mlsanityData to 7 Oct 2026

3D Equivariant Graph Implicit Functions

arXiv 2203.17178 ↗First posted 31 Mar 2022cs.CV cs.AIcited by 18

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Abstract (arXiv)

In recent years, neural implicit representations have made remarkable progress in modeling of 3D shapes with arbitrary topology. In this work, we address two key limitations of such representations, in failing to capture local 3D geometric fine details, and to learn from and generalize to shapes with unseen 3D transformations. To this end, we introduce a novel family of graph implicit functions with equivariant layers that facilitates modeling fine local details and guaranteed robustness to various groups of geometric transformations, through local k-NN graph embeddings with sparse point set observations at multiple resolutions. Our method improves over the existing rotation-equivariant implicit function from 0.69 to 0.89 (IoU) on the ShapeNet reconstruction task. We also show that our equivariant implicit function can be extended to other types of similarity transformations and generalizes to unseen translations and scaling.

Key facts. Cited by 18 papers in the map (data through 7 Oct 2026). Builds on 47 of its 58 references that are in the map. First posted on arXiv 31 Mar 2022.

Builds on

47 of 58 references.

References · 47

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  3. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  4. 2016PointNet: Deep Learning on Point Sets for 3D Classification and Segmentationcited by 5,223
  5. 2017PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Spacecited by 4,384
  6. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  7. 2017ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenescited by 3,088
  8. 2015ShapeNet: An Information-Rich 3D Model Repositorycited by 2,880
  9. 2019DeepSDF: Learning Continuous Signed Distance Functions for Shape Representationcited by 2,682
  10. 2018Dynamic Graph CNN for Learning on Point Cloudscited by 2,220
  11. 2018Occupancy Networks: Learning 3D Reconstruction in Function Spacecited by 2,037
  12. 2017Deep Setscited by 1,394
35 more
  1. 2016Group Equivariant Convolutional Networkscited by 1,154
  2. 2018Learning Implicit Fields for Generative Shape Modelingcited by 1,060
  3. 2021E(n) Equivariant Graph Neural Networkscited by 951
  4. 2019PIFu: Pixel-Aligned Implicit Function for High-Resolution Clothed Human Digitizationcited by 818
  5. 2020Convolutional Occupancy Networkscited by 760
  6. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
  7. 2019Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervisioncited by 699
  8. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 602
  9. 2021Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapescited by 426
  10. 2019SAL: Sign Agnostic Learning of Shapes from Raw Datacited by 389
  11. 2020Local Implicit Grid Representations for 3D Scenescited by 372
  12. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 348
  13. 2020Implicit Functions in Feature Space for 3D Shape Reconstruction and Completioncited by 343
  14. 2019DISN: Deep Implicit Surface Network for High-quality Single-view 3D Reconstructioncited by 332
  15. 2020Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstructioncited by 321
  16. 2021Vector Neurons: A General Framework for SO(3)-Equivariant Networkscited by 304
  17. 2016Steerable CNNscited by 298
  18. 2016Harmonic Networks: Deep Translation and Rotation Equivariancecited by 293
  19. 2020MetaSDF: Meta-learning Signed Distance Functionscited by 214
  20. 2018SO-Net: Self-Organizing Network for Point Cloud Analysiscited by 210
  21. 2021Neural Descriptor Fields: SE(3)-Equivariant Object Representations for Manipulationcited by 204
  22. 2017Learning Steerable Filters for Rotation Equivariant CNNscited by 193
  23. 2019SDFDiff: Differentiable Rendering of Signed Distance Fields for 3D Shape Optimizationcited by 159
  24. 2020Points2Surf: Learning Implicit Surfaces from Point Cloud Patchescited by 122
  25. 2020SALD: Sign Agnostic Learning with Derivativescited by 115
  26. 2019Scale-Equivariant Steerable Networkscited by 110
  27. 2020PointMixup: Augmentation for Point Cloudscited by 104
  28. 2019Learning to Infer Implicit Surfaces without 3D Supervisioncited by 103
  29. 2016Universal Correspondence Networkcited by 82
  30. 2019Controlling Neural Level Setscited by 76
  31. 20193D-Rotation-Equivariant Quaternion Neural Networkscited by 30
  32. 2021OctField: Hierarchical Implicit Functions for 3D Modelingcited by 25
  33. 2020Ladybird: Quasi-Monte Carlo Sampling for Deep Implicit Field Based 3D Reconstruction with Symmetrycited by 24
  34. 2019Local Deep Implicit Functions for 3D Shapecited by 18
  35. 2020On the generalization of learning-based 3D reconstructioncited by 12

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 7; 2024: 6; 2025: 2; 2026: 1.

18 papers.

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  1. 2022SE(3)-Equivariant Relational Rearrangement with Neural Descriptor Fieldscited by 51
  2. 2023Leveraging SE(3) Equivariance for Learning 3D Geometric Shape Assemblycited by 27
  3. 2022SE(3)-Equivariant Attention Networks for Shape Reconstruction in Function Spacecited by 26
  4. 2023EFEM: Equivariant Neural Field Expectation Maximization for 3D Object Segmentation Without Scene Supervisioncited by 18
  5. 2023Living Scenes: Multi-object Relocalization and Reconstruction in Changing 3D Environmentscited by 15
  6. 2023Shape-conditioned 3D Molecule Generation via Equivariant Diffusion Modelscited by 7
  7. 2023ShapeMatcher: Self-Supervised Joint Shape Canonicalization, Segmentation, Retrieval and Deformationcited by 7
  8. 2024SE(3) Equivariant Ray Embeddings for Implicit Multi-View Depth Estimationcited by 6
  9. 2023Learning Any-View 6DoF Robotic Grasping in Cluttered Scenes via Neural Surface Renderingcited by 5
  10. 2024An intuitive multi-frequency feature representation for SO(3)-equivariant networkscited by 5
  11. 2024Approximately Piecewise E(3) Equivariant Point Networkscited by 4
  12. 2024ESCAPE: Equivariant Shape Completion via Anchor Point Encodingcited by 4
6 more
  1. 2024Current Symmetry Group Equivariant Convolution Frameworks for Representation Learningcited by 2
  2. 2025Learning Generalizable Shape Completion with SIM(3) Equivariancecited by 2
  3. 2024BiEquiFormer: Bi-Equivariant Representations for Global Point Cloud Registrationcited by 1
  4. 2025Equivariant Eikonal Neural Networks: Grid-Free, Scalable Travel-Time Prediction on Homogeneous Spacescited by 1
  5. 2023Implicit representation priors meet Riemannian geometry for Bayesian robotic graspingcited by 0
  6. 2026REVNET: Rotation-Equivariant Point Cloud Completion via Vector Neuron Anchor Transformercited by 0