# A Systematic IoU-Related Method: Beyond Simplified Regression for Better Localization

arXiv: https://arxiv.org/abs/2112.01793 · HTML: https://mlsanity.com/paper/2112.01793/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 44 references that are in the map.
- First posted on arXiv 3 Dec 2021.

## Builds on (most cited first, 30 of 34)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Feature Pyramid Networks for Object Detection](https://mlsanity.com/paper/1612.03144/) (2016)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [SSD: Single Shot MultiBox Detector](https://mlsanity.com/paper/1512.02325/) (2015)
- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [YOLOv3: An Incremental Improvement](https://mlsanity.com/paper/1804.02767/) (2018)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [Rich feature hierarchies for accurate object detection and semantic segmentation](https://mlsanity.com/paper/1311.2524/) (2013)
- [FCOS: Fully Convolutional One-Stage Object Detection](https://mlsanity.com/paper/1904.01355/) (2019)
- [YOLO9000: Better, Faster, Stronger](https://mlsanity.com/paper/1612.08242/) (2016)
- [Generalized Intersection over Union: A Metric and A Loss for Bounding Box Regression](https://mlsanity.com/paper/1902.09630/) (2019)
- [Cascade R-CNN: Delving into High Quality Object Detection](https://mlsanity.com/paper/1712.00726/) (2017)
- [Objects as Points](https://mlsanity.com/paper/1904.07850/) (2019)
- [Stacked Hourglass Networks for Human Pose Estimation](https://mlsanity.com/paper/1603.06937/) (2016)
- [CornerNet: Detecting Objects as Paired Keypoints](https://mlsanity.com/paper/1808.01244/) (2018)
- [CenterNet: Keypoint Triplets for Object Detection](https://mlsanity.com/paper/1904.08189/) (2019)
- [Distance-IoU Loss: Faster and Better Learning for Bounding Box Regression](https://mlsanity.com/paper/1911.08287/) (2019)
- [R-FCN: Object Detection via Region-based Fully Convolutional Networks](https://mlsanity.com/paper/1605.06409/) (2016)
- [Object Detection in Optical Remote Sensing Images: A Survey and A New Benchmark](https://mlsanity.com/paper/1909.00133/) (2019)
- [UnitBox: An Advanced Object Detection Network](https://mlsanity.com/paper/1608.01471/) (2016)
- [Acquisition of Localization Confidence for Accurate Object Detection](https://mlsanity.com/paper/1807.11590/) (2018)
- [Scale-Aware Trident Networks for Object Detection](https://mlsanity.com/paper/1901.01892/) (2019)
- [Feature Selective Anchor-Free Module for Single-Shot Object Detection](https://mlsanity.com/paper/1903.00621/) (2019)
- [DSSD : Deconvolutional Single Shot Detector](https://mlsanity.com/paper/1701.06659/) (2017)
- [Single-Shot Refinement Neural Network for Object Detection](https://mlsanity.com/paper/1711.06897/) (2017)
- [Grid R-CNN](https://mlsanity.com/paper/1811.12030/) (2018)

## Built on by (most cited first, 4 of 4)

- [AutoShot: A Short Video Dataset and State-of-the-Art Shot Boundary Detection](https://mlsanity.com/paper/2304.06116/) (2023)
- [CitDet: A Benchmark Dataset for Citrus Fruit Detection](https://mlsanity.com/paper/2309.05645/) (2023)
- [Decoupled IoU Regression for Object Detection](https://mlsanity.com/paper/2202.00866/) (2022)
- [Geometry Meets Semantics: Fractional Gradient Stabilization for Semantic-Driven Bounding Box Optimization in Visual Detection Tasks](https://mlsanity.com/paper/2607.23530/) (2026)

## Abstract (arXiv)

Four-variable-independent-regression localization losses, such as Smooth-ℓ1 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-ℓ1 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 AP90.