# SO(3)-Pose: SO(3)-Equivariance Learning for 6D Object Pose Estimation

arXiv: https://arxiv.org/abs/2208.08338 · HTML: https://mlsanity.com/paper/2208.08338/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 58 references that are in the map.
- First posted on arXiv 17 Aug 2022.

## Builds on (most cited first, 30 of 35)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Pyramid Scene Parsing Network](https://mlsanity.com/paper/1612.01105/) (2016)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [ORB-SLAM: a Versatile and Accurate Monocular SLAM System](https://mlsanity.com/paper/1502.00956/) (2015)
- [PoseCNN: A Convolutional Neural Network for 6D Object Pose Estimation in Cluttered Scenes](https://mlsanity.com/paper/1711.00199/) (2017)
- [PVNet: Pixel-wise Voting Network for 6DoF Pose Estimation](https://mlsanity.com/paper/1812.11788/) (2018)
- [DenseFusion: 6D Object Pose Estimation by Iterative Dense Fusion](https://mlsanity.com/paper/1901.04780/) (2019)
- [MaX-DeepLab: End-to-End Panoptic Segmentation with Mask Transformers](https://mlsanity.com/paper/2012.00759/) (2020)
- [XCiT: Cross-Covariance Image Transformers](https://mlsanity.com/paper/2106.09681/) (2021)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [DeepIM: Deep Iterative Matching for 6D Pose Estimation](https://mlsanity.com/paper/1804.00175/) (2018)
- [SSD-6D: Making RGB-based 3D detection and 6D pose estimation great again](https://mlsanity.com/paper/1711.10006/) (2017)
- [BB8: A Scalable, Accurate, Robust to Partial Occlusion Method for Predicting the 3D Poses of Challenging Objects without Using Depth](https://mlsanity.com/paper/1703.10896/) (2017)
- [Pix2Pose: Pixel-Wise Coordinate Regression of Objects for 6D Pose Estimation](https://mlsanity.com/paper/1908.07433/) (2019)
- [Real-Time Seamless Single Shot 6D Object Pose Prediction](https://mlsanity.com/paper/1711.08848/) (2017)
- [PVN3D: A Deep Point-wise 3D Keypoints Voting Network for 6DoF Pose Estimation](https://mlsanity.com/paper/1911.04231/) (2019)
- [DPOD: 6D Pose Object Detector and Refiner](https://mlsanity.com/paper/1902.11020/) (2019)
- [PointFusion: Deep Sensor Fusion for 3D Bounding Box Estimation](https://mlsanity.com/paper/1711.10871/) (2017)
- [Implicit 3D Orientation Learning for 6D Object Detection from RGB Images](https://mlsanity.com/paper/1902.01275/) (2019)
- [FFB6D: A Full Flow Bidirectional Fusion Network for 6D Pose Estimation](https://mlsanity.com/paper/2103.02242/) (2021)
- [HybridPose: 6D Object Pose Estimation under Hybrid Representations](https://mlsanity.com/paper/2001.01869/) (2020)
- [Segmentation-driven 6D Object Pose Estimation](https://mlsanity.com/paper/1812.02541/) (2018)
- [In Defense of Classical Image Processing: Fast Depth Completion on the CPU](https://mlsanity.com/paper/1802.00036/) (2018)
- [Single-Stage 6D Object Pose Estimation](https://mlsanity.com/paper/1911.08324/) (2019)
- [A comprehensive survey on point cloud registration](https://mlsanity.com/paper/2103.02690/) (2021)
- [Effective Rotation-invariant Point CNN with Spherical Harmonics kernels](https://mlsanity.com/paper/1906.11555/) (2019)
- [Leveraging SE(3) Equivariance for Self-Supervised Category-Level Object Pose Estimation](https://mlsanity.com/paper/2111.00190/) (2021)
- [G2L-Net: Global to Local Network for Real-time 6D Pose Estimation with Embedding Vector Features](https://mlsanity.com/paper/2003.11089/) (2020)
- [Going Further with Point Pair Features](https://mlsanity.com/paper/1711.04061/) (2017)

## Built on by (most cited first, 4 of 4)

- [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)
- [Approximately Piecewise E(3) Equivariant Point Networks](https://mlsanity.com/paper/2402.08529/) (2024)
- [Learning Generalizable Shape Completion with SIM(3) Equivariance](https://mlsanity.com/paper/2509.26631/) (2025)

## Abstract (arXiv)

6D pose estimation of rigid objects from RGB-D images is crucial for object grasping and manipulation in robotics. Although RGB channels and the depth (D) channel are often complementary, providing respectively the appearance and geometry information, it is still non-trivial how to fully benefit from the two cross-modal data. From the simple yet new observation, when an object rotates, its semantic label is invariant to the pose while its keypoint offset direction is variant to the pose. To this end, we present SO(3)-Pose, a new representation learning network to explore SO(3)-equivariant and SO(3)-invariant features from the depth channel for pose estimation. The SO(3)-invariant features facilitate to learn more distinctive representations for segmenting objects with similar appearance from RGB channels. The SO(3)-equivariant features communicate with RGB features to deduce the (missed) geometry for detecting keypoints of an object with the reflective surface from the depth channel. Unlike most of existing pose estimation methods, our SO(3)-Pose not only implements the information communication between the RGB and depth channels, but also naturally absorbs the SO(3)-equivariance geometry knowledge from depth images, leading to better appearance and geometry representation learning. Comprehensive experiments show that our method achieves the state-of-the-art performance on three benchmarks.