# VRP-UDF: Towards Unbiased Learning of Unsigned Distance Functions from Multi-view Images with Volume Rendering Priors

arXiv: https://arxiv.org/abs/2407.16396 · HTML: https://mlsanity.com/paper/2407.16396/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 60 of its 94 references that are in the map.
- First posted on arXiv 23 Jul 2024.

## Builds on (most cited first, 30 of 60)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [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)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (2021)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [2D Gaussian Splatting for Geometrically Accurate Radiance Fields](https://mlsanity.com/paper/2403.17888/) (2024)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [The Replica Dataset: A Digital Replica of Indoor Spaces](https://mlsanity.com/paper/1906.05797/) (2019)
- [MVSNet: Depth Inference for Unstructured Multi-view Stereo](https://mlsanity.com/paper/1804.02505/) (2018)
- [Objaverse-XL: A Universe of 10M+ 3D Objects](https://mlsanity.com/paper/2307.05663/) (2023)
- [Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervision](https://mlsanity.com/paper/1912.07372/) (2019)
- [Mip-Splatting: Alias-free 3D Gaussian Splatting](https://mlsanity.com/paper/2311.16493/) (2023)
- [UNISURF: Unifying Neural Implicit Surfaces and Radiance Fields for Multi-View Reconstruction](https://mlsanity.com/paper/2104.10078/) (2021)
- [SuGaR: Surface-Aligned Gaussian Splatting for Efficient 3D Mesh Reconstruction and High-Quality Mesh Rendering](https://mlsanity.com/paper/2311.12775/) (2023)
- [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)
- [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)
- [PGSR: Planar-based Gaussian Splatting for Efficient and High-Fidelity Surface Reconstruction](https://mlsanity.com/paper/2406.06521/) (2024)
- [Neural Unsigned Distance Fields for Implicit Function Learning](https://mlsanity.com/paper/2010.13938/) (2020)
- [SparseNeuS: Fast Generalizable Neural Surface Reconstruction from Sparse Views](https://mlsanity.com/paper/2206.05737/) (2022)
- [NICER-SLAM: Neural Implicit Scene Encoding for RGB SLAM](https://mlsanity.com/paper/2302.03594/) (2023)
- [Neural-Pull: Learning Signed Distance Functions from Point Clouds by Learning to Pull Space onto Surfaces](https://mlsanity.com/paper/2011.13495/) (2020)
- [NeuSG: Neural Implicit Surface Reconstruction with 3D Gaussian Splatting Guidance](https://mlsanity.com/paper/2312.00846/) (2023)
- [Improving neural implicit surfaces geometry with patch warping](https://mlsanity.com/paper/2112.09648/) (2021)
- [NeuRIS: Neural Reconstruction of Indoor Scenes Using Normal Priors](https://mlsanity.com/paper/2206.13597/) (2022)
- [TransMVSNet: Global Context-aware Multi-view Stereo Network with Transformers](https://mlsanity.com/paper/2111.14600/) (2021)
- [Deep Fashion3D: A Dataset and Benchmark for 3D Garment Reconstruction from Single Images](https://mlsanity.com/paper/2003.12753/) (2020)

## Built on by (most cited first, 17 of 17)

- [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)
- [Neural Signed Distance Function Inference through Splatting 3D Gaussians Pulled on Zero-Level Set](https://mlsanity.com/paper/2410.14189/) (2024)
- [Zero-Shot Scene Reconstruction from Single Images with Deep Prior Assembly](https://mlsanity.com/paper/2410.15971/) (2024)
- [MonoInstance: Enhancing Monocular Priors via Multi-view Instance Alignment for Neural Rendering and Reconstruction](https://mlsanity.com/paper/2503.18363/) (2025)
- [GaussianUDF: Inferring Unsigned Distance Functions through 3D Gaussian Splatting](https://mlsanity.com/paper/2503.19458/) (2025)
- [NeRFPrior: Learning Neural Radiance Field as a Prior for Indoor Scene Reconstruction](https://mlsanity.com/paper/2503.18361/) (2025)
- [VTGaussian-SLAM: RGBD SLAM for Large Scale Scenes with Splatting View-Tied 3D Gaussians](https://mlsanity.com/paper/2506.02741/) (2025)
- [Learning Bijective Surface Parameterization for Inferring Signed Distance Functions from Sparse Point Clouds with Grid Deformation](https://mlsanity.com/paper/2503.23670/) (2025)
- [U-CAN: Unsupervised Point Cloud Denoising with Consistency-Aware Noise2Noise Matching](https://mlsanity.com/paper/2510.25210/) (2025)
- [Sensing Surface Patches in Volume Rendering for Inferring Signed Distance Functions](https://mlsanity.com/paper/2412.16467/) (2024)
- [3D Gaussian Splatting with Self-Constrained Priors for High Fidelity Surface Reconstruction](https://mlsanity.com/paper/2603.19682/) (2026)
- [SGAD-SLAM: Splatting Gaussians at Adjusted Depth for Better Radiance Fields in RGBD SLAM](https://mlsanity.com/paper/2603.21055/) (2026)
- [VidSplat: Gaussian Splatting Reconstruction with Geometry-Guided Video Diffusion Priors](https://mlsanity.com/paper/2605.11424/) (2026)
- [City-Level 3D Surface Reconstruction with Viewpoint Orientation Partitioning and Scene Completion](https://mlsanity.com/paper/2607.03771/) (2026)
- [MIND: Material Interface Generation from UDFs for Non-Manifold Surface Reconstruction](https://mlsanity.com/paper/2506.02938/) (2025)
- [Sparse-View Surface Reconstruction using Gaussian Splatting through High-Confidence Depth Propagation with Normal Priors](https://mlsanity.com/paper/2607.03765/) (2026)

## Abstract (arXiv)

Unsigned distance functions (UDFs) have been a vital representation for open surfaces. With different differentiable renderers, current methods are able to train neural networks to infer a UDF by minimizing the rendering errors with the UDF to the multi-view ground truth. However, these differentiable renderers are mainly handcrafted, which makes them either biased on ray-surface intersections, or sensitive to unsigned distance outliers, or not scalable to large scenes. To resolve these issues, we present a novel differentiable renderer to infer UDFs more accurately. Instead of using handcrafted equations, our differentiable renderer is a neural network which is pre-trained in a data-driven manner. It learns how to render unsigned distances into depth images, leading to a prior knowledge, dubbed volume rendering priors. To infer a UDF for an unseen scene from multiple RGB images, we generalize the learned volume rendering priors to map inferred unsigned distances in alpha blending for RGB image rendering. To reduce the bias of sampling in UDF inference, we utilize an auxiliary point sampling prior as an indicator of ray-surface intersection, and propose novel schemes towards more accurate and uniform sampling near the zero-level sets. We also propose a new strategy that leverages our pretrained volume rendering prior to serve as a general surface refiner, which can be integrated with various Gaussian reconstruction methods to optimize the Gaussian distributions and refine geometric details. Our results show that the learned volume rendering prior is unbiased, robust, scalable, 3D aware, and more importantly, easy to learn. Further experiments show that the volume rendering prior is also a general strategy to enhance other neural implicit representations such as signed distance function and occupancy.