mlsanityData to 14 Oct 2026

Leveraging SE(3) Equivariance for Learning 3D Geometric Shape Assembly

arXiv 2309.06810 ↗First posted 13 Sep 2023cs.CV cs.AIcited by 28

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Abstract (arXiv)

Shape assembly aims to reassemble parts (or fragments) into a complete object, which is a common task in our daily life. Different from the semantic part assembly (e.g., assembling a chair's semantic parts like legs into a whole chair), geometric part assembly (e.g., assembling bowl fragments into a complete bowl) is an emerging task in computer vision and robotics. Instead of semantic information, this task focuses on geometric information of parts. As the both geometric and pose space of fractured parts are exceptionally large, shape pose disentanglement of part representations is beneficial to geometric shape assembly. In our paper, we propose to leverage SE(3) equivariance for such shape pose disentanglement. Moreover, while previous works in vision and robotics only consider SE(3) equivariance for the representations of single objects, we move a step forward and propose leveraging SE(3) equivariance for representations considering multi-part correlations, which further boosts the performance of the multi-part assembly. Experiments demonstrate the significance of SE(3) equivariance and our proposed method for geometric shape assembly. Project page: https://crtie.github.io/SE-3-part-assembly/

Key facts. Cited by 28 papers in the map (data through 14 Oct 2026). Builds on 31 of its 39 references that are in the map. First posted on arXiv 13 Sep 2023.

Builds on

31 of 39 references.

References · 31

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2015ShapeNet: An Information-Rich 3D Model Repositorycited by 2,897
  3. 2018Dynamic Graph CNN for Learning on Point Cloudscited by 2,223
  4. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 746
  5. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 607
  6. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 354
  7. 2021Vector Neurons: A General Framework for SO(3)-Equivariant Networkscited by 305
  8. 2021Neural Descriptor Fields: SE(3)-Equivariant Object Representations for Manipulationcited by 209
  9. 2017Visual Translation Embedding Network for Visual Relation Detectioncited by 112
  10. 2021Equivariant Point Network for 3D Point Cloud Analysiscited by 81
  11. 2021JoinABLe: Learning Bottom-up Assembly of Parametric CAD Jointscited by 78
  12. 2019IKEA Furniture Assembly Environment for Long-Horizon Complex Manipulation Taskscited by 69
19 more
  1. 2020Generative 3D Part Assembly via Dynamic Graph Learningcited by 67
  2. 2022Equivariant Descriptor Fields: SE(3)-Equivariant Energy-Based Models for End-to-End Visual Robotic Manipulation Learningcited by 56
  3. 2020Learning 3D Part Assembly from a Single Imagecited by 52
  4. 2019Form2Fit: Learning Shape Priors for Generalizable Assembly from Disassemblycited by 51
  5. 2022SE(3)-Equivariant Relational Rearrangement with Neural Descriptor Fieldscited by 51
  6. 2021Leveraging SE(3) Equivariance for Self-Supervised Category-Level Object Pose Estimationcited by 45
  7. 2022Neural Shape Mating: Self-Supervised Object Assembly with Adversarial Shape Priorscited by 43
  8. 2019Quaternion Equivariant Capsule Networks for 3D Point Cloudscited by 41
  9. 2022Breaking Bad: A Dataset for Geometric Fracture and Reassemblycited by 41
  10. 2021RGL-NET: A Recurrent Graph Learning framework for Progressive Part Assemblycited by 36
  11. 2020COALESCE: Component Assembly by Learning to Synthesize Connectionscited by 30
  12. 2022USEEK: Unsupervised SE(3)-Equivariant 3D Keypoints for Generalizable Manipulationcited by 27
  13. 2023Self-Supervised Category-Level Articulated Object Pose Estimation with Part-Level SE(3) Equivariancecited by 26
  14. 2022Rotationally Equivariant 3D Object Detectioncited by 21
  15. 20223D Equivariant Graph Implicit Functionscited by 18
  16. 2022Shape-Pose Disentanglement using SE(3)-equivariant Vector Neuronscited by 16
  17. 2022Coarse-to-Fine Point Cloud Registration with SE(3)-Equivariant Representationscited by 9
  18. 2021Scene Editing as Teleoperation: A Case Study in 6DoF Kit Assemblycited by 6
  19. 2021Kit-Net: Self-Supervised Learning to Kit Novel 3D Objects into Novel 3D Cavitiescited by 4

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 12; 2025: 9; 2026: 6.

28 papers.

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  1. 2024DiffAssemble: A Unified Graph-Diffusion Model for 2D and 3D Reassemblycited by 33
  2. 2024ET-SEED: Efficient Trajectory-Level SE(3) Equivariant Diffusion Policycited by 26
  3. 2025Seek-CAD: A Self-refined Generative Modeling for 3D Parametric CAD Using Local Inference via DeepSeekcited by 24
  4. 2024Re-assembling the past: The RePAIR dataset and benchmark for real world 2D and 3D puzzle solvingcited by 19
  5. 2024PuzzleFusion++: Auto-agglomerative 3D Fracture Assembly by Denoise and Verifycited by 15
  6. 2023Scalable Geometric Fracture Assembly via Co-creation Space among Assemblerscited by 14
  7. 2025Manual2Skill: Learning to Read Manuals and Acquire Robotic Skills for Furniture Assembly Using Vision-Language Modelscited by 14
  8. 2025Rectified Point Flow: Generic Point Cloud Pose Estimationcited by 14
  9. 2025GARF: Learning Generalizable 3D Reassembly for Real-World Fracturescited by 13
  10. 2025Two by Two: Learning Multi-Task Pairwise Objects Assembly for Generalizable Robot Manipulationcited by 13
  11. 2024SPAFormer: Sequential 3D Part Assembly with Transformerscited by 12
  12. 20243D Geometric Shape Assembly via Efficient Point Cloud Matchingcited by 9
16 more
  1. 2024A Survey on Computational Solutions for Reconstructing Complete Objects by Reassembling Their Fractured Partscited by 9
  2. 2024EqvAfford: SE(3) Equivariance for Point-Level Affordance Learningcited by 6
  3. 2024Jigsaw++: Imagining Complete Shape Priors for Object Reassemblycited by 6
  4. 2025BiAssemble: Learning Collaborative Affordance for Bimanual Geometric Assemblycited by 5
  5. 2025Manual2Skill++: Connector-Aware General Robotic Assembly from Instruction Manuals via Vision-Language Modelscited by 5
  6. 2024SE(3)-bi-equivariant Transformers for Point Cloud Assemblycited by 4
  7. 2026TORA: Topological Representation Alignment for 3D Shape Assemblycited by 4
  8. 2024TreeSBA: Tree-Transformer for Self-Supervised Sequential Brick Assemblycited by 3
  9. 2024Geometric Point Attention Transformer for 3D Shape Reassemblycited by 3
  10. 2025Combinative Matching for Geometric Shape Assemblycited by 3
  11. 2025Equivariant Flow Matching for Point Cloud Assemblycited by 2
  12. 2026SARe: Structure-Aware Generative 3D Fragment Reassemblycited by 1
  13. 2026Transparent Fragments Contour Estimation via Visual-Tactile Fusion for Autonomous Reassemblycited by 0
  14. 2026LAMP: Lift Image-Editing as General 3D Priors for Open-world Manipulationcited by 0
  15. 2026PVRA: A Pointwise Key-point Voting Framework for Robotic Assemblycited by 0
  16. 2026LLM2R: From Large Language Models to 3D Reassemblerscited by 0