mlsanityData to 7 Oct 2026

Neural Splines: Fitting 3D Surfaces with Infinitely-Wide Neural Networks

arXiv 2006.13782 ↗First posted 24 Jun 2020cs.CV cs.GRcited by 52

Not on the map. Why?

Abstract (arXiv)

We present Neural Splines, a technique for 3D surface reconstruction that is based on random feature kernels arising from infinitely-wide shallow ReLU networks. Our method achieves state-of-the-art results, outperforming recent neural network-based techniques and widely used Poisson Surface Reconstruction (which, as we demonstrate, can also be viewed as a type of kernel method). Because our approach is based on a simple kernel formulation, it is easy to analyze and can be accelerated by general techniques designed for kernel-based learning. We provide explicit analytical expressions for our kernel and argue that our formulation can be seen as a generalization of cubic spline interpolation to higher dimensions. In particular, the RKHS norm associated with Neural Splines biases toward smooth interpolants.

Key facts. Cited by 52 papers in the map (data through 7 Oct 2026). First posted on arXiv 24 Jun 2020.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 6; 2022: 13; 2023: 14; 2024: 12; 2025: 6; 2026: 1.

52 papers.

Sort:

By area:

  1. 2022LION: Latent Point Diffusion Models for 3D Shape Generationcited by 552
  2. 2021Neural Fields in Visual Computing and Beyondcited by 539
  3. 2021Deep Marching Tetrahedra: a Hybrid Representation for High-Resolution 3D Shape Synthesiscited by 459
  4. 2023Neural Kernel Surface Reconstructioncited by 102
  5. 2022POCO: Point Convolution for Surface Reconstructioncited by 91
  6. 2022Learning Smooth Neural Functions via Lipschitz Regularizationcited by 86
  7. 2021DiGS : Divergence guided shape implicit neural representation for unoriented point cloudscited by 76
  8. 2022Dual Octree Graph Networks for Learning Adaptive Volumetric Shape Representationscited by 71
  9. 2023NeuRBF: A Neural Fields Representation with Adaptive Radial Basis Functionscited by 65
  10. 2021Neural Fields as Learnable Kernels for 3D Reconstructioncited by 58
  11. 2022Surface Reconstruction from Point Clouds: A Survey and a Benchmarkcited by 41
  12. 2023Towards Better Gradient Consistency for Neural Signed Distance Functions via Level Set Alignmentcited by 39
38 more
  1. 2021Phase Transitions, Distance Functions, and Implicit Neural Representationscited by 38
  2. 2023PET-NeuS: Positional Encoding Tri-Planes for Neural Surfacescited by 37
  3. 2023Neural-Singular-Hessian: Implicit Neural Representation of Unoriented Point Clouds by Enforcing Singular Hessiancited by 34
  4. 2023Unsupervised Inference of Signed Distance Functions from Single Sparse Point Clouds without Learning Priorscited by 28
  5. 2023Choose Your Simulator Wisely: A Review on Open-source Simulators for Autonomous Drivingcited by 26
  6. 2022Few 'Zero Level Set'-Shot Learning of Shape Signed Distance Functions in Feature Spacecited by 22
  7. 2023StEik: Stabilizing the Optimization of Neural Signed Distance Functions and Finer Shape Representationcited by 22
  8. 2023VisCo Grids: Surface Reconstruction with Viscosity and Coarea Gridscited by 20
  9. 2024Unsupervised Occupancy Learning from Sparse Point Cloudcited by 15
  10. 2021Neural-IMLS: Self-supervised Implicit Moving Least-Squares Network for Surface Reconstructioncited by 13
  11. 2023Mixing-Denoising Generalizable Occupancy Networkscited by 12
  12. 2023Robustifying Generalizable Implicit Shape Networks with a Tunable Non-Parametric Modelcited by 10
  13. 2022Deep Surface Reconstruction from Point Clouds with Visibility Informationcited by 8
  14. 2024HotSpot: Signed Distance Function Optimization with an Asymptotically Sufficient Conditioncited by 8
  15. 2024Inferring Neural Signed Distance Functions by Overfitting on Single Noisy Point Clouds through Finetuning Data-Driven based Priorscited by 7
  16. 2025Learning Bijective Surface Parameterization for Inferring Signed Distance Functions from Sparse Point Clouds with Grid Deformationcited by 7
  17. 2022ROAD: Learning an Implicit Recursive Octree Auto-Decoder to Efficiently Encode 3D Shapescited by 6
  18. 2024CanFields: Consolidating Diffeomorphic Flows for Non-Rigid 4D Interpolation from Arbitrary-Length Sequencescited by 6
  19. 2024Few-Shot Unsupervised Implicit Neural Shape Representation Learning with Spatial Adversariescited by 5
  20. 2024Toward Robust Neural Reconstruction from Sparse Point Setscited by 5
  21. 2022Implicit Conversion of Manifold B-Rep Solids by Neural Halfspace Representationcited by 4
  22. 2023A Review of Deep Learning-Powered Mesh Reconstruction Methodscited by 3
  23. 2025NoKSR: Kernel-Free Neural Surface Reconstruction via Point Cloud Serializationcited by 3
  24. 2022A Simple And Effective Filtering Scheme For Improving Neural Fieldscited by 2
  25. 2025OffsetOPT: Explicit Surface Reconstruction without Normalscited by 2
  26. 2022Isomorphic mesh generation from point clouds with multilayer perceptronscited by 1
  27. 2023Optimizing Implicit Neural Representations from Point Clouds via Energy-Based Modelscited by 1
  28. 2024Neural varifolds: an aggregate representation for quantifying the geometry of point cloudscited by 1
  29. 2025GNF: Gaussian Neural Fields for Multidimensional Signal Representation and Reconstructioncited by 1
  30. 2022Taylor3DNet: Fast 3D Shape Inference With Landmark Points Based Taylor Seriescited by 0
  31. 2022Top-Tuning: a study on transfer learning for an efficient alternative to fine tuning for image classification with fast kernel methodscited by 0
  32. 2023Outlier-robust neural network training: variation regularization meets trimmed loss to prevent functional breakdowncited by 0
  33. 2024On Optimal Sampling for Learning SDF Using MLPs Equipped with Positional Encodingcited by 0
  34. 2024Few-shot point cloud reconstruction and denoising via learned Guassian splats renderings and fine-tuned diffusion featurescited by 0
  35. 2024Mat'ern Kernels for Tunable Implicit Surface Reconstructioncited by 0
  36. 2024Shrinking: Reconstruction of Parameterized Surfaces from Signed Distance Fieldscited by 0
  37. 2024CCNDF: Curvature Constrained Neural Distance Fields from 3D LiDAR Sequencescited by 0
  38. 2025HessianForge: Scalable LiDAR reconstruction with Physics-Informed Neural Representation and Smoothness Energy Constraintscited by 0

50 most cited of 52 All 52 (JSON)