# Transformation-Equivariant 3D Object Detection for Autonomous Driving

arXiv: https://arxiv.org/abs/2211.11962 · HTML: https://mlsanity.com/paper/2211.11962/

## Key facts

- Cited by 52 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 44 references that are in the map.
- First posted on arXiv 22 Nov 2022.

## Builds on (most cited first, 30 of 37)

- [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)
- [VoxelNet: End-to-End Learning for Point Cloud Based 3D Object Detection](https://mlsanity.com/paper/1711.06396/) (2017)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [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)
- [3D Semantic Segmentation with Submanifold Sparse Convolutional Networks](https://mlsanity.com/paper/1711.10275/) (2017)
- [Multi-View 3D Object Detection Network for Autonomous Driving](https://mlsanity.com/paper/1611.07759/) (2016)
- [Frustum PointNets for 3D Object Detection from RGB-D Data](https://mlsanity.com/paper/1711.08488/) (2017)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [3DSSD: Point-based 3D Single Stage Object Detector](https://mlsanity.com/paper/2002.10187/) (2020)
- [Voxel R-CNN: Towards High Performance Voxel-based 3D Object Detection](https://mlsanity.com/paper/2012.15712/) (2020)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [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)
- [STD: Sparse-to-Dense 3D Object Detector for Point Cloud](https://mlsanity.com/paper/1907.10471/) (2019)
- [PV-RCNN++: Point-Voxel Feature Set Abstraction With Local Vector Representation for 3D Object Detection](https://mlsanity.com/paper/2102.00463/) (2021)
- [ReDet: A Rotation-equivariant Detector for Aerial Object Detection](https://mlsanity.com/paper/2103.07733/) (2021)
- [Learning Steerable Filters for Rotation Equivariant CNNs](https://mlsanity.com/paper/1711.07289/) (2017)
- [Multimodal Virtual Point 3D Detection](https://mlsanity.com/paper/2111.06881/) (2021)
- [EPNet: Enhancing Point Features with Image Semantics for 3D Object Detection](https://mlsanity.com/paper/2007.08856/) (2020)
- [PENet: Towards Precise and Efficient Image Guided Depth Completion](https://mlsanity.com/paper/2103.00783/) (2021)
- [Not All Points Are Equal: Learning Highly Efficient Point-based Detectors for 3D LiDAR Point Clouds](https://mlsanity.com/paper/2203.11139/) (2022)
- [Frustum ConvNet: Sliding Frustums to Aggregate Local Point-Wise Features for Amodal 3D Object Detection](https://mlsanity.com/paper/1903.01864/) (2019)
- [Better Aggregation in Test-Time Augmentation](https://mlsanity.com/paper/2011.11156/) (2020)
- [SE-SSD: Self-Ensembling Single-Stage Object Detector From Point Cloud](https://mlsanity.com/paper/2104.09804/) (2021)
- [Improving 3D Object Detection with Channel-wise Transformer](https://mlsanity.com/paper/2108.10723/) (2021)
- [Sparse Fuse Dense: Towards High Quality 3D Detection with Depth Completion](https://mlsanity.com/paper/2203.09780/) (2022)
- [Equivariant Point Network for 3D Point Cloud Analysis](https://mlsanity.com/paper/2103.14147/) (2021)

