# Towards Better Gradient Consistency for Neural Signed Distance Functions via Level Set Alignment

arXiv: https://arxiv.org/abs/2305.11601 · HTML: https://mlsanity.com/paper/2305.11601/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- Builds on 63 of its 78 references that are in the map.
- First posted on arXiv 19 May 2023.

## Builds on (most cited first, 30 of 63)

- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [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)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervision](https://mlsanity.com/paper/1912.07372/) (2019)
- [UNISURF: Unifying Neural Implicit Surfaces and Radiance Fields for Multi-View Reconstruction](https://mlsanity.com/paper/2104.10078/) (2021)
- [NICE-SLAM: Neural Implicit Scalable Encoding for SLAM](https://mlsanity.com/paper/2112.12130/) (2021)
- [MonoSDF: Exploring Monocular Geometric Cues for Neural Implicit Surface Reconstruction](https://mlsanity.com/paper/2206.00665/) (2022)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [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)
- [Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstruction](https://mlsanity.com/paper/2003.10983/) (2020)
- [Neural RGB-D Surface Reconstruction](https://mlsanity.com/paper/2104.04532/) (2021)
- [Neural Unsigned Distance Fields for Implicit Function Learning](https://mlsanity.com/paper/2010.13938/) (2020)
- [Learning Shape Templates with Structured Implicit Functions](https://mlsanity.com/paper/1904.06447/) (2019)
- [Geo-Neus: Geometry-Consistent Neural Implicit Surfaces Learning for Multi-view Reconstruction](https://mlsanity.com/paper/2205.15848/) (2022)
- [Shape As Points: A Differentiable Poisson Solver](https://mlsanity.com/paper/2106.03452/) (2021)
- [SDFDiff: Differentiable Rendering of Signed Distance Fields for 3D Shape Optimization](https://mlsanity.com/paper/1912.07109/) (2019)
- [Neural-Pull: Learning Signed Distance Functions from Point Clouds by Learning to Pull Space onto Surfaces](https://mlsanity.com/paper/2011.13495/) (2020)
- [NeuRIS: Neural Reconstruction of Indoor Scenes Using Normal Priors](https://mlsanity.com/paper/2206.13597/) (2022)
- [Neural 3D Scene Reconstruction with the Manhattan-world Assumption](https://mlsanity.com/paper/2205.02836/) (2022)
- [Points2Surf: Learning Implicit Surfaces from Point Cloud Patches](https://mlsanity.com/paper/2007.10453/) (2020)
- [HF-NeuS: Improved Surface Reconstruction Using High-Frequency Details](https://mlsanity.com/paper/2206.07850/) (2022)

