# Rotationally Equivariant 3D Object Detection

arXiv: https://arxiv.org/abs/2204.13630 · HTML: https://mlsanity.com/paper/2204.13630/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 31 references that are in the map.
- First posted on arXiv 28 Apr 2022.

## Builds on (most cited first, 29 of 29)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [PointPillars: Fast Encoders for Object Detection from Point Clouds](https://mlsanity.com/paper/1812.05784/) (2018)
- [VoxelNet: End-to-End Learning for Point Cloud Based 3D Object Detection](https://mlsanity.com/paper/1711.06396/) (2017)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [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)
- [PV-RCNN: Point-Voxel Feature Set Abstraction for 3D Object Detection](https://mlsanity.com/paper/1912.13192/) (2019)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Deep Hough Voting for 3D Object Detection in Point Clouds](https://mlsanity.com/paper/1904.09664/) (2019)
- [Understanding the Effective Receptive Field in Deep Convolutional Neural Networks](https://mlsanity.com/paper/1701.04128/) (2017)
- [Class-balanced Grouping and Sampling for Point Cloud 3D Object Detection](https://mlsanity.com/paper/1908.09492/) (2019)
- [Point-GNN: Graph Neural Network for 3D Object Detection in a Point Cloud](https://mlsanity.com/paper/2003.01251/) (2020)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [Harmonic Networks: Deep Translation and Rotation Equivariance](https://mlsanity.com/paper/1612.04642/) (2016)
- [Gauge Equivariant Convolutional Networks and the Icosahedral CNN](https://mlsanity.com/paper/1902.04615/) (2019)
- [Learning SO(3) Equivariant Representations with Spherical CNNs](https://mlsanity.com/paper/1711.06721/) (2017)
- [Group-Free 3D Object Detection via Transformers](https://mlsanity.com/paper/2104.00678/) (2021)
- [ReDet: A Rotation-equivariant Detector for Aerial Object Detection](https://mlsanity.com/paper/2103.07733/) (2021)
- [3D Object Detection with Pointformer](https://mlsanity.com/paper/2012.11409/) (2020)
- [Scan2CAD: Learning CAD Model Alignment in RGB-D Scans](https://mlsanity.com/paper/1811.11187/) (2018)
- [H3DNet: 3D Object Detection Using Hybrid Geometric Primitives](https://mlsanity.com/paper/2006.05682/) (2020)
- [Equivariant Point Network for 3D Point Cloud Analysis](https://mlsanity.com/paper/2103.14147/) (2021)
- [MLCVNet: Multi-Level Context VoteNet for 3D Object Detection](https://mlsanity.com/paper/2004.05679/) (2020)
- [Leveraging SE(3) Equivariance for Self-Supervised Category-Level Object Pose Estimation](https://mlsanity.com/paper/2111.00190/) (2021)
- [Discrete Rotation Equivariance for Point Cloud Recognition](https://mlsanity.com/paper/1904.00319/) (2019)
- [Sampling Equivariant Self-attention Networks for Object Detection in Aerial Images](https://mlsanity.com/paper/2111.03420/) (2021)

## Built on by (most cited first, 21 of 21)

- [Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications](https://mlsanity.com/paper/2211.08064/) (2022)
- [Transformation-Equivariant 3D Object Detection for Autonomous Driving](https://mlsanity.com/paper/2211.11962/) (2022)
- [Equivariant Adaptation of Large Pretrained Models](https://mlsanity.com/paper/2310.01647/) (2023)
- [EquivAct: SIM(3)-Equivariant Visuomotor Policies beyond Rigid Object Manipulation](https://mlsanity.com/paper/2310.16050/) (2023)
- [Latent Space Symmetry Discovery](https://mlsanity.com/paper/2310.00105/) (2023)
- [Leveraging SE(3) Equivariance for Learning 3D Geometric Shape Assembly](https://mlsanity.com/paper/2309.06810/) (2023)
- [4D Panoptic Segmentation as Invariant and Equivariant Field Prediction](https://mlsanity.com/paper/2303.15651/) (2023)
- [Banana: Banach Fixed-Point Network for Pointcloud Segmentation with Inter-Part Equivariance](https://mlsanity.com/paper/2305.16314/) (2023)
- [EFEM: Equivariant Neural Field Expectation Maximization for 3D Object Segmentation Without Scene Supervision](https://mlsanity.com/paper/2303.15440/) (2023)
- [Diffusion-SS3D: Diffusion Model for Semi-supervised 3D Object Detection](https://mlsanity.com/paper/2312.02966/) (2023)
- [Relaxed Equivariance via Multitask Learning](https://mlsanity.com/paper/2410.17878/) (2024)
- [Multi-body SE(3) Equivariance for Unsupervised Rigid Segmentation and Motion Estimation](https://mlsanity.com/paper/2306.05584/) (2023)
- [Improved Canonicalization for Model Agnostic Equivariance](https://mlsanity.com/paper/2405.14089/) (2024)
- [Vitruvio: 3D Building Meshes via Single Perspective Sketches](https://mlsanity.com/paper/2210.13634/) (2022)
- [Approximately Piecewise E(3) Equivariant Point Networks](https://mlsanity.com/paper/2402.08529/) (2024)
- [SUP-NeRF: A Streamlined Unification of Pose Estimation and NeRF for Monocular 3D Object Reconstruction](https://mlsanity.com/paper/2403.15705/) (2024)
- [Current Symmetry Group Equivariant Convolution Frameworks for Representation Learning](https://mlsanity.com/paper/2409.07327/) (2024)
- [Learning Generalizable Shape Completion with SIM(3) Equivariance](https://mlsanity.com/paper/2509.26631/) (2025)
- [SUIT: Learning Significance-guided Information for 3D Temporal Detection](https://mlsanity.com/paper/2307.01807/) (2023)
- [RIDE: Boosting 3D Object Detection for LiDAR Point Clouds via Rotation-Invariant Analysis](https://mlsanity.com/paper/2408.15643/) (2024)
- [Learning Geometric Invariance for Gait Recognition](https://mlsanity.com/paper/2601.05604/) (2026)

## Abstract (arXiv)

Rotation equivariance has recently become a strongly desired property in the 3D deep learning community. Yet most existing methods focus on equivariance regarding a global input rotation while ignoring the fact that rotation symmetry has its own spatial support. Specifically, we consider the object detection problem in 3D scenes, where an object bounding box should be equivariant regarding the object pose, independent of the scene motion. This suggests a new desired property we call object-level rotation equivariance. To incorporate object-level rotation equivariance into 3D object detectors, we need a mechanism to extract equivariant features with local object-level spatial support while being able to model cross-object context information. To this end, we propose Equivariant Object detection Network (EON) with a rotation equivariance suspension design to achieve object-level equivariance. EON can be applied to modern point cloud object detectors, such as VoteNet and PointRCNN, enabling them to exploit object rotation symmetry in scene-scale inputs. Our experiments on both indoor scene and autonomous driving datasets show that significant improvements are obtained by plugging our EON design into existing state-of-the-art 3D object detectors.