mlsanityData to 7 Oct 2026

Phase Transitions, Distance Functions, and Implicit Neural Representations

arXiv 2106.07689 ↗First posted 14 Jun 2021cs.LGcited by 38

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Abstract (arXiv)

Representing surfaces as zero level sets of neural networks recently emerged as a powerful modeling paradigm, named Implicit Neural Representations (INRs), serving numerous downstream applications in geometric deep learning and 3D vision. Training INRs previously required choosing between occupancy and distance function representation and different losses with unknown limit behavior and/or bias. In this paper we draw inspiration from the theory of phase transitions of fluids and suggest a loss for training INRs that learns a density function that converges to a proper occupancy function, while its log transform converges to a distance function. Furthermore, we analyze the limit minimizer of this loss showing it satisfies the reconstruction constraints and has minimal surface perimeter, a desirable inductive bias for surface reconstruction. Training INRs with this new loss leads to state-of-the-art reconstructions on a standard benchmark.

Key facts. Cited by 38 papers in the map (data through 7 Oct 2026). Builds on 16 of its 36 references that are in the map. First posted on arXiv 14 Jun 2021.

Builds on

16 of 36 references.

References · 16

  1. 2019DeepSDF: Learning Continuous Signed Distance Functions for Shape Representationcited by 2,682
  2. 2020Implicit Neural Representations with Periodic Activation Functionscited by 2,214
  3. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,170
  4. 2018Occupancy Networks: Learning 3D Reconstruction in Function Spacecited by 2,037
  5. 2018Learning Implicit Fields for Generative Shape Modelingcited by 1,060
  6. 2019PIFu: Pixel-Aligned Implicit Function for High-Resolution Clothed Human Digitizationcited by 818
  7. 2020Implicit Geometric Regularization for Learning Shapescited by 707
  8. 2019Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervisioncited by 699
  9. 2019SAL: Sign Agnostic Learning of Shapes from Raw Datacited by 389
  10. 2020Local Implicit Grid Representations for 3D Scenescited by 372
  11. 2020Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstructioncited by 321
  12. 2020SALD: Sign Agnostic Learning with Derivativescited by 115
4 more
  1. 2018Deep Geometric Prior for Surface Reconstructioncited by 110
  2. 2019Controlling Neural Level Setscited by 76
  3. 2020Curriculum DeepSDFcited by 62
  4. 2020Neural Splines: Fitting 3D Surfaces with Infinitely-Wide Neural Networkscited by 52

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 5; 2022: 6; 2023: 9; 2024: 10; 2025: 4; 2026: 4.

38 papers.

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  1. 2021Volume Rendering of Neural Implicit Surfacescited by 990
  2. 2021DiGS : Divergence guided shape implicit neural representation for unoriented point cloudscited by 76
  3. 2022ImFace: A Nonlinear 3D Morphable Face Model with Implicit Neural Representationscited by 64
  4. 2022Surface Reconstruction from Point Clouds: A Survey and a Benchmarkcited by 41
  5. 2023Neural-Singular-Hessian: Implicit Neural Representation of Unoriented Point Clouds by Enforcing Singular Hessiancited by 34
  6. 2022Generalised Implicit Neural Representationscited by 31
  7. 2022Few 'Zero Level Set'-Shot Learning of Shape Signed Distance Functions in Feature Spacecited by 22
  8. 2023StEik: Stabilizing the Optimization of Neural Signed Distance Functions and Finer Shape Representationcited by 22
  9. 2023VisCo Grids: Surface Reconstruction with Viscosity and Coarea Gridscited by 20
  10. 2021Frame Averaging for Equivariant Shape Space Learningcited by 18
  11. 2024Unsupervised Occupancy Learning from Sparse Point Cloudcited by 15
  12. 2021Neural-IMLS: Self-supervised Implicit Moving Least-Squares Network for Surface Reconstructioncited by 13
26 more
  1. 2021DeepCurrents: Learning Implicit Representations of Shapes with Boundariescited by 12
  2. 2023Mixing-Denoising Generalizable Occupancy Networkscited by 12
  3. 2024NeurCADRecon: Neural Representation for Reconstructing CAD Surfaces by Enforcing Zero Gaussian Curvaturecited by 12
  4. 20243D Reconstruction with Fast Dipole Sumscited by 12
  5. 2023Robustifying Generalizable Implicit Shape Networks with a Tunable Non-Parametric Modelcited by 10
  6. 2023ImFace++: A Sophisticated Nonlinear 3D Morphable Face Model with Implicit Neural Representationscited by 10
  7. 2022UNIF: United Neural Implicit Functions for Clothed Human Reconstruction and Animationcited by 8
  8. 2023Progressive Learning for Physics-informed Neural Motion Planningcited by 8
  9. 2023p-Poisson surface reconstruction in curl-free flow from point cloudscited by 8
  10. 2024NeurCross: A Neural Approach to Computing Cross Fields for Quad Mesh Generationcited by 8
  11. 20241-Lipschitz Neural Distance Fieldscited by 8
  12. 2024HotSpot: Signed Distance Function Optimization with an Asymptotically Sufficient Conditioncited by 8
  13. 2022Neural PDE Solvers for Irregular Domainscited by 6
  14. 2023Implicit Gaussian process representation of vector fields over arbitrary latent manifoldscited by 6
  15. 2024DiffCD: A Symmetric Differentiable Chamfer Distance for Neural Implicit Surface Fittingcited by 5
  16. 2024Toward Robust Neural Reconstruction from Sparse Point Setscited by 5
  17. 2024Self-Supervised Dual Contouringcited by 2
  18. 2025NeuVAS: Neural Implicit Surfaces for Variational Shape Modelingcited by 1
  19. 2025StyleMM: Stylized 3D Morphable Face Model via Text-Driven Aligned Image Translationcited by 1
  20. 2025Enhancing Robustness of Implicit Neural Representations Against Weight Perturbationscited by 1
  21. 2024On Optimal Sampling for Learning SDF Using MLPs Equipped with Positional Encodingcited by 0
  22. 2025Neural Shortest Path for Surface Reconstruction from Point Cloudscited by 0
  23. 2026Generative Shape Reconstruction with Geometry-Guided Langevin Dynamicscited by 0
  24. 2026Medial Axis Aware Learning of Signed Distance Functionscited by 0
  25. 2026Patchwork: A compact representation for 3D polygonal shapescited by 0
  26. 2026Points as Tori: Fast Pointwise Signed Distance for Point Cloudscited by 0