# High-fidelity Multi-view Normal Integration with Scale-encoded Neural Surface Representation

arXiv: https://arxiv.org/abs/2603.20337 · HTML: https://mlsanity.com/paper/2603.20337/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 41 references that are in the map.
- First posted on arXiv 20 Mar 2026.

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

- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (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)
- [K-Planes: Explicit Radiance Fields in Space, Time, and Appearance](https://mlsanity.com/paper/2301.10241/) (2023)
- [Zip-NeRF: Anti-Aliased Grid-Based Neural Radiance Fields](https://mlsanity.com/paper/2304.06706/) (2023)
- [Mip-Splatting: Alias-free 3D Gaussian Splatting](https://mlsanity.com/paper/2311.16493/) (2023)
- [Neuralangelo: High-Fidelity Neural Surface Reconstruction](https://mlsanity.com/paper/2306.03092/) (2023)
- [NeuS2: Fast Learning of Neural Implicit Surfaces for Multi-view Reconstruction](https://mlsanity.com/paper/2212.05231/) (2022)
- [Tri-MipRF: Tri-Mip Representation for Efficient Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2307.11335/) (2023)
- [HF-NeuS: Improved Surface Reconstruