mlsanityData to 14 Oct 2026

Shape As Points: A Differentiable Poisson Solver

arXiv 2106.03452 ↗First posted 7 Jun 2021cs.CV cs.GRcited by 187

Not on the map. Why?

Cited by 25 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

In recent years, neural implicit representations gained popularity in 3D reconstruction due to their expressiveness and flexibility. However, the implicit nature of neural implicit representations results in slow inference time and requires careful initialization. In this paper, we revisit the classic yet ubiquitous point cloud representation and introduce a differentiable point-to-mesh layer using a differentiable formulation of Poisson Surface Reconstruction (PSR) that allows for a GPU-accelerated fast solution of the indicator function given an oriented point cloud. The differentiable PSR layer allows us to efficiently and differentiably bridge the explicit 3D point representation with the 3D mesh via the implicit indicator field, enabling end-to-end optimization of surface reconstruction metrics such as Chamfer distance. This duality between points and meshes hence allows us to represent shapes as oriented point clouds, which are explicit, lightweight and expressive. Compared to neural implicit representations, our Shape-As-Points (SAP) model is more interpretable, lightweight, and accelerates inference time by one order of magnitude. Compared to other explicit representations such as points, patches, and meshes, SAP produces topology-agnostic, watertight manifold surfaces. We demonstrate the effectiveness of SAP on the task of surface reconstruction from unoriented point clouds and learning-based reconstruction.

Key facts. Cited by 187 papers in the map (data through 14 Oct 2026). Builds on 53 of its 74 references that are in the map. First posted on arXiv 7 Jun 2021.

Builds on

53 of 74 references.

References · 53

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  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  3. 2016PointNet: Deep Learning on Point Sets for 3D Classification and Segmentationcited by 5,248
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  6. 2019DeepSDF: Learning Continuous Signed Distance Functions for Shape Representationcited by 2,689
  7. 2020Implicit Neural Representations with Periodic Activation Functionscited by 2,238
  8. 2018Dynamic Graph CNN for Learning on Point Cloudscited by 2,223
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  11. 2020NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collectionscited by 1,232
  12. 2018Learning Implicit Fields for Generative Shape Modelingcited by 1,060
38 more
  1. 2016A Point Set Generation Network for 3D Object Reconstruction from a Single Imagecited by 979
  2. 2020GIRAFFE: Representing Scenes as Compositional Generative Neural Feature Fieldscited by 785
  3. 2020Accelerating 3D Deep Learning with PyTorch3Dcited by 784
  4. 2020Convolutional Occupancy Networkscited by 761
  5. 2018Open3D: A Modern Library for 3D Data Processingcited by 721
  6. 2020Implicit Geometric Regularization for Learning Shapescited by 710
  7. 2019Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervisioncited by 700
  8. 2021KiloNeRF: Speeding up Neural Radiance Fields with Thousands of Tiny MLPscited by 673
  9. 2018Pixel2Mesh: Generating 3D Mesh Models from Single RGB Imagescited by 651
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  12. 2016Learning a Probabilistic Latent Space of Object Shapes via 3D Generative-Adversarial Modelingcited by 558
  13. 2018AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generationcited by 539
  14. 2019PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flowscited by 488
  15. 2018DeepVoxels: Learning Persistent 3D Feature Embeddingscited by 405
  16. 2019SAL: Sign Agnostic Learning of Shapes from Raw Datacited by 390
  17. 2020Local Implicit Grid Representations for 3D Scenescited by 373
  18. 2019DISN: Deep Implicit Surface Network for High-quality Single-view 3D Reconstructioncited by 333
  19. 2020Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstructioncited by 321
  20. 2019Texture Fields: Learning Texture Representations in Function Spacecited by 210
  21. 2016Thingi10K: A Dataset of 10,000 3D-Printing Modelscited by 183
  22. 2019DIST: Rendering Deep Implicit Signed Distance Function with Differentiable Sphere Tracingcited by 180
  23. 2019Neural Rerendering in the Wildcited by 121
  24. 2020MeshSDF: Differentiable Iso-Surface Extractioncited by 112
  25. 2018Deep Geometric Prior for Surface Reconstructioncited by 110
  26. 2021LEAP: Learning Articulated Occupancy of Peoplecited by 107
  27. 2017ScanComplete: Large-Scale Scene Completion and Semantic Segmentation for 3D Scanscited by 103
  28. 2017PCPNET: Learning Local Shape Properties from Raw Point Cloudscited by 98
  29. 2019Spherical CNNs on Unstructured Gridscited by 79
  30. 2019SG-NN: Sparse Generative Neural Networks for Self-Supervised Scene Completion of RGB-D Scanscited by 77
  31. 2021SCALE: Modeling Clothed Humans with a Surface Codec of Articulated Local Elementscited by 72
  32. 2020SurfelGAN: Synthesizing Realistic Sensor Data for Autonomous Drivingcited by 68
  33. 2020Neural Mesh Flow: 3D Manifold Mesh Generation via Diffeomorphic Flowscited by 61
  34. 2018Robust Watertight Manifold Surface Generation Method for ShapeNet Modelscited by 59
  35. 2018Nesti-Net: Normal Estimation for Unstructured 3D Point Clouds using Convolutional Neural Networkscited by 44
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  38. 2020Dynamic Plane Convolutional Occupancy Networkscited by 24

50 most cited of 53 All 53 (JSON)

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 9; 2022: 33; 2023: 56; 2024: 46; 2025: 26; 2026: 17.

