# Spatially Invariant Unsupervised 3D Object-Centric Learning and Scene Decomposition

arXiv: https://arxiv.org/abs/2106.05607 · HTML: https://mlsanity.com/paper/2106.05607/

## Key facts

- Cited by 2 papers in the map (data through 7 Oct 2026).
- Builds on 29 of its 41 references that are in the map.
- First posted on arXiv 10 Jun 2021.

## Builds on (most cited first, 29 of 29)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [Object-Centric Learning with Slot Attention](https://mlsanity.com/paper/2006.15055/) (2020)
- [AI2-THOR: An Interactive 3D Environment for Visual AI](https://mlsanity.com/paper/1712.05474/) (2017)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [PointConv: Deep Convolutional Networks on 3D Point Clouds](https://mlsanity.com/paper/1811.07246/) (2018)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [Joint 2D-3D-Semantic Data for Indoor Scene Understanding](https://mlsanity.com/paper/1702.01105/) (2017)
- [MONet: Unsupervised Scene Decomposition and Representation](https://mlsanity.com/paper/1901.11390/) (2019)
- [Multi-Object Representation Learning with Iterative Variational Inference](https://mlsanity.com/paper/1903.00450/) (2019)
- [Point-GNN: Graph Neural Network for 3D Object Detection in a Point Cloud](https://mlsanity.com/paper/2003.01251/) (2020)
- [PointGroup: Dual-Set Point Grouping for 3D Instance Segmentation](https://mlsanity.com/paper/2004.01658/) (2020)
- [Unity: A General Platform for Intelligent Agents](https://mlsanity.com/paper/1809.02627/) (2018)
- [GENESIS: Generative Scene Inference and Sampling with Object-Centric Latent Representations](https://mlsanity.com/paper/1907.13052/) (2019)
- [Attend, Infer, Repeat: Fast Scene Understanding with Generative Models](https://mlsanity.com/paper/1603.08575/) (2016)
- [SPACE: Unsupervised Object-Oriented Scene Representation via Spatial Attention and Decomposition](https://mlsanity.com/paper/2001.02407/) (2020)
- [How Much Position Information Do Convolutional Neural Networks Encode?](https://mlsanity.com/paper/2001.08248/) (2020)
- [Neural Expectation Maximization](https://mlsanity.com/paper/1708.03498/) (2017)
- [A Compositional Object-Based Approach to Learning Physical Dynamics](https://mlsanity.com/paper/1612.00341/) (2016)
- [Multiresolution Tree Networks for 3D Point Cloud Processing](https://mlsanity.com/paper/1807.03520/) (2018)
- [Decomposing 3D Scenes into Objects via Unsupervised Volume Segmentation](https://mlsanity.com/paper/2104.01148/) (2021)
- [Schema Networks: Zero-shot Transfer with a Generative Causal Model of Intuitive Physics](https://mlsanity.com/paper/1706.04317/) (2017)
- [Exploiting Spatial Invariance for Scalable Unsupervised Object Tracking](https://mlsanity.com/paper/1911.09033/) (2019)
- [ROOTS: Object-Centric Representation and Rendering of 3D Scenes](https://mlsanity.com/paper/2006.06130/) (2020)
- [Unsupervised object-centric video generation and decomposition in 3D](https://mlsanity.com/paper/2007.06705/) (2020)
- [Variational Memory Addressing in Generative Models](https://mlsanity.com/paper/1709.07116/) (2017)

## Built on by (most cited first, 2 of 2)

- [Unsupervised Discovery of Object-Centric Neural Fields](https://mlsanity.com/paper/2402.07376/) (2024)
- [3D-DLP: Self-Supervised 3D Object-Centric Scene Representation Learning](https://mlsanity.com/paper/2606.19451/) (2026)

## Abstract (arXiv)

We tackle the problem of object-centric learning on point clouds, which is crucial for high-level relational reasoning and scalable machine intelligence. In particular, we introduce a framework, SPAIR3D, to factorize a 3D point cloud into a spatial mixture model where each component corresponds to one object. To model the spatial mixture model on point clouds, we derive the Chamfer Mixture Loss, which fits naturally into our variational training pipeline. Moreover, we adopt an object-specification scheme that describes each object's location relative to its local voxel grid cell. Such a scheme allows SPAIR3D to model scenes with an arbitrary number of objects. We evaluate our method on the task of unsupervised scene decomposition. Experimental results demonstrate that SPAIR3D has strong scalability and is capable of detecting and segmenting an unknown number of objects from a point cloud in an unsupervised manner.