# Intersection over Union with smoothing for bounding box regression

arXiv: https://arxiv.org/abs/2303.15067 · HTML: https://mlsanity.com/paper/2303.15067/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 22 references that are in the map.
- First posted on arXiv 27 Mar 2023.

## Builds on (most cited first, 14 of 14)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [YOLOv3: An Incremental Improvement](https://mlsanity.com/paper/1804.02767/) (2018)
- [Rich feature hierarchies for accurate object detection and semantic segmentation](https://mlsanity.com/paper/1311.2524/) (2013)
- [Generalized Intersection over Union: A Metric and A Loss for Bounding Box Regression](https://mlsanity.com/paper/1902.09630/) (2019)
- [EfficientNetV2: Smaller Models and Faster Training](https://mlsanity.com/paper/2104.00298/) (2021)
- [When Does Label Smoothing Help?](https://mlsanity.com/paper/1906.02629/) (2019)
- [Distance-IoU Loss: Faster and Better Learning for Bounding Box Regression](https://mlsanity.com/paper/1911.08287/) (2019)
- [Libra R-CNN: Towards Balanced Learning for Object Detection](https://mlsanity.com/paper/1904.02701/) (2019)
- [UnitBox: An Advanced Object Detection Network](https://mlsanity.com/paper/1608.01471/) (2016)
- [Dynamic R-CNN: Towards High Quality Object Detection via Dynamic Training](https://mlsanity.com/paper/2004.06002/) (2020)
- [Focal and Efficient IOU Loss for Accurate Bounding Box Regression](https://mlsanity.com/paper/2101.08158/) (2021)
- [SIoU Loss: More Powerful Learning for Bounding Box Regression](https://mlsanity.com/paper/2205.12740/) (2022)

## Built on by (most cited first, 1 of 1)

- [DiTOX: Fault Detection and Localization in the ONNX Optimizer](https://mlsanity.com/paper/2505.01892/) (2025)

## Abstract (arXiv)

We focus on the construction of a loss function for the bounding box regression. The Intersection over Union (IoU) metric is improved to converge faster, to make the surface of the loss function smooth and continuous over the whole searched space, and to reach a more precise approximation of the labels. The main principle is adding a smoothing part to the original IoU, where the smoothing part is given by a linear space with values that increases from the ground truth bounding box to the border of the input image, and thus covers the whole spatial search space. We show the motivation and formalism behind this loss function and experimentally prove that it outperforms IoU, DIoU, CIoU, and SIoU by a large margin. We experimentally show that the proposed loss function is robust with respect to the noise in the dimension of ground truth bounding boxes. The reference implementation is available at gitlab.com/irafm-ai/smoothing-iou.