# ND-SDF: Learning Normal Deflection Fields for High-Fidelity Indoor Reconstruction

arXiv: https://arxiv.org/abs/2408.12598 · HTML: https://mlsanity.com/paper/2408.12598/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 53 references that are in the map.
- First posted on arXiv 22 Aug 2024.

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

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [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)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [Direct Voxel Grid Optimization: Super-fast Convergence for Radiance Fields Reconstruction](https://mlsanity.com/paper/2111.11215/) (2021)
- [The Replica Dataset: A Digital Replica of Indoor Spaces](https://mlsanity.com/paper/1906.05797/) (2019)
- [NeRF++: Analyzing and Improving Neural Radiance Fields](https://mlsanity.com/paper/2010.07492/) (2020)
- [ScanNet++: A High-Fidelity Dataset of 3D Indoor Scenes](https://mlsanity.com/paper/2308.11417/) (2023)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [UNISURF: Unifying Neural Implicit Surfaces and Radiance Fields for Multi-View Reconstruction](https://mlsanity.com/paper/2104.10078/) (2021)
- [MonoSDF: Exploring Monocular Geometric Cues for Neural Implicit Surface Reconstruction](https://mlsanity.com/paper/2206.00665/) (2022)
- [Neuralangelo: High-Fidelity Neural Surface Reconstruction](https://mlsanity.com/paper/2306.03092/) (2023)
- [Omnidata: A Scalable Pipeline for Making Multi-Task Mid-Level Vision Datasets from 3D Scans](https://mlsanity.com/paper/2110.04994/) (2021)
- [NeuS2: Fast Learning of Neural Implicit Surfaces for Multi-view Reconstruction](https://mlsanity.com/paper/2212.05231/) (2022)
- [GeoWizard: Unleashing the Diffusion Priors for 3D Geometry Estimation from a Single Image](https://mlsanity.com/paper/2403.12013/) (2024)
- [PGSR: Planar-based Gaussian Splatting for Efficient and High-Fidelity Surface Reconstruction](https://mlsanity.com/paper/2406.06521/) (2024)
- [BakedSDF: Meshing Neural SDFs for Real-Time View Synthesis](https://mlsanity.com/paper/2302.14859/) (2023)
- [Geo-Neus: Geometry-Consistent Neural Implicit Surfaces Learning for Multi-view Reconstruction](https://mlsanity.com/paper/2205.15848/) (2022)
- [Pixel Difference Networks for Efficient Edge Detection](https://mlsanity.com/paper/2108.07009/) (2021)
- [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)
- [PermutoSDF: Fast Multi-View Reconstruction with Implicit Surfaces using Permutohedral Lattices](https://mlsanity.com/paper/2211.12562/) (2022)
- [IntrinsicNeRF: Learning Intrinsic Neural Radiance Fields for Editable Novel View Synthesis](https://mlsanity.com/paper/2210.00647/) (2022)
- [Vox-Surf: Voxel-based Implicit Surface Representation](https://mlsanity.com/paper/2208.10925/) (2022)
- [PVO: Panoptic Visual Odometry](https://mlsanity.com/paper/2207.01610/) (2022)

## Built on by (most cited first, 11 of 11)

- [DiffPano: Scalable and Consistent Text to Panorama Generation with Spherical Epipolar-Aware Diffusion](https://mlsanity.com/paper/2410.24203/) (2024)
- [PhysFlow: Unleashing the Potential of Multi-modal Foundation Models and Video Diffusion for 4D Dynamic Physical Scene Simulation](https://mlsanity.com/paper/2411.14423/) (2024)
- [CityGS-X: A Scalable Architecture for Efficient and Geometrically Accurate Large-Scale Scene Reconstruction](https://mlsanity.com/paper/2503.23044/) (2025)
- [GigaGS: Scaling up Planar-Based 3D Gaussians for Large Scene Surface Reconstruction](https://mlsanity.com/paper/2409.06685/) (2024)
- [DynaSurfGS: Dynamic Surface Reconstruction with Planar-based Gaussian Splatting](https://mlsanity.com/paper/2408.13972/) (2024)
- [StreetSurfGS: Scalable Urban Street Surface Reconstruction with Planar-based Gaussian Splatting](https://mlsanity.com/paper/2410.04354/) (2024)
- [MonoInstance: Enhancing Monocular Priors via Multi-view Instance Alignment for Neural Rendering and Reconstruction](https://mlsanity.com/paper/2503.18363/) (2025)
- [3DGAA: Realistic and Robust 3D Gaussian-based Adversarial Attack for Autonomous Driving](https://mlsanity.com/paper/2507.09993/) (2025)
- [PlanarGS: High-Fidelity Indoor 3D Gaussian Splatting Guided by Vision-Language Planar Priors](https://mlsanity.com/paper/2510.23930/) (2025)
- [3D Gaussian Splatting with Self-Constrained Priors for High Fidelity Surface Reconstruction](https://mlsanity.com/paper/2603.19682/) (2026)
- [CASA-SDF: Curriculum-Aware Spatial Adaptation with Curvature-Guided Density for Neural Implicit Surface Reconstruction](https://mlsanity.com/paper/2607.13492/) (2026)

## Abstract (arXiv)

Neural implicit reconstruction via volume rendering has demonstrated its effectiveness in recovering dense 3D surfaces. However, it is non-trivial to simultaneously recover meticulous geometry and preserve smoothness across regions with differing characteristics. To address this issue, previous methods typically employ geometric priors, which are often constrained by the performance of the prior models. In this paper, we propose ND-SDF, which learns a Normal Deflection field to represent the angular deviation between the scene normal and the prior normal. Unlike previous methods that uniformly apply geometric priors on all samples, introducing significant bias in accuracy, our proposed normal deflection field dynamically learns and adapts the utilization of samples based on their specific characteristics, thereby improving both the accuracy and effectiveness of the model. Our method not only obtains smooth weakly textured regions such as walls and floors but also preserves the geometric details of complex structures. In addition, we introduce a novel ray sampling strategy based on the deflection angle to facilitate the unbiased rendering process, which significantly improves the quality and accuracy of intricate surfaces, especially on thin structures. Consistent improvements on various challenging datasets demonstrate the superiority of our method.