mlsanityData to 7 Oct 2026

Spline Positional Encoding for Learning 3D Implicit Signed Distance Fields

arXiv 2106.01553 ↗First posted 3 Jun 2021cs.CV cs.GRcited by 21

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Abstract (arXiv)

Multilayer perceptrons (MLPs) have been successfully used to represent 3D shapes implicitly and compactly, by mapping 3D coordinates to the corresponding signed distance values or occupancy values. In this paper, we propose a novel positional encoding scheme, called Spline Positional Encoding, to map the input coordinates to a high dimensional space before passing them to MLPs, for helping to recover 3D signed distance fields with fine-scale geometric details from unorganized 3D point clouds. We verified the superiority of our approach over other positional encoding schemes on tasks of 3D shape reconstruction from input point clouds and shape space learning. The efficacy of our approach extended to image reconstruction is also demonstrated and evaluated.

Key facts. Cited by 21 papers in the map (data through 7 Oct 2026). Builds on 18 of its 29 references that are in the map. First posted on arXiv 3 Jun 2021.

Builds on

18 of 29 references.

References · 18

  1. 2017Attention Is All You Needcited by 59,932
  2. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  3. 2019DeepSDF: Learning Continuous Signed Distance Functions for Shape Representationcited by 2,682
  4. 2020Implicit Neural Representations with Periodic Activation Functionscited by 2,214
  5. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,170
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  7. 2018On the Spectral Bias of Neural Networkscited by 1,321
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  10. 2020Convolutional Occupancy Networkscited by 760
  11. 2020Implicit Geometric Regularization for Learning Shapescited by 707
  12. 2019SAL: Sign Agnostic Learning of Shapes from Raw Datacited by 389
6 more
  1. 2020Local Implicit Grid Representations for 3D Scenescited by 372
  2. 2020Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstructioncited by 321
  3. 2019Texture Fields: Learning Texture Representations in Function Spacecited by 210
  4. 2018Training behavior of deep neural network in frequency domaincited by 174
  5. 2020SALD: Sign Agnostic Learning with Derivativescited by 115
  6. 2019Reconstructing continuous distributions of 3D protein structure from cryo-EM imagescited by 56

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 7; 2023: 3; 2024: 4; 2025: 4; 2026: 2.

21 papers.

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  1. 2021Neural Fields in Visual Computing and Beyondcited by 539
  2. 2022E-NeRV: Expedite Neural Video Representation with Disentangled Spatial-Temporal Contextcited by 76
  3. 2023NeuRBF: A Neural Fields Representation with Adaptive Radial Basis Functionscited by 65
  4. 2022Surface Reconstruction from Point Clouds: A Survey and a Benchmarkcited by 41
  5. 2022Intrinsic Neural Fields: Learning Functions on Manifoldscited by 20
  6. 2022PINs: Progressive Implicit Networks for Multi-Scale Neural Representationscited by 19
  7. 2022Learning Local Implicit Fourier Representation for Image Warpingcited by 14
  8. 2024From Activation to Initialization: Scaling Insights for Optimizing Neural Fieldscited by 11
  9. 2022PREF: Phasorial Embedding Fields for Compact Neural Representationscited by 10
  10. 2025Training-Free Hierarchical Scene Understanding for Gaussian Splatting with Superpoint Graphscited by 10
  11. 2025BF-STVSR: B-Splines and Fourier-Best Friends for High Fidelity Spatial-Temporal Video Super-Resolutioncited by 9
  12. 2023Curvature-Aware Training for Coordinate Networkscited by 8
9 more
  1. 2024RBF-PINN: Non-Fourier Positional Embedding in Physics-Informed Neural Networkscited by 5
  2. 2023CoNeS: Conditional neural fields with shift modulation for multi-sequence MRI translationcited by 3
  3. 2025How Learnable Grids Recover Fine Detail in Low Dimensions: A Neural Tangent Kernel Analysis of Multigrid Parametric Encodingscited by 3
  4. 2022A Simple And Effective Filtering Scheme For Improving Neural Fieldscited by 2
  5. 2024Feature Mapping in Physics-Informed Neural Networks (PINNs)cited by 2
  6. 2025MetricGrids: Arbitrary Nonlinear Approximation with Elementary Metric Grids based Implicit Neural Representationcited by 2
  7. 2024On Optimal Sampling for Learning SDF Using MLPs Equipped with Positional Encodingcited by 0
  8. 2026Dual-Prior Guided Null-Space Learning with Mixture-of-Splines for Arbitrary Medical Slice Super-Resolutioncited by 0
  9. 2026CARA: Collision-Aware Resolution Adaptation for Multiresolution Hash Encoding Based Image Fittingcited by 0