# Leveraging SE(3) Equivariance for Self-Supervised Category-Level Object Pose Estimation

arXiv: https://arxiv.org/abs/2111.00190 · HTML: https://mlsanity.com/paper/2111.00190/

## Key facts

- Cited by 45 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 27 references that are in the map.
- First posted on arXiv 30 Oct 2021.

## Builds on (most cited first, 22 of 22)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [PoseCNN: A Convolutional Neural Network for 6D Object Pose Estimation in Cluttered Scenes](https://mlsanity.com/paper/1711.00199/) (2017)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Normalized Object Coordinate Space for Category-Level 6D Object Pose and Size Estimation](https://mlsanity.com/paper/1901.02970/) (2019)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [Shape Prior Deformation for Categorical 6D Object Pose and Size Estimation](https://mlsanity.com/paper/2007.08454/) (2020)
- [Category-Level Articulated Object Pose Estimation](https://mlsanity.com/paper/1912.11913/) (2019)
- [Learning Canonical Shape Space for Category-Level 6D Object Pose and Size Estimation](https://mlsanity.com/paper/2001.09322/) (2020)
- [Category Level Object Pose Estimation via Neural Analysis-by-Synthesis](https://mlsanity.com/paper/2008.08145/) (2020)
- [Unsupervised Learning of Shape and Pose with Differentiable Point Clouds](https://mlsanity.com/paper/1810.09381/) (2018)
- [Equivariant Point Network for 3D Point Cloud Analysis](https://mlsanity.com/paper/2103.14147/) (2021)
- [Self6D: Self-Supervised Monocular 6D Object Pose Estimation](https://mlsanity.com/paper/2004.06468/) (2020)
- [6-PACK: Category-level 6D Pose Tracker with Anchor-Based Keypoints](https://mlsanity.com/paper/1910.10750/) (2019)
- [Effective Rotation-invariant Point CNN with Spherical Harmonics kernels](https://mlsanity.com/paper/1906.11555/) (2019)
- [Multi-view Consistency as Supervisory Signal for Learning Shape and Pose Prediction](https://mlsanity.com/paper/1801.03910/) (2018)
- [Quaternion Equivariant Capsule Networks for 3D Point Clouds](https://mlsanity.com/paper/1912.12098/) (2019)
- [Pointwise Rotation-Invariant Network with Adaptive Sampling and 3D Spherical Voxel Convolution](https://mlsanity.com/paper/1811.09361/) (2018)
- [Domain Transfer for 3D Pose Estimation from Color Images without Manual Annotations](https://mlsanity.com/paper/1810.03707/) (2018)