## Built on by (most cited first, 30 of 52)

- [Equivariant Adaptation of Large Pretrained Models](https://mlsanity.com/paper/2310.01647/) (2023)
- [Learning Occupancy for Monocular 3D Object Detection](https://mlsanity.com/paper/2305.15694/) (2023)
- [4D Panoptic Segmentation as Invariant and Equivariant Field Prediction](https://mlsanity.com/paper/2303.15651/) (2023)
- [DPFT: Dual Perspective Fusion Transformer for Camera-Radar-based Object Detection](https://mlsanity.com/paper/2404.03015/) (2024)
- [Neural Radiance Field in Autonomous Driving: A Survey](https://mlsanity.com/paper/2404.13816/) (2024)
- [V2X-R: Cooperative LiDAR-4D Radar Fusion with Denoising Diffusion for 3D Object Detection](https://mlsanity.com/paper/2411.08402/) (2024)
- [Human-centric Scene Understanding for 3D Large-scale Scenarios](https://mlsanity.com/paper/2307.14392/) (2023)
- [Data-Centric Evolution in Autonomous Driving: A Comprehensive Survey of Big Data System, Data Mining, and Closed-Loop Technologies](https://mlsanity.com/paper/2401.12888/) (2024)
- [Unlocking Textual and Visual Wisdom: Open-Vocabulary 3D Object Detection Enhanced by Comprehensive Guidance from Text and Image](https://mlsanity.com/paper/2407.05256/) (2024)
- [PointSeg: A Training-Free Paradigm for 3D Scene Segmentation via Foundation Models](https://mlsanity.com/paper/2403.06403/) (2024)
- [ContextualFusion: Context-Based Multi-Sensor Fusion for 3D Object Detection in Adverse Operating Conditions](https://mlsanity.com/paper/2404.14780/) (2024)
- [Improved Canonicalization for Model Agnostic Equivariance](https://mlsanity.com/paper/2405.14089/) (2024)
- [CT3D++: Improving 3D Object Detection with Keypoint-induced Channel-wise Transformer](https://mlsanity.com/paper/2406.08152/) (2024)
- [TripleMixer: A 3D Point Cloud Denoising Model for Adverse Weather](https://mlsanity.com/paper/2408.13802/) (2024)
- [CurveCloudNet: Processing Point Clouds with 1D Structure](https://mlsanity.com/paper/2303.12050/) (2023)
- [INTACT: Inducing Noise Tolerance through Adversarial Curriculum Training for LiDAR-based Safety-Critical Perception and Autonomy](https://mlsanity.com/paper/2502.01896/) (2025)
- [INSTINCT: Instance-Level Interaction Architecture for Query-Based Collaborative Perception](https://mlsanity.com/paper/2509.23700/) (2025)
- [Towards Accurate and Efficient 3D Object Detection for Autonomous Driving: A Mixture of Experts Computing System on Edge](https://mlsanity.com/paper/2507.04123/) (2025)
- [Reflectance Prediction-based Knowledge Distillation for Robust 3D Object Detection in Compressed Point Clouds](https://mlsanity.com/paper/2505.17442/) (2025)
- [LiDAR-BEVMTN: Real-Time LiDAR Bird's-Eye View Multi-Task Perception Network for Autonomous Driving](https://mlsanity.com/paper/2307.08850/) (2023)
- [NIV-SSD: Neighbor IoU-Voting Single-Stage Object Detector From Point Cloud](https://mlsanity.com/paper/2401.12447/) (2024)
- [SeePerSea: Multi-modal Perception Dataset of In-water Objects for Autonomous Surface Vehicles](https://mlsanity.com/paper/2404.18411/) (2024)
- [Semi-Supervised 3D Object Detection with Channel Augmentation using Transformation Equivariance](https://mlsanity.com/paper/2409.06583/) (2024)
- [Current Symmetry Group Equivariant Convolution Frameworks for Representation Learning](https://mlsanity.com/paper/2409.07327/) (2024)
- [RALAD: Bridging the Real-to-Sim Domain Gap in Autonomous Driving with Retrieval-Augmented Learning](https://mlsanity.com/paper/2501.12296/) (2025)
- [A Multimodal Hybrid Late-Cascade Fusion Network for Enhanced 3D Object Detection](https://mlsanity.com/paper/2504.18419/) (2025)
- [Multistream Network for LiDAR and Camera-based 3D Object Detection in Outdoor Scenes](https://mlsanity.com/paper/2507.19304/) (2025)
- [Propagating Sparse Depth via Depth Foundation Model for Out-of-Distribution Depth Completion](https://mlsanity.com/paper/2508.04984/) (2025)
- [CMF-IoU: Multi-Stage Cross-Modal Fusion 3D Object Detection with IoU Joint Prediction](https://mlsanity.com/paper/2508.12917/) (2025)
- [Towards Open-Vocabulary Multimodal 3D Object Detection with Attributes](https://mlsanity.com/paper/2508.16812/) (2025)

## Abstract (arXiv)

3D object detection received increasing attention in autonomous driving recently. Objects in 3D scenes are distributed with diverse orientations. Ordinary detectors do not explicitly model the variations of rotation and reflection transformations. Consequently, large networks and extensive data augmentation are required for robust detection. Recent equivariant networks explicitly model the transformation variations by applying shared networks on multiple transformed point clouds, showing great potential in object geometry modeling. However, it is difficult to apply such networks to 3D object detection in autonomous driving due to its large computation cost and slow reasoning speed. In this work, we present TED, an efficient Transformation-Equivariant 3D Detector to overcome the computation cost and speed issues. TED first applies a sparse convolution backbone to extract multi-channel transformation-equivariant voxel features; and then aligns and aggregates these equivariant features into lightweight and compact representations for high-performance 3D object detection. On the highly competitive KITTI 3D car detection leaderboard, TED ranked 1st among all submissions with competitive efficiency.