# Polygon Intersection-over-Union Loss for Viewpoint-Agnostic Monocular 3D Vehicle Detection

arXiv: https://arxiv.org/abs/2309.07104 · HTML: https://mlsanity.com/paper/2309.07104/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 38 references that are in the map.
- First posted on arXiv 13 Sep 2023.

## Builds on (most cited first, 25 of 25)

- [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)
- [YOLOv3: An Incremental Improvement](https://mlsanity.com/paper/1804.02767/) (2018)
- [Scalability in Perception for Autonomous Driving: Waymo Open Dataset](https://mlsanity.com/paper/1912.04838/) (2019)
- [PointPillars: Fast Encoders for Object Detection from Point Clouds](https://mlsanity.com/paper/1812.05784/) (2018)
- [YOLOv4: Optimal Speed and Accuracy of Object Detection](https://mlsanity.com/paper/2004.10934/) (2020)
- [Generalized Intersection over Union: A Metric and A Loss for Bounding Box Regression](https://mlsanity.com/paper/1902.09630/) (2019)
- [Objects as Points](https://mlsanity.com/paper/1904.07850/) (2019)
- [PointRCNN: 3D Object Proposal Generation and Detection from Point Cloud](https://mlsanity.com/paper/1812.04244/) (2018)
- [PV-RCNN: Point-Voxel Feature Set Abstraction for 3D Object Detection](https://mlsanity.com/paper/1912.13192/) (2019)
- [Frustum PointNets for 3D Object Detection from RGB-D Data](https://mlsanity.com/paper/1711.08488/) (2017)
- [Distance-IoU Loss: Faster and Better Learning for Bounding Box Regression](https://mlsanity.com/paper/1911.08287/) (2019)
- [3D Bounding Box Estimation Using Deep Learning and Geometry](https://mlsanity.com/paper/1612.00496/) (2016)
- [Orthographic Feature Transform for Monocular 3D Object Detection](https://mlsanity.com/paper/1811.08188/) (2018)
- [Objects are Different: Flexible Monocular 3D Object Detection](https://mlsanity.com/paper/2104.02323/) (2021)
- [RTM3D: Real-time Monocular 3D Detection from Object Keypoints for Autonomous Driving](https://mlsanity.com/paper/2001.03343/) (2020)
- [IoU Loss for 2D/3D Object Detection](https://mlsanity.com/paper/1908.03851/) (2019)
- [Enhancing Geometric Factors in Model Learning and Inference for Object Detection and Instance Segmentation](https://mlsanity.com/paper/2005.03572/) (2020)
- [Deep MANTA: A Coarse-to-fine Many-Task Network for joint 2D and 3D vehicle analysis from monocular image](https://mlsanity.com/paper/1703.07570/) (2017)
- [Geometry-based Distance Decomposition for Monocular 3D Object Detection](https://mlsanity.com/paper/2104.03775/) (2021)
- [Joint Monocular 3D Vehicle Detection and Tracking](https://mlsanity.com/paper/1811.10742/) (2018)
- [Learning Auxiliary Monocular Contexts Helps Monocular 3D Object Detection](https://mlsanity.com/paper/2112.04628/) (2021)
- [Mono3D++: Monocular 3D Vehicle Detection with Two-Scale 3D Hypotheses and Task Priors](https://mlsanity.com/paper/1901.03446/) (2019)
- [Shift R-CNN: Deep Monocular 3D Object Detection with Closed-Form Geometric Constraints](https://mlsanity.com/paper/1905.09970/) (2019)
- [3D Bounding Box Estimation for Autonomous Vehicles by Cascaded Geometric Constraints and Depurated 2D Detections Using 3D Results](https://mlsanity.com/paper/1909.01867/) (2019)

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

- [SAR2Struct: Extracting 3D Semantic Structural Representation of Aircraft Targets from Single-View SAR Image](https://mlsanity.com/paper/2506.06757/) (2025)

## Abstract (arXiv)

Monocular 3D object detection is a challenging task because depth information is difficult to obtain from 2D images. A subset of viewpoint-agnostic monocular 3D detection methods also do not explicitly leverage scene homography or geometry during training, meaning that a model trained thusly can detect objects in images from arbitrary viewpoints. Such works predict the projections of the 3D bounding boxes on the image plane to estimate the location of the 3D boxes, but these projections are not rectangular so the calculation of IoU between these projected polygons is not straightforward. This work proposes an efficient, fully differentiable algorithm for the calculation of IoU between two convex polygons, which can be utilized to compute the IoU between two 3D bounding box footprints viewed from an arbitrary angle. We test the performance of the proposed polygon IoU loss (PIoU loss) on three state-of-the-art viewpoint-agnostic 3D detection models. Experiments demonstrate that the proposed PIoU loss converges faster than L1 loss and that in 3D detection models, a combination of PIoU loss and L1 loss gives better results than L1 loss alone (+1.64% AP70 for MonoCon on cars, +0.18% AP70 for RTM3D on cars, and +0.83%/+2.46% AP50/AP25 for MonoRCNN on cyclists).