# EFEM: Equivariant Neural Field Expectation Maximization for 3D Object Segmentation Without Scene Supervision

arXiv: https://arxiv.org/abs/2303.15440 · HTML: https://mlsanity.com/paper/2303.15440/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 70 of its 91 references that are in the map.
- First posted on arXiv 27 Mar 2023.

## Builds on (most cited first, 30 of 70)

- [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)
- [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)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Matterport3D: Learning from RGB-D Data in Indoor Environments](https://mlsanity.com/paper/1709.06158/) (2017)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [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)
- [SAPIEN: A SimulAted Part-based Interactive ENvironment](https://mlsanity.com/paper/2003.08515/) (2020)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [PointContrast: Unsupervised Pre-training for 3D Point Cloud Understanding](https://mlsanity.com/paper/2007.10985/) (2020)
- [3D-FRONT: 3D Furnished Rooms with layOuts and semaNTics](https://mlsanity.com/paper/2011.09127/) (2020)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [DISN: Deep Implicit Surface Network for High-quality Single-view 3D Reconstruction](https://mlsanity.com/paper/1905.10711/) (2019)
- [PointGroup: Dual-Set Point Grouping for 3D Instance Segmentation](https://mlsanity.com/paper/2004.01658/) (2020)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups](https://mlsanity.com/paper/1802.03690/) (2018)
- [A General Theory of Equivariant CNNs on Homogeneous Spaces](https://mlsanity.com/paper/1811.02017/) (2018)
- [3D-SIS: 3D Semantic Instance Segmentation of RGB-D Scans](https://mlsanity.com/paper/1812.07003/) (2018)
- [Exploring Data-Efficient 3D Scene Understanding with Contrastive Scene Contexts](https://mlsanity.com/paper/2012.09165/) (2020)
- [Neural Descriptor Fields: SE(3)-Equivariant Object Representations for Manipulation](https://mlsanity.com/paper/2112.05124/) (2021)
- [SoftGroup for 3D Instance Segmentation on Point Clouds](https://mlsanity.com/paper/2203.01509/) (2022)
- [OccuSeg: Occupancy-aware 3D Instance Segmentation](https://mlsanity.com/paper/2003.06537/) (2020)
- [SGPN: Similarity Group Proposal Network for 3D Point Cloud Instance Segmentation](https://mlsanity.com/paper/1711.08588/) (2017)

## Built on by (most cited first, 18 of 18)

- [EquiBot: SIM(3)-Equivariant Diffusion Policy for Generalizable and Data Efficient Learning](https://mlsanity.com/paper/2407.01479/) (2024)
- [Diffusion-EDFs: Bi-equivariant Denoising Generative Modeling on SE(3) for Visual Robotic Manipulation](https://mlsanity.com/paper/2309.02685/) (2023)
- [EquivAct: SIM(3)-Equivariant Visuomotor Policies beyond Rigid Object Manipulation](https://mlsanity.com/paper/2310.16050/) (2023)
- [Banana: Banach Fixed-Point Network for Pointcloud Segmentation with Inter-Part Equivariance](https://mlsanity.com/paper/2305.16314/) (2023)
- [ZeroPS: High-quality Cross-modal Knowledge Transfer for Zero-Shot 3D Part Segmentation](https://mlsanity.com/paper/2311.14262/) (2023)
- [U3DS3: Unsupervised 3D Semantic Scene Segmentation](https://mlsanity.com/paper/2311.06018/) (2023)
- [A Survey of Robotic Navigation and Manipulation with Physics Simulators in the Era of Embodied AI](https://mlsanity.com/paper/2505.01458/) (2025)
- [Living Scenes: Multi-object Relocalization and Reconstruction in Changing 3D Environments](https://mlsanity.com/paper/2312.09138/) (2023)
- [RiEMann: Near Real-Time SE(3)-Equivariant Robot Manipulation without Point Cloud Segmentation](https://mlsanity.com/paper/2403.19460/) (2024)
- [GAGrasp: Geometric Algebra Diffusion for Dexterous Grasping](https://mlsanity.com/paper/2503.04123/) (2025)
- [Multi-body SE(3) Equivariance for Unsupervised Rigid Segmentation and Motion Estimation](https://mlsanity.com/paper/2306.05584/) (2023)
- [EqvAfford: SE(3) Equivariance for Point-Level Affordance Learning](https://mlsanity.com/paper/2408.01953/) (2024)
- [GrabS: Generative Embodied Agent for 3D Object Segmentation without Scene Supervision](https://mlsanity.com/paper/2504.11754/) (2025)
- [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)
- [Bayesian Self-Training for Semi-Supervised 3D Segmentation](https://mlsanity.com/paper/2409.08102/) (2024)
- [EvObj: Learning Evolving Object-centric Representations for 3D Instance Segmentation without Scene Supervision](https://mlsanity.com/paper/2605.13152/) (2026)
- [FoundObj: Self-supervised Foundation Models as Rewards for Label-free 3D Object Segmentation](https://mlsanity.com/paper/2605.27178/) (2026)

## Abstract (arXiv)

We introduce Equivariant Neural Field Expectation Maximization (EFEM), a simple, effective, and robust geometric algorithm that can segment objects in 3D scenes without annotations or training on scenes. We achieve such unsupervised segmentation by exploiting single object shape priors. We make two novel steps in that direction. First, we introduce equivariant shape representations to this problem to eliminate the complexity induced by the variation in object configuration. Second, we propose a novel EM algorithm that can iteratively refine segmentation masks using the equivariant shape prior. We collect a novel real dataset Chairs and Mugs that contains various object configurations and novel scenes in order to verify the effectiveness and robustness of our method. Experimental results demonstrate that our method achieves consistent and robust performance across different scenes where the (weakly) supervised methods may fail. Code and data available at https://www.cis.upenn.edu/~leijh/projects/efem