# Shape-Pose Disentanglement using SE(3)-equivariant Vector Neurons

arXiv: https://arxiv.org/abs/2204.01159 · HTML: https://mlsanity.com/paper/2204.01159/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 31 references that are in the map.
- First posted on arXiv 3 Apr 2022.

## Builds on (most cited first, 28 of 28)

- [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)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [PointRCNN: 3D Object Proposal Generation and Detection from Point Cloud](https://mlsanity.com/paper/1812.04244/) (2018)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [3DSSD: Point-based 3D Single Stage Object Detector](https://mlsanity.com/paper/2002.10187/) (2020)
- [Rethinking Network Design and Local Geometry in Point Cloud: A Simple Residual MLP Framework](https://mlsanity.com/paper/2202.07123/) (2022)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [DISN: Deep Implicit Surface Network for High-quality Single-view 3D Reconstruction](https://mlsanity.com/paper/1905.10711/) (2019)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [Learning SO(3) Equivariant Representations with Spherical CNNs](https://mlsanity.com/paper/1711.06721/) (2017)
- [MVTN: Multi-View Transformation Network for 3D Shape Recognition](https://mlsanity.com/paper/2011.13244/) (2020)
- [TANet: Robust 3D Object Detection from Point Clouds with Triple Attention](https://mlsanity.com/paper/1912.05163/) (2019)
- [Learning elementary structures for 3D shape generation and matching](https://mlsanity.com/paper/1908.04725/) (2019)
- [C3DPO: Canonical 3D Pose Networks for Non-Rigid Structure From Motion](https://mlsanity.com/paper/1909.02533/) (2019)
- [CaSPR: Learning Canonical Spatiotemporal Point Cloud Representations](https://mlsanity.com/paper/2008.02792/) (2020)
- [Leveraging SE(3) Equivariance for Self-Supervised Category-Level Object Pose Estimation](https://mlsanity.com/paper/2111.00190/) (2021)
- [Weakly-supervised 3D Shape Completion in the Wild](https://mlsanity.com/paper/2008.09110/) (2020)
- [ConDor: Self-Supervised Canonicalization of 3D Pose for Partial Shapes](https://mlsanity.com/paper/2201.07788/) (2022)
- [Canonical Capsules: Self-Supervised Capsules in Canonical Pose](https://mlsanity.com/paper/2012.04718/) (2020)
- [Learning to Orient Surfaces by Self-supervised Spherical CNNs](https://mlsanity.com/paper/2011.03298/) (2020)

## Built on by (most cited first, 16 of 16)

- [EquivAct: SIM(3)-Equivariant Visuomotor Policies beyond Rigid Object Manipulation](https://mlsanity.com/paper/2310.16050/) (2023)
- [Leveraging SE(3) Equivariance for Learning 3D Geometric Shape Assembly](https://mlsanity.com/paper/2309.06810/) (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)
- [Generalizing Neural Human Fitting to Unseen Poses With Articulated SE(3) Equivariance](https://mlsanity.com/paper/2304.10528/) (2023)
- [ShapeMatcher: Self-Supervised Joint Shape Canonicalization, Segmentation, Retrieval and Deformation](https://mlsanity.com/paper/2311.11106/) (2023)
- [Approximately Piecewise E(3) Equivariant Point Networks](https://mlsanity.com/paper/2402.08529/) (2024)
- [CrossJEPA: Cross-Modal Joint-Embedding Predictive Architecture for Efficient 3D Representation Learning from 2D Images](https://mlsanity.com/paper/2511.18424/) (2025)
- [Category-Level Global Camera Pose Estimation with Multi-Hypothesis Point Cloud Correspondences](https://mlsanity.com/paper/2209.14419/) (2022)
- [Stable and Consistent Prediction of 3D Characteristic Orientation via Invariant Residual Learning](https://mlsanity.com/paper/2306.11406/) (2023)
- [Learning SO(3)-Invariant Semantic Correspondence via Local Shape Transform](https://mlsanity.com/paper/2404.11156/) (2024)
- [3D Surface Reconstruction in the Wild by Deforming Shape Priors from Synthetic Data](https://mlsanity.com/paper/2302.12883/) (2023)
- [Learning Generalizable Shape Completion with SIM(3) Equivariance](https://mlsanity.com/paper/2509.26631/) (2025)
- [Symmetry-Robust 3D Orientation Estimation](https://mlsanity.com/paper/2410.02101/) (2024)
- [Coalgebras for categorical deep learning: Representability and universal approximation](https://mlsanity.com/paper/2603.03227/) (2026)
- [SCAPO: Self-Supervised Category-Level Articulated Pose Estimation from a Single 3D Observation](https://mlsanity.com/paper/2606.01940/) (2026)

## Abstract (arXiv)

We introduce an unsupervised technique for encoding point clouds into a canonical shape representation, by disentangling shape and pose. Our encoder is stable and consistent, meaning that the shape encoding is purely pose-invariant, while the extracted rotation and translation are able to semantically align different input shapes of the same class to a common canonical pose. Specifically, we design an auto-encoder based on Vector Neuron Networks, a rotation-equivariant neural network, whose layers we extend to provide translation-equivariance in addition to rotation-equivariance only. The resulting encoder produces pose-invariant shape encoding by construction, enabling our approach to focus on learning a consistent canonical pose for a class of objects. Quantitative and qualitative experiments validate the superior stability and consistency of our approach.