187 papers.

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  1. 2022Point-E: A System for Generating 3D Point Clouds from Complex Promptscited by 699
  2. 2023Mip-Splatting: Alias-free 3D Gaussian Splattingcited by 667
  3. 2021NICE-SLAM: Neural Implicit Scalable Encoding for SLAMcited by 589
  4. 2022LION: Latent Point Diffusion Models for 3D Shape Generationcited by 553
  5. 2021Neural Fields in Visual Computing and Beyondcited by 540
  6. 2022MonoSDF: Exploring Monocular Geometric Cues for Neural Implicit Surface Reconstructioncited by 470
  7. 2023MeshGPT: Generating Triangle Meshes with Decoder-Only Transformerscited by 259
  8. 2023MeshDiffusion: Score-based Generative 3D Mesh Modelingcited by 199
  9. 20233DGS-Avatar: Animatable Avatars via Deformable 3D Gaussian Splattingcited by 195
  10. 2023GPS-Gaussian: Generalizable Pixel-wise 3D Gaussian Splatting for Real-time Human Novel View Synthesiscited by 170
  11. 2023NICER-SLAM: Neural Implicit Scene Encoding for RGB SLAMcited by 164
  12. 2024MeshAnything: Artist-Created Mesh Generation with Autoregressive Transformerscited by 144
38 more
  1. 2021BACON: Band-limited Coordinate Networks for Multiscale Scene Representationcited by 143
  2. 2022ARAH: Animatable Volume Rendering of Articulated Human SDFscited by 139
  3. 2022D2NeRF: Self-Supervised Decoupling of Dynamic and Static Objects from a Monocular Videocited by 137
  4. 2023Locally Attentional SDF Diffusion for Controllable 3D Shape Generationcited by 130
  5. 2023CompGS: Smaller and Faster Gaussian Splatting with Vector Quantizationcited by 130
  6. 2024RadSplat: Radiance Field-Informed Gaussian Splatting for Robust Real-Time Rendering with 900+ FPScited by 113
  7. 2023Neural Kernel Surface Reconstructioncited by 104
  8. 2022POCO: Point Convolution for Surface Reconstructioncited by 92
  9. 2021The Power of Points for Modeling Humans in Clothingcited by 90
  10. 2025SparseFlex: High-Resolution and Arbitrary-Topology 3D Shape Modelingcited by 79
  11. 2021MetaAvatar: Learning Animatable Clothed Human Models from Few Depth Imagescited by 78
  12. 2021DiGS : Divergence guided shape implicit neural representation for unoriented point cloudscited by 77
  13. 2024End-to-End Rate-Distortion Optimized 3D Gaussian Representationcited by 75
  14. 2022Neural Dual Contouringcited by 71
  15. 20223D-LDM: Neural Implicit 3D Shape Generation with Latent Diffusion Modelscited by 67
  16. 2022Reconstructing Surfaces for Sparse Point Clouds with On-Surface Priorscited by 60
  17. 2022AlignSDF: Pose-Aligned Signed Distance Fields for Hand-Object Reconstructioncited by 59
  18. 2021Neural Fields as Learnable Kernels for 3D Reconstructioncited by 58
  19. 2022Masked Wavelet Representation for Compact Neural Radiance Fieldscited by 57
  20. 2022Surface Reconstruction from Point Clouds by Learning Predictive Context Priorscited by 54
  21. 2022CAP-UDF: Learning Unsigned Distance Functions Progressively from Raw Point Clouds with Consistency-Aware Field Optimizationcited by 47
  22. 2022Low-Rank Tensor Function Representation for Multi-Dimensional Data Recoverycited by 46
  23. 2022Surface Reconstruction from Point Clouds: A Survey and a Benchmarkcited by 41
  24. 2023Controllable Mesh Generation Through Sparse Latent Point Diffusion Modelscited by 41
  25. 2023Towards Better Gradient Consistency for Neural Signed Distance Functions via Level Set Alignmentcited by 39
  26. 2023Dynamic Point Fieldscited by 37
  27. 2023Learning a More Continuous Zero Level Set in Unsigned Distance Fields through Level Set Projectioncited by 36
  28. 2023Neural-Singular-Hessian: Implicit Neural Representation of Unoriented Point Clouds by Enforcing Singular Hessiancited by 35
  29. 2024Zero-Shot Scene Reconstruction from Single Images with Deep Prior Assemblycited by 35
  30. 2023DiffuseBot: Breeding Soft Robots With Physics-Augmented Generative Diffusion Modelscited by 31
  31. 2023UGG: Unified Generative Graspingcited by 30
  32. 2022GeoUDF: Surface Reconstruction from 3D Point Clouds via Geometry-guided Distance Representationcited by 29
  33. 2023Unsupervised Inference of Signed Distance Functions from Single Sparse Point Clouds without Learning Priorscited by 28
  34. 2023PartDistill: 3D Shape Part Segmentation by Vision-Language Model Distillationcited by 28
  35. 2023Learning Signed Distance Functions from Noisy 3D Point Clouds via Noise to Noise Mappingcited by 27
  36. 2021Unsupervised Learning of Fine Structure Generation for 3D Point Clouds by 2D Projection Matchingcited by 26
  37. 2023AI-Generated Content (AIGC) for Various Data Modalities: A Surveycited by 25
  38. 2023Ghost on the Shell: An Expressive Representation of General 3D Shapescited by 24

50 most cited of 187 All 187 (JSON)