# FRED: Towards a Full Rotation-Equivariance in Aerial Image Object Detection

arXiv: https://arxiv.org/abs/2401.06159 · HTML: https://mlsanity.com/paper/2401.06159/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 32 references that are in the map.
- First posted on arXiv 22 Dec 2023.

## Builds on (most cited first, 26 of 26)

- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Generalized Intersection over Union: A Metric and A Loss for Bounding Box Regression](https://mlsanity.com/paper/1902.09630/) (2019)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Deformable ConvNets v2: More Deformable, Better Results](https://mlsanity.com/paper/1811.11168/) (2018)
- [DOTA: A Large-scale Dataset for Object Detection in Aerial Images](https://mlsanity.com/paper/1711.10398/) (2017)
- [Hybrid Task Cascade for Instance Segmentation](https://mlsanity.com/paper/1901.07518/) (2019)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [Rotation Equivariant CNNs for Digital Pathology](https://mlsanity.com/paper/1806.03962/) (2018)
- [RepPoints: Point Set Representation for Object Detection](https://mlsanity.com/paper/1904.11490/) (2019)
- [Object Detection in Aerial Images: A Large-Scale Benchmark and Challenges](https://mlsanity.com/paper/2102.12219/) (2021)
- [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)
- [Align Deep Features for Oriented Object Detection](https://mlsanity.com/paper/2008.09397/) (2020)
- [Gliding vertex on the horizontal bounding box for multi-oriented object detection](https://mlsanity.com/paper/1911.09358/) (2019)
- [MMRotate: A Rotated Object Detection Benchmark using PyTorch](https://mlsanity.com/paper/2204.13317/) (2022)
- [Oriented RepPoints for Aerial Object Detection](https://mlsanity.com/paper/2105.11111/) (2021)
- [Learning Modulated Loss for Rotated Object Detection](https://mlsanity.com/paper/1911.08299/) (2019)
- [The KFIoU Loss for Rotated Object Detection](https://mlsanity.com/paper/2201.12558/) (2022)
- [Dynamic Refinement Network for Oriented and Densely Packed Object Detection](https://mlsanity.com/paper/2005.09973/) (2020)
- [Dynamic Anchor Learning for Arbitrary-Oriented Object Detection](https://mlsanity.com/paper/2012.04150/) (2020)
- [Attentive Group Equivariant Convolutional Networks](https://mlsanity.com/paper/2002.03830/) (2020)
- [PIoU Loss: Towards Accurate Oriented Object Detection in Complex Environments](https://mlsanity.com/paper/2007.09584/) (2020)
- [Oriented Objects as pairs of Middle Lines](https://mlsanity.com/paper/1912.10694/) (2019)
- [Learning Rotation-Equivariant Features for Visual Correspondence](https://mlsanity.com/paper/2303.15472/) (2023)
- [RSDet++: Point-based Modulated Loss for More Accurate Rotated Object Detection](https://mlsanity.com/paper/2109.11906/) (2021)
- [Rotation Equivariant Siamese Networks for Tracking](https://mlsanity.com/paper/2012.13078/) (2020)

## Built on by (most cited first, 7 of 7)

- [GauCho: Gaussian Distributions with Cholesky Decomposition for Oriented Object Detection](https://mlsanity.com/paper/2502.01565/) (2025)
- [R2Det: Exploring Relaxed Rotation Equivariance in 2D object detection](https://mlsanity.com/paper/2408.11760/) (2024)
- [Measuring the Impact of Rotation Equivariance on Aerial Object Detection](https://mlsanity.com/paper/2507.09896/) (2025)
- [Real-Time Oriented Object Detection Transformer in Remote Sensing Images](https://mlsanity.com/paper/2603.15497/) (2026)
- [Semantic-decoupled Spatial Partition Guided Point-supervised Oriented Object Detection](https://mlsanity.com/paper/2506.10601/) (2025)
- [Learning Geometric Invariance for Gait Recognition](https://mlsanity.com/paper/2601.05604/) (2026)
- [Geometric Causal Models](https://mlsanity.com/paper/2607.05153/) (2026)

## Abstract (arXiv)

Rotation-equivariance is an essential yet challenging property in oriented object detection. While general object detectors naturally leverage robustness to spatial shifts due to the translation-equivariance of the conventional CNNs, achieving rotation-equivariance remains an elusive goal. Current detectors deploy various alignment techniques to derive rotation-invariant features, but still rely on high capacity models and heavy data augmentation with all possible rotations. In this paper, we introduce a Fully Rotation-Equivariant Oriented Object Detector (FRED), whose entire process from the image to the bounding box prediction is strictly equivariant. Specifically, we decouple the invariant task (object classification) and the equivariant task (object localization) to achieve end-to-end equivariance. We represent the bounding box as a set of rotation-equivariant vectors to implement rotation-equivariant localization. Moreover, we utilized these rotation-equivariant vectors as offsets in the deformable convolution, thereby enhancing the existing advantages of spatial adaptation. Leveraging full rotation-equivariance, our FRED demonstrates higher robustness to image-level rotation compared to existing methods. Furthermore, we show that FRED is one step closer to non-axis aligned learning through our experiments. Compared to state-of-the-art methods, our proposed method delivers comparable performance on DOTA-v1.0 and outperforms by 1.5 mAP on DOTA-v1.5, all while significantly reducing the model parameters to 16%.