## Built on by (most cited first, 30 of 45)

- [BundleSDF: Neural 6-DoF Tracking and 3D Reconstruction of Unknown Objects](https://mlsanity.com/paper/2303.14158/) (2023)
- [Zero-Shot Category-Level Object Pose Estimation](https://mlsanity.com/paper/2204.03635/) (2022)
- [Equivariant Descriptor Fields: SE(3)-Equivariant Energy-Based Models for End-to-End Visual Robotic Manipulation Learning](https://mlsanity.com/paper/2206.08321/) (2022)
- [Deep Learning-Based Object Pose Estimation: A Comprehensive Survey](https://mlsanity.com/paper/2405.07801/) (2024)
- [OPDMulti: Openable Part Detection for Multiple Objects](https://mlsanity.com/paper/2303.14087/) (2023)
- [Leveraging SE(3) Equivariance for Learning 3D Geometric Shape Assembly](https://mlsanity.com/paper/2309.06810/) (2023)
- [USEEK: Unsupervised SE(3)-Equivariant 3D Keypoints for Generalizable Manipulation](https://mlsanity.com/paper/2209.13864/) (2022)
- [Self-Supervised Category-Level Articulated Object Pose Estimation with Part-Level SE(3) Equivariance](https://mlsanity.com/paper/2302.14268/) (2023)
- [UDA-COPE: Unsupervised Domain Adaptation for Category-level Object Pose Estimation](https://mlsanity.com/paper/2111.12580/) (2021)
- [Rotationally Equivariant 3D Object Detection](https://mlsanity.com/paper/2204.13630/) (2022)
- [A General Theory of Correct, Incorrect, and Extrinsic Equivariance](https://mlsanity.com/paper/2303.04745/) (2023)
- [Banana: Banach Fixed-Point Network for Pointcloud Segmentation with Inter-Part Equivariance](https://mlsanity.com/paper/2305.16314/) (2023)
- [StereoPose: Category-Level 6D Transparent Object Pose Estimation from Stereo Images via Back-View NOCS](https://mlsanity.com/paper/2211.01644/) (2022)
- [EFEM: Equivariant Neural Field Expectation Maximization for 3D Object Segmentation Without Scene Supervision](https://mlsanity.com/paper/2303.15440/) (2023)
- [Shape-Pose Disentanglement using SE(3)-equivariant Vector Neurons](https://mlsanity.com/paper/2204.01159/) (2022)
- [Generalizing Neural Human Fitting to Unseen Poses With Articulated SE(3) Equivariance](https://mlsanity.com/paper/2304.10528/) (2023)
- [SOCS: Semantically-aware Object Coordinate Space for Category-Level 6D Object Pose Estimation under Large Shape Variations](https://mlsanity.com/paper/2303.10346/) (2023)
- [Certifiable 3D Object Pose Estimation: Foundations, Learning Models, and Self-Training](https://mlsanity.com/paper/2206.11215/) (2022)
- [UNOPose: Unseen Object Pose Estimation with an Unposed RGB-D Reference Image](https://mlsanity.com/paper/2411.16106/) (2024)
- [Towards Self-Supervised Category-Level Object Pose and Size Estimation](https://mlsanity.com/paper/2203.02884/) (2022)
- [OP-Align: Object-level and Part-level Alignment for Self-supervised Category-level Articulated Object Pose Estimation](https://mlsanity.com/paper/2408.16547/) (2024)
- [Optimal and Robust Category-level Perception: Object Pose and Shape Estimation from 2D and 3D Semantic Keypoints](https://mlsanity.com/paper/2206.12498/) (2022)
- [Multi-body SE(3) Equivariance for Unsupervised Rigid Segmentation and Motion Estimation](https://mlsanity.com/paper/2306.05584/) (2023)
- [A Correct-and-Certify Approach to Self-Supervise Object Pose Estimators via Ensemble Self-Training](https://mlsanity.com/paper/2302.06019/) (2023)
- [PRISM-DP: Spatial Pose-based Observations for Diffusion-Policies via Segmentation, Mesh Generation, and Pose Tracking](https://mlsanity.com/paper/2504.20359/) (2025)
- [PCRP: Unsupervised Point Cloud Object Retrieval and Pose Estimation](https://mlsanity.com/paper/2202.07843/) (2022)
- [SO(3)-Pose: SO(3)-Equivariance Learning for 6D Object Pose Estimation](https://mlsanity.com/paper/2208.08338/) (2022)
- [Approximately Piecewise E(3) Equivariant Point Networks](https://mlsanity.com/paper/2402.08529/) (2024)
- [Category-Level Global Camera Pose Estimation with Multi-Hypothesis Point Cloud Correspondences](https://mlsanity.com/paper/2209.14419/) (2022)
- [S3I-PointHop: SO(3)-Invariant PointHop for 3D Point Cloud Classification](https://mlsanity.com/paper/2302.11506/) (2023)

## Abstract (arXiv)

Category-level object pose estimation aims to find 6D object poses of previously unseen object instances from known categories without access to object CAD models. To reduce the huge amount of pose annotations needed for category-level learning, we propose for the first time a self-supervised learning framework to estimate category-level 6D object pose from single 3D point clouds.During training, our method assumes no ground-truth pose annotations, no CAD models, and no multi-view supervision. The key to our method is to disentangle shape and pose through an invariant shape reconstruction module and an equivariant pose estimation module, empowered by SE(3) equivariant point cloud networks.The invariant shape reconstruction module learns to perform aligned reconstructions, yielding a category-level reference frame without using any annotations. In addition, the equivariant pose estimation module achieves category-level pose estimation accuracy that is comparable to some fully supervised methods. Extensive experiments demonstrate the effectiveness of our approach on both complete and partial depth point clouds from the ModelNet40 benchmark, and on real depth point clouds from the NOCS-REAL 275 dataset. The project page with code and visualizations can be found at: https://dragonlong.github.io/equi-pose.