  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 \textbf{4.2 mAP} gain on
VOC2007 and \textbf{2.3 mAP} gain on COCO2017 over the baseline Smooth-$\ell_1$
Loss, at almost \textbf{no training and inferencing computational cost}.
Specifically, the stricter the metric is, the more notable the gain is,
improving \textbf{8.2 mAP} on VOC2007 and \textbf{5.4 mAP} on COCO2017 at
metric $AP_{90}$.
