# Neural-IMLS: Self-supervised Implicit Moving Least-Squares Network for Surface Reconstruction

arXiv: https://arxiv.org/abs/2109.04398 · HTML: https://mlsanity.com/paper/2109.04398/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 69 references that are in the map.
- First posted on arXiv 9 Sep 2021.

## Builds on (most cited first, 30 of 36)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [Accelerating 3D Deep Learning with PyTorch3D](https://mlsanity.com/paper/2007.08501/) (2020)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [Shape As Points: A Differentiable Poisson Solver](https://mlsanity.com/paper/2106.03452/) (2021)
- [Thingi10K: A Dataset of 10,000 3D-Printing Models](https://mlsanity.com/paper/1605.04797/) (2016)
- [Neural-Pull: Learning Signed Distance Functions from Point Clouds by Learning to Pull Space onto Surfaces](https://mlsanity.com/paper/2011.13495/) (2020)
- [Points2Surf: Learning Implicit Surfaces from Point Cloud Patches](https://mlsanity.com/paper/2007.10453/) (2020)
- [SALD: Sign Agnostic Learning with Derivatives](https://mlsanity.com/paper/2006.05400/) (2020)
- [Deep Geometric Prior for Surface Reconstruction](https://mlsanity.com/paper/1811.10943/) (2018)
- [PCPNET: Learning Local Shape Properties from Raw Point Clouds](https://mlsanity.com/paper/1710.04954/) (2017)
- [Kaolin: A PyTorch Library for Accelerating 3D Deep Learning Research](https://mlsanity.com/paper/1911.05063/) (2019)
- [ParSeNet: A Parametric Surface Fitting Network for 3D Point Clouds](https://mlsanity.com/paper/2003.12181/) (2020)
- [DiGS : Divergence guided shape implicit neural representation for unoriented point clouds](https://mlsanity.com/paper/2106.10811/) (2021)
- [Deep Implicit Moving Least-Squares Functions for 3D Reconstruction](https://mlsanity.com/paper/2103.12266/) (2021)
- [SA-ConvONet: Sign-Agnostic Optimization of Convolutional Occupancy Networks](https://mlsanity.com/paper/2105.03582/) (2021)
- [Neural Splines: Fitting 3D Surfaces with Infinitely-Wide Neural Networks](https://mlsanity.com/paper/2006.13782/) (2020)

## Built on by (most cited first, 13 of 13)

- [Fast Learning of Signed Distance Functions from Noisy Point Clouds via Noise to Noise Mapping](https://mlsanity.com/paper/2407.14225/) (2024)
- [OReX: Object Reconstruction from Planar Cross-sections Using Neural Fields](https://mlsanity.com/paper/2211.12886/) (2022)
- [A Lightweight UDF Learning Framework for 3D Reconstruction Based on Local Shape Functions](https://mlsanity.com/paper/2407.01330/) (2024)
- [GSurf: Learning Signed Distance Fields from Splatting Opaque Gaussians for High-quality 3D Reconstruction](https://mlsanity.com/paper/2411.15723/) (2024)
- [PPSURF: Combining Patches and Point Convolutions for Detailed Surface Reconstruction](https://mlsanity.com/paper/2401.08518/) (2024)
- [MergeNet: Explicit Mesh Reconstruction from Sparse Point Clouds via Edge Prediction](https://mlsanity.com/paper/2407.11610/) (2024)
- [CrossSDF: 3D Reconstruction of Thin Structures From Cross-Sections](https://mlsanity.com/paper/2412.04120/) (2024)
- [Mesh2SSM++: A Probabilistic Framework for Unsupervised Learning of Statistical Shape Model of Anatomies from Surface Meshes](https://mlsanity.com/paper/2502.07145/) (2025)
- [OAAFormer: Robust and Efficient Point Cloud Registration Through Overlapping-Aware Attention in Transformer](https://mlsanity.com/paper/2310.09817/) (2023)
- [Polyhedral Surface: Self-supervised Point Cloud Reconstruction Based on Polyhedral Surface](https://mlsanity.com/paper/2310.14560/) (2023)
- [D3Former: Jointly Learning Repeatable Dense Detectors and Feature-enhanced Descriptors via Saliency-guided Transformer](https://mlsanity.com/paper/2312.12970/) (2023)
- [NoiseSDF2NoiseSDF: Learning Clean Neural Fields from Noisy Supervision](https://mlsanity.com/paper/2507.13595/) (2025)
- [Joint Orientation and Weight Optimization for Robust Watertight Surface Reconstruction via Dirichlet-Regularized Winding Fields](https://mlsanity.com/paper/2602.13801/) (2026)

## Abstract (arXiv)

Surface reconstruction is very challenging when the input point clouds, particularly real scans, are noisy and lack normals. Observing that the Multilayer Perceptron (MLP) and the implicit moving least-square function (IMLS) provide a dual representation of the underlying surface, we introduce Neural-IMLS, a novel approach that directly learns the noise-resistant signed distance function (SDF) from unoriented raw point clouds in a self-supervised fashion. We use the IMLS to regularize the distance values reported by the MLP while using the MLP to regularize the normals of the data points for running the IMLS. We also prove that at the convergence, our neural network, benefiting from the mutual learning mechanism between the MLP and the IMLS, produces a faithful SDF whose zero-level set approximates the underlying surface. We conducted extensive experiments on various benchmarks, including synthetic scans and real scans. The experimental results show that em Neural-IMLS can reconstruct faithful shapes on various benchmarks with noise and missing parts. The source code can be found at~urlhttps://github.com/bearprin/Neural-IMLS.