## Built on by (most cited first, 30 of 39)

- [MV-DUSt3R+: Single-Stage Scene Reconstruction from Sparse Views In 2 Seconds](https://mlsanity.com/paper/2412.06974/) (2024)
- [Neural Kernel Surface Reconstruction](https://mlsanity.com/paper/2305.19590/) (2023)
- [You See it, You Got it: Learning 3D Creation on Pose-Free Videos at Scale](https://mlsanity.com/paper/2412.06699/) (2024)
- [DiffGS: Functional Gaussian Splatting Diffusion](https://mlsanity.com/paper/2410.19657/) (2024)
- [Binocular-Guided 3D Gaussian Splatting with View Consistency for Sparse View Synthesis](https://mlsanity.com/paper/2410.18822/) (2024)
- [Differentiable Registration of Images and LiDAR Point Clouds with VoxelPoint-to-Pixel Matching](https://mlsanity.com/paper/2312.04060/) (2023)
- [NeuSurf: On-Surface Priors for Neural Surface Reconstruction from Sparse Input Views](https://mlsanity.com/paper/2312.13977/) (2023)
- [Learning a More Continuous Zero Level Set in Unsigned Distance Fields through Level Set Projection](https://mlsanity.com/paper/2308.11441/) (2023)
- [Zero-Shot Scene Reconstruction from Single Images with Deep Prior Assembly](https://mlsanity.com/paper/2410.15971/) (2024)
- [Learning Signed Distance Functions from Noisy 3D Point Clouds via Noise to Noise Mapping](https://mlsanity.com/paper/2306.01405/) (2023)
- [Federated Domain Generalization: A Survey](https://mlsanity.com/paper/2306.01334/) (2023)
- [UDiFF: Generating Conditional Unsigned Distance Fields with Optimal Wavelet Diffusion](https://mlsanity.com/paper/2404.06851/) (2024)
- [Learning Continuous Implicit Field with Local Distance Indicator for Arbitrary-Scale Point Cloud Upsampling](https://mlsanity.com/paper/2312.15133/) (2023)
- [Fast Learning of Signed Distance Functions from Noisy Point Clouds via Noise to Noise Mapping](https://mlsanity.com/paper/2407.14225/) (2024)
- [4D-LRM: Large Space-Time Reconstruction Model From and To Any View at Any Time](https://mlsanity.com/paper/2506.18890/) (2025)
- [Geometry-Informed Neural Networks](https://mlsanity.com/paper/2402.14009/) (2024)
- [GridPull: Towards Scalability in Learning Implicit Representations from 3D Point Clouds](https://mlsanity.com/paper/2308.13175/) (2023)
- [Learning Neural Implicit through Volume Rendering with Attentive Depth Fusion Priors](https://mlsanity.com/paper/2310.11598/) (2023)
- [MultiPull: Detailing Signed Distance Functions by Pulling Multi-Level Queries at Multi-Step](https://mlsanity.com/paper/2411.01208/) (2024)
- [NeuralGF: Unsupervised Point Normal Estimation by Learning Neural Gradient Function](https://mlsanity.com/paper/2311.00389/) (2023)
- [DUDF: Differentiable Unsigned Distance Fields with Hyperbolic Scaling](https://mlsanity.com/paper/2402.08876/) (2024)
- [GridFormer: Point-Grid Transformer for Surface Reconstruction](https://mlsanity.com/paper/2401.02292/) (2024)
- [Implicit Filtering for Learning Neural Signed Distance Functions from 3D Point Clouds](https://mlsanity.com/paper/2407.13342/) (2024)
- [Inferring Neural Signed Distance Functions by Overfitting on Single Noisy Point Clouds through Finetuning Data-Driven based Priors](https://mlsanity.com/paper/2410.19680/) (2024)
- [Learning Bijective Surface Parameterization for Inferring Signed Distance Functions from Sparse Point Clouds with Grid Deformation](https://mlsanity.com/paper/2503.23670/) (2025)
- [GAP: Gaussianize Any Point Clouds with Text Guidance](https://mlsanity.com/paper/2508.05631/) (2025)
- [Retro-FPN: Retrospective Feature Pyramid Network for Point Cloud Semantic Segmentation](https://mlsanity.com/paper/2308.09314/) (2023)
- [Unsigned Orthogonal Distance Fields: An Accurate Neural Implicit Representation for Diverse 3D Shapes](https://mlsanity.com/paper/2403.01414/) (2024)
- [DiffCD: A Symmetric Differentiable Chamfer Distance for Neural Implicit Surface Fitting](https://mlsanity.com/paper/2407.17058/) (2024)
- [Geometric implicit neural representations for signed distance functions](https://mlsanity.com/paper/2511.07206/) (2025)

## Abstract (arXiv)

Neural signed distance functions (SDFs) have shown remarkable capability in representing geometry with details. However, without signed distance supervision, it is still a challenge to infer SDFs from point clouds or multi-view images using neural networks. In this paper, we claim that gradient consistency in the field, indicated by the parallelism of level sets, is the key factor affecting the inference accuracy. Hence, we propose a level set alignment loss to evaluate the parallelism of level sets, which can be minimized to achieve better gradient consistency. Our novelty lies in that we can align all level sets to the zero level set by constraining gradients at queries and their projections on the zero level set in an adaptive way. Our insight is to propagate the zero level set to everywhere in the field through consistent gradients to eliminate uncertainty in the field that is caused by the discreteness of 3D point clouds or the lack of observations from multi-view images. Our proposed loss is a general term which can be used upon different methods to infer SDFs from 3D point clouds and multi-view images. Our numerical and visual comparisons demonstrate that our loss can significantly improve the accuracy of SDFs inferred from point clouds or multi-view images under various benchmarks. Code and data are available at https://github.com/mabaorui/TowardsBetterGradient .