# Gaussian Bounding Boxes and Probabilistic Intersection-over-Union for Object Detection

arXiv: https://arxiv.org/abs/2106.06072 · HTML: https://mlsanity.com/paper/2106.06072/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 68 references that are in the map.
- First posted on arXiv 10 Jun 2021.

## Builds on (most cited first, 30 of 36)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [Feature Pyramid Networks for Object Detection](https://mlsanity.com/paper/1612.03144/) (2016)
- [SSD: Single Shot MultiBox Detector](https://mlsanity.com/paper/1512.02325/) (2015)
- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [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)
- [LVIS: A Dataset for Large Vocabulary Instance Segmentation](https://mlsanity.com/paper/1908.03195/) (2019)
- [EfficientDet: Scalable and Efficient Object Detection](https://mlsanity.com/paper/1911.09070/) (2019)
- [Panoptic Segmentation](https://mlsanity.com/paper/1801.00868/) (2018)
- [Path Aggregation Network for Instance Segmentation](https://mlsanity.com/paper/1803.01534/) (2018)
- [DOTA: A Large-scale Dataset for Object Detection in Aerial Images](https://mlsanity.com/paper/1711.10398/) (2017)
- [Object Detection in 20 Years: A Survey](https://mlsanity.com/paper/1905.05055/) (2019)
- [Distance-IoU Loss: Faster and Better Learning for Bounding Box Regression](https://mlsanity.com/paper/1911.08287/) (2019)
- [Deep Learning for Generic Object Detection: A Survey](https://mlsanity.com/paper/1809.02165/) (2018)
- [UnitBox: An Advanced Object Detection Network](https://mlsanity.com/paper/1608.01471/) (2016)
- [ReDet: A Rotation-equivariant Detector for Aerial Object Detection](https://mlsanity.com/paper/2103.07733/) (2021)
- [iSAID: A Large-scale Dataset for Instance Segmentation in Aerial Images](https://mlsanity.com/paper/1905.12886/) (2019)
- [R3Det: Refined Single-Stage Detector with Feature Refinement for Rotating Object](https://mlsanity.com/paper/1908.05612/) (2019)
- [Align Deep Features for Oriented Object Detection](https://mlsanity.com/paper/2008.09397/) (2020)
- [Arbitrary-Oriented Scene Text Detection via Rotation Proposals](https://mlsanity.com/paper/1703.01086/) (2017)
- [Rethinking Rotated Object Detection with Gaussian Wasserstein Distance Loss](https://mlsanity.com/paper/2101.11952/) (2021)
- [Learning High-Precision Bounding Box for Rotated Object Detection via Kullback-Leibler Divergence](https://mlsanity.com/paper/2106.01883/) (2021)
- [IoU Loss for 2D/3D Object Detection](https://mlsanity.com/paper/1908.03851/) (2019)
- [TextBoxes++: A Single-Shot Oriented Scene Text Detector](https://mlsanity.com/paper/1801.02765/) (2018)
- [Imbalance Problems in Object Detection: A Review](https://mlsanity.com/paper/1909.00169/) (2019)
- [LambdaNetworks: Modeling Long-Range Interactions Without Attention](https://mlsanity.com/paper/2102.08602/) (2021)
- [Oriented RepPoints for Aerial Object Detection](https://mlsanity.com/paper/2105.11111/) (2021)
- [Rethinking Classification and Localization for Object Detection](https://mlsanity.com/paper/1904.06493/) (2019)

## Built on by (most cited first, 18 of 18)

- [MMRotate: A Rotated Object Detection Benchmark using PyTorch](https://mlsanity.com/paper/2204.13317/) (2022)
- [The KFIoU Loss for Rotated Object Detection](https://mlsanity.com/paper/2201.12558/) (2022)
- [PointOBB-v2: Towards Simpler, Faster, and Stronger Single Point Supervised Oriented Object Detection](https://mlsanity.com/paper/2410.08210/) (2024)
- [Point2RBox-v2: Rethinking Point-supervised Oriented Object Detection with Spatial Layout Among Instances](https://mlsanity.com/paper/2502.04268/) (2025)
- [FCOSR: A Simple Anchor-free Rotated Detector for Aerial Object Detection](https://mlsanity.com/paper/2111.10780/) (2021)
- [FROSS: Faster-than-Real-Time Online 3D Semantic Scene Graph Generation from RGB-D Images](https://mlsanity.com/paper/2507.19993/) (2025)
- [GauCho: Gaussian Distributions with Cholesky Decomposition for Oriented Object Detection](https://mlsanity.com/paper/2502.01565/) (2025)
- [PP-YOLOE-R: An Efficient Anchor-Free Rotated Object Detector](https://mlsanity.com/paper/2211.02386/) (2022)
- [Cell Tracking-by-detection using Elliptical Bounding Boxes](https://mlsanity.com/paper/2310.04895/) (2023)
- [DeWorldSG: Depth-Aware 3D Semantic Scene Graph Generation via World-Model Priors](https://mlsanity.com/paper/2607.00889/) (2026)
- [Soft Labels for Rapid Satellite Object Detection](https://mlsanity.com/paper/2212.00585/) (2022)
- [Object Detection performance variation on compressed satellite image datasets with iquaflow](https://mlsanity.com/paper/2301.05892/) (2023)
- [FPDIoU Loss: A Loss Function for Efficient Bounding Box Regression of Rotated Object Detection](https://mlsanity.com/paper/2405.09942/) (2024)
- [Advanced YOLO-based Real-time Power Line Detection for Vegetation Management](https://mlsanity.com/paper/2503.00044/) (2025)
- [Pixel-level Quality Assessment for Oriented Object Detection](https://mlsanity.com/paper/2511.08186/) (2025)
- [Fourier Series Coder: A Novel Perspective on Angle Boundary Discontinuity Problem for Oriented Object Detection](https://mlsanity.com/paper/2604.20281/) (2026)
- [PUF: Plug-and-Play Uncertainty-Aware Fusion for Online 3D Scene Graph Generation](https://mlsanity.com/paper/2607.07170/) (2026)
- [Multi-Modal Graph Neural Network-Inspired Vessel Identification and Tracking for UAV-Based Maritime Surveillance](https://mlsanity.com/paper/2610.13220/) (2026)

## Abstract (arXiv)

Most object detection methods use bounding boxes to encode and represent the object shape and location. In this work, we explore a fuzzy representation of object regions using Gaussian distributions, which provides an implicit binary representation as (potentially rotated) ellipses. We also present a similarity measure for the Gaussian distributions based on the Hellinger Distance, which can be viewed as a Probabilistic Intersection-over-Union (ProbIoU). Our experimental results show that the proposed Gaussian representations are closer to annotated segmentation masks in publicly available datasets, and that loss functions based on ProbIoU can be successfully used to regress the parameters of the Gaussian representation. Furthermore, we present a simple mapping scheme from traditional (or rotated) bounding boxes to Gaussian representations, allowing the proposed ProbIoU-based losses to be seamlessly integrated into any object detector.