# Learning Bijective Surface Parameterization for Inferring Signed Distance Functions from Sparse Point Clouds with Grid Deformation

arXiv: https://arxiv.org/abs/2503.23670 · HTML: https://mlsanity.com/paper/2503.23670/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 59 of its 75 references that are in the map.
- First posted on arXiv 31 Mar 2025.

## Builds on (most cited first, 30 of 59)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Deep Marching Tetrahedra: a Hybrid Representation for High-Resolution 3D Shape Synthesis](https://mlsanity.com/paper/2111.04276/) (2021)
- [GET3D: A Generative Model of High Quality 3D Textured Shapes Learned from Images](https://mlsanity.com/paper/2209.11163/) (2022)
- [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)
- [Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstruction](https://mlsanity.com/paper/2003.10983/) (2020)
- [Triplane Meets Gaussian Splatting: Fast and Generalizable Single-View 3D Reconstruction with Transformers](https://mlsanity.com/paper/2312.09147/) (2023)
- [Learning Shape Templates with Structured Implicit Functions](https://mlsanity.com/paper/1904.06447/) (2019)
- [Uni3D: Exploring Unified 3D Representation at Scale](https://mlsanity.com/paper/2310.06773/) (2023)
- [GeoNeRF: Generalizing NeRF with Geometry Priors](https://mlsanity.com/paper/2111.13539/) (2021)
- [Shape As Points: A Differentiable Poisson Solver](https://mlsanity.com/paper/2106.03452/) (2021)
- [Neural-Pull: Learning Signed Distance Functions from Point Clouds by Learning to Pull Space onto Surfaces](https://mlsanity.com/paper/2011.13495/) (2020)
- [Flexible Isosurface Extraction for Gradient-Based Mesh Optimization](https://mlsanity.com/paper/2308.05371/) (2023)
- [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)
- [PatchNets: Patch-Based Generalizable Deep Implicit 3D Shape Representations](https://mlsanity.com/paper/2008.01639/) (2020)
- [Deep Implicit Moving Least-Squares Functions for 3D Reconstruction](https://mlsanity.com/paper/2103.12266/) (2021)
- [Curriculum DeepSDF](https://mlsanity.com/paper/2003.08593/) (2020)
- [Reconstructing Surfaces for Sparse Point Clouds with On-Surface Priors](https://mlsanity.com/paper/2204.10603/) (2022)
- [SA-ConvONet: Sign-Agnostic Optimization of Convolutional Occupancy Networks](https://mlsanity.com/paper/2105.03582/) (2021)
- [Surface Reconstruction from Point Clouds by Learning Predictive Context Priors](https://mlsanity.com/paper/2204.11015/) (2022)
- [Neural Splines: Fitting 3D Surfaces with Infinitely-Wide Neural Networks](https://mlsanity.com/paper/2006.13782/) (2020)
- [DiffGS: Functional Gaussian Splatting Diffusion](https://mlsanity.com/paper/2410.19657/) (2024)

## Built on by (most cited first, 7 of 7)

- [MaterialRefGS: Reflective Gaussian Splatting with Multi-view Consistent Material Inference](https://mlsanity.com/paper/2510.11387/) (2025)
- [SparseRecon: Neural Implicit Surface Reconstruction from Sparse Views with Feature and Depth Consistencies](https://mlsanity.com/paper/2508.00366/) (2025)
- [GAP: Gaussianize Any Point Clouds with Text Guidance](https://mlsanity.com/paper/2508.05631/) (2025)
- [U-CAN: Unsupervised Point Cloud Denoising with Consistency-Aware Noise2Noise Matching](https://mlsanity.com/paper/2510.25210/) (2025)
- [SGAD-SLAM: Splatting Gaussians at Adjusted Depth for Better Radiance Fields in RGBD SLAM](https://mlsanity.com/paper/2603.21055/) (2026)
- [GaussianGrow: Geometry-aware Gaussian Growing from 3D Point Clouds with Text Guidance](https://mlsanity.com/paper/2604.05721/) (2026)
- [Learning Manifolds in High-D Point Embedding for Anisotropic Surface Approximation from Unstructured Point Clouds](https://mlsanity.com/paper/2607.28855/) (2026)

## Abstract (arXiv)

Inferring signed distance functions (SDFs) from sparse point clouds remains a challenge in surface reconstruction. The key lies in the lack of detailed geometric information in sparse point clouds, which is essential for learning a continuous field. To resolve this issue, we present a novel approach that learns a dynamic deformation network to predict SDFs in an end-to-end manner. To parameterize a continuous surface from sparse points, we propose a bijective surface parameterization (BSP) that learns the global shape from local patches. Specifically, we construct a bijective mapping for sparse points from the parametric domain to 3D local patches, integrating patches into the global surface. Meanwhile, we introduce grid deformation optimization (GDO) into the surface approximation to optimize the deformation of grid points and further refine the parametric surfaces. Experimental results on synthetic and real scanned datasets demonstrate that our method significantly outperforms the current state-of-the-art methods. Project page: https://takeshie.github.io/Bijective-SDF