SODA-D, the AP of our method is 1.8 and 1.6 points higher, respectively, than that of its best competitor. On VisDrone2019, which contains both tiny and general-sized objects, our method also performs well, in particular, it achieves a 1.3 points improvement over RFLA. In Table V, the AP_0.5 is almost at the same level with RFLA but AP_0.75 is much higher, this may indicate that our method is more capable of tiny object detection. Some typical visual comparisons between the IoU metric and SimD are shown in Fig. 3. We can find there is an obvious improvement of detection performance after using our method.
除了AI-TOD之外，我们的方法在AI-TODv2、VisDrone2019和SODA-D上也取得了最佳性能，分别如表III、表IV和表V所示。在AI-TODv2和SODA-D上，我们方法的AP分别比其最佳竞争对手高出1.8和1.6分。在包含微小和一般尺寸物体的 VisDrone2019 上，我们的方法也表现良好，特别是它比 RFLA 提高了 1.3 分。在表V中，AP _0.5 与RFLA几乎处于同一水平，但AP _0.75 要高得多，这可能表明我们的方法更有能力检测微小物体。图 3 显示了 IoU 指标和 SimD 之间的一些典型视觉比较。我们可以发现，使用我们的方法后，检测性能有了明显的提高。

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In our proposed method, an important operation is normalization based on the width and height of the ground truth and anchor. To verify the effectiveness of the normalization operation, we conduct a set of ablation study. As shown in Table VI, we respectively compare not normalizing, normalizing only width, only height, and both width and height. The experimental results show that normalization operation achieves a 3.5 points improvement, mainly benefit by the ability to adapt to objects of different sizes in a dataset, and the normalization parameters $m$, $n$ can be adaptively adjusted according to different datasets.
在我们提出的方法中，一个重要的操作是基于地面实况和锚的宽度和高度进行归一化。为了验证归一化操作的有效性，我们进行了一系列消融研究。如表VI所示，我们分别比较了不归一化、仅归一化宽度、仅归一化高度以及宽度和高度。实验结果表明，归一化操作实现了3.5分的提升，主要得益于能够适应数据集中不同大小的对象，并且归一化参数 $m$ 可以 $n$ 根据不同的数据集进行自适应调整。

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From the experimental results shown in Table II to Table V, we find that our method achieves the best AP on all four datasets. In addition, on the AI-TOD, AI-TODv2, and VisDrone2019 datasets, our method achieves the best results for very tiny, tiny and small objects. Three main achievements of our method can be summarized.
从表二到表五所示的实验结果中，我们发现我们的方法在所有四个数据集上都获得了最佳的AP。此外，在 AI-TOD、AI-TODv2 和 VisDrone2019 数据集上，我们的方法对非常小、微小和很小的物体取得了最佳结果。可以总结我们方法的三个主要成就。

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First, our method effectively solves the problem of low accuracy for tiny objects. The most fundamental reason is that our method fully accounts for the similarity between two bounding boxes, including both location and shape similarity, therefore, only the highest-quality anchors will be chosen as positive samples when using the SimD metric. Compared with VisDrone2019, the performance improvements on AI-TOD and AI-TODv2 are more obvious because the objects are much smaller in these two datasets, this phenomenon may also reflects the effectiveness of our method on tiny object detection.
首先，该方法有效地解决了微小物体精度低的问题。最根本的原因是，我们的方法充分考虑了两个边界框之间的相似性，包括位置和形状相似性，因此，在使用 SimD 度量时，只会选择质量最高的锚点作为正样本。与VisDrone2019相比，AI-TOD和AI-TODv2的性能提升更为明显，因为这两个数据集中的物体要小得多，这种现象也可能反映了我们的方法在微小物体检测上的有效性。

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Second, our method can adapt well to different object sizes in a dataset. In Table IV, both the AP and AP_vt values of our method are the best and much higher than those of other methods. The main reason is that normalization is applied in the SimD metric when calculating the similarity between bounding boxes, so it can eliminate the differences arising from bounding boxes of different sizes. Some typical detection results are shown in Fig. 4.
其次，我们的方法能够很好地适应数据集中不同的对象大小。在表IV中，我们方法的AP值和AP _vt 值都是最好的，远高于其他方法。主要原因是在计算边界框之间的相似度时，SimD 指标中应用了归一化，因此可以消除因不同大小的边界框而产生的差异。一些典型的检测结果如图4所示。

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Finally, our method achieves the state-of-the-art results on four different datasets. Although the characteristics of the objects in different datasets vary, we use the relationships between the ground truths and anchors in the train set when computing the normalization parameters, enabling our metric to automatically adapt to different datasets. In addition, there are no hyperparameters that need to be set in our formula.
最后，我们的方法在四个不同的数据集上实现了最先进的结果。尽管不同数据集中对象的特征各不相同，但在计算归一化参数时，我们利用了训练集中的地面实况和锚点之间的关系，使我们的度量能够自动适应不同的数据集。此外，我们的公式中不需要设置超参数。

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