# Detecting Rotated Objects as Gaussian Distributions and Its 3-D Generalization

arXiv: https://arxiv.org/abs/2209.10839 · HTML: https://mlsanity.com/paper/2209.10839/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- Builds on 61 of its 93 references that are in the map.
- First posted on arXiv 22 Sep 2022.

## Builds on (most cited first, 30 of 61)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Feature Pyramid Networks for Object Detection](https://mlsanity.com/paper/1612.03144/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [SSD: Single Shot MultiBox Detector](https://mlsanity.com/paper/1512.02325/) (2015)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [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)
- [FCOS: Fully Convolutional One-Stage Object Detection](https://mlsanity.com/paper/1904.01355/) (2019)
- [MMDetection: Open MMLab Detection Toolbox and Benchmark](https://mlsanity.com/paper/1906.07155/) (2019)
- [Generalized Intersection over Union: A Metric and A Loss for Bounding Box Regression](https://mlsanity.com/paper/1902.09630/) (2019)
- [VoxelNet: End-to-End Learning for Point Cloud Based 3D Object Detection](https://mlsanity.com/paper/1711.06396/) (2017)
- [Center-based 3D Object Detection and Tracking](https://mlsanity.com/paper/2006.11275/) (2020)
- [PointRCNN: 3D Object Proposal Generation and Detection from Point Cloud](https://mlsanity.com/paper/1812.04244/) (2018)
- [Stacked Hourglass Networks for Human Pose Estimation](https://mlsanity.com/paper/1603.06937/) (2016)
- [DOTA: A Large-scale Dataset for Object Detection in Aerial Images](https://mlsanity.com/paper/1711.10398/) (2017)
- [Bridging the Gap Between Anchor-based and Anchor-free Detection via Adaptive Training Sample Selection](https://mlsanity.com/paper/1912.02424/) (2019)
- [Distance-IoU Loss: Faster and Better Learning for Bounding Box Regression](https://mlsanity.com/paper/1911.08287/) (2019)
- [Deep Layer Aggregation](https://mlsanity.com/paper/1707.06484/) (2017)
- [Conditional Convolutions for Instance Segmentation](https://mlsanity.com/paper/2003.05664/) (2020)
- [SOLO: Segmenting Objects by Locations](https://mlsanity.com/paper/1912.04488/) (2019)
- [EAST: An Efficient and Accurate Scene Text Detector](https://mlsanity.com/paper/1704.03155/) (2017)
- [ReDet: A Rotation-equivariant Detector for Aerial Object Detection](https://mlsanity.com/paper/2103.07733/) (2021)
- [R3Det: Refined Single-Stage Detector with Feature Refinement for Rotating Object](https://mlsanity.com/paper/1908.05612/) (2019)
- [PolarMask: Single Shot Instance Segmentation with Polar Representation](https://mlsanity.com/paper/1909.13226/) (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)

