Four-variable-independent-regression localization losses, such as Smooth- $\ell _{1}$ Loss, are used by default in modern detectors. Nevertheless, this kind of loss is oversimplified so that it is inconsistent with the final evaluation metric, intersection over union (IoU). Directly employing the standard IoU is also not infeasible, since the constant-zero plateau in the case of non-overlapping boxes and the non-zero gradient at the minimum may make it not trainable. Accordingly, we propose a systematic method to address these problems. Firstly, we propose a new metric, the extended IoU (EIoU), which is well-defined when two boxes are not overlapping and reduced to the standard IoU when overlapping. Secondly, we present the convexification technique (CT) to construct a loss on the basis of EIoU, which can guarantee the gradient at the minimum to be zero. Thirdly, we propose a steady optimization technique (SOT) to make the fractional EIoU loss approaching the minimum more steadily and smoothly. Fourthly, to fully exploit the capability of the EIoU based loss, we introduce an interrelated IoU-predicting head to further boost localization accuracy. With the proposed contributions, the new method incorporated into Faster R-CNN with ResNet50+FPN as the backbone yields 4.2 mAP gain on VOC2007 and 2.3 mAP gain on COCO2017 over the baseline Smooth- $\ell _{1}$ Loss, at almost no training and inferencing computational cost. Specifically, the stricter the metric is, the more notable the gain is, improving 8.2 mAP on VOC2007 and 5.4 mAP on COCO2017 at metric $AP_{90}$ .

中文翻译：

---

与IoU相关的系统方法：超越简化回归方法，以实现更好的本地化

四变量独立回归本地化损失，例如Smooth- $ \ ell _ {1} $ 损耗，默认情况下在现代探测器中使用。然而，这种损失被过分简化，以致与最终评估指标“联合相交”（IoU）不一致。直接采用标准IoU也是不可行的，因为在不重叠框的情况下恒定为零的平稳期以及最小的非零梯度可能使其无法训练。因此，我们提出了一种解决这些问题的系统方法。首先，我们提出了一种新的度量标准，即扩展IoU（EIoU），当两个框不重叠时定义明确，而在重叠时降低为标准IoU。其次，我们提出了基于EIoU构造损失的凸化技术（CT），可以保证最小梯度为零。第三，我们提出了一种稳定的优化技术（SOT），以使分数EIoU损耗更加稳定和平稳地接近最小值。第四，为了充分利用基于EIoU的损失的能力，我们引入了一个相互关联的IoU预测头，以进一步提高定位精度。根据拟议的贡献，该新方法将ResNet50 + FPN作为主干并入Faster R-CNN中，在基线上，VOC2007的收益为4.2 mAP，COCO2017的收益为2.3 mAP。 $ \ ell _ {1} $ 损失，几乎无需培训和推理计算成本。具体来说，指标越严格，收益就越显着，在指标上，VOC2007的8.2 mAP和COCO2017的5.4 mAP提高了 $ AP_ {90} $ 。