## Built on by (most cited first, 30 of 36)

- [SkySenseGPT: A Fine-Grained Instruction Tuning Dataset and Model for Remote Sensing Vision-Language Understanding](https://mlsanity.com/paper/2406.10100/) (2024)
- [Adaptive Rotated Convolution for Rotated Object Detection](https://mlsanity.com/paper/2303.07820/) (2023)
- [Dynamic Coarse-to-Fine Learning for Oriented Tiny Object Detection](https://mlsanity.com/paper/2304.08876/) (2023)
- [H2RBox: Horizontal Box Annotation is All You Need for Oriented Object Detection](https://mlsanity.com/paper/2210.06742/) (2022)
- [Towards Vision-Language Geo-Foundation Model: A Survey](https://mlsanity.com/paper/2406.09385/) (2024)
- [H2RBox-v2: Incorporating Symmetry for Boosting Horizontal Box Supervised Oriented Object Detection](https://mlsanity.com/paper/2304.04403/) (2023)
- [PointOBB: Learning Oriented Object Detection via Single Point Supervision](https://mlsanity.com/paper/2311.14757/) (2023)
- [Box2Mask: Box-supervised Instance Segmentation via Level-set Evolution](https://mlsanity.com/paper/2212.01579/) (2022)
- [Point2RBox: Combine Knowledge from Synthetic Visual Patterns for End-to-end Oriented Object Detection with Single Point Supervision](https://mlsanity.com/paper/2311.14758/) (2023)
- [E2E-MFD: Towards End-to-End Synchronous Multimodal Fusion Detection](https://mlsanity.com/paper/2403.09323/) (2024)
- [Remote Sensing Object Detection Meets Deep Learning: A Meta-review of Challenges and Advances](https://mlsanity.com/paper/2309.06751/) (2023)
- [Learning to Holistically Detect Bridges from Large-Size VHR Remote Sensing Imagery](https://mlsanity.com/paper/2312.02481/) (2023)
- [GRA: Detecting Oriented Objects through Group-wise Rotating and Attention](https://mlsanity.com/paper/2403.11127/) (2024)
- [PointOBB-v2: Towards Simpler, Faster, and Stronger Single Point Supervised Oriented Object Detection](https://mlsanity.com/paper/2410.08210/) (2024)
- [SOOD++: Leveraging Unlabeled Data to Boost Oriented Object Detection](https://mlsanity.com/paper/2407.01016/) (2024)
- [Multi-clue Consistency Learning to Bridge Gaps Between General and Oriented Object in Semi-supervised Detection](https://mlsanity.com/paper/2407.05909/) (2024)
- [Point2RBox-v2: Rethinking Point-supervised Oriented Object Detection with Spatial Layout Among Instances](https://mlsanity.com/paper/2502.04268/) (2025)
- [PointOBB-v3: Expanding Performance Boundaries of Single Point-Supervised Oriented Object Detection](https://mlsanity.com/paper/2501.13898/) (2025)
- [PatchDCT: Patch Refinement for High Quality Instance Segmentation](https://mlsanity.com/paper/2302.02693/) (2023)
- [Oriented object detection in optical remote sensing images using deep learning: a survey](https://mlsanity.com/paper/2302.10473/) (2023)
- [GauCho: Gaussian Distributions with Cholesky Decomposition for Oriented Object Detection](https://mlsanity.com/paper/2502.01565/) (2025)
- [Wholly-WOOD: Wholly Leveraging Diversified-quality Labels for Weakly-supervised Oriented Object Detection](https://mlsanity.com/paper/2502.09471/) (2025)
- [MutDet: Mutually Optimizing Pre-training for Remote Sensing Object Detection](https://mlsanity.com/paper/2407.09920/) (2024)
- [Exploiting Unlabeled Data with Multiple Expert Teachers for Open Vocabulary Aerial Object Detection and Its Orientation Adaptation](https://mlsanity.com/paper/2411.02057/) (2024)
- [DVGBench: Implicit-to-Explicit Visual Grounding Benchmark in UAV Imagery with Large Vision-Language Models](https://mlsanity.com/paper/2601.00998/) (2026)
- [Linear Gaussian Bounding Box Representation and Ring-Shaped Rotated Convolution for Oriented Object Detection](https://mlsanity.com/paper/2311.05410/) (2023)
- [Oriented Tiny Object Detection: A Dataset, Benchmark, and Dynamic Unbiased Learning](https://mlsanity.com/paper/2412.11582/) (2024)
- [Partial Weakly-Supervised Oriented Object Detection](https://mlsanity.com/paper/2507.02751/) (2025)
- [AirSpatialBot: A Spatially-Aware Aerial Agent for Fine-Grained Vehicle Attribute Recognization and Retrieval](https://mlsanity.com/paper/2601.01416/) (2026)
- [Deep Learning-Based Object Detection in Maritime Unmanned Aerial Vehicle Imagery: Review and Experimental Comparisons](https://mlsanity.com/paper/2311.07955/) (2023)

## Abstract (arXiv)

Existing detection methods commonly use a parameterized bounding box (BBox) to model and detect (horizontal) objects and an additional rotation angle parameter is used for rotated objects. We argue that such a mechanism has fundamental limitations in building an effective regression loss for rotation detection, especially for high-precision detection with high IoU (e.g. 0.75). Instead, we propose to model the rotated objects as Gaussian distributions. A direct advantage is that our new regression loss regarding the distance between two Gaussians e.g. Kullback-Leibler Divergence (KLD), can well align the actual detection performance metric, which is not well addressed in existing methods. Moreover, the two bottlenecks i.e. boundary discontinuity and square-like problem also disappear. We also propose an efficient Gaussian metric-based label assignment strategy to further boost the performance. Interestingly, by analyzing the BBox parameters' gradients under our Gaussian-based KLD loss, we show that these parameters are dynamically updated with interpretable physical meaning, which help explain the effectiveness of our approach, especially for high-precision detection. We extend our approach from 2-D to 3-D with a tailored algorithm design to handle the heading estimation, and experimental results on twelve public datasets (2-D/3-D, aerial/text/face images) with various base detectors show its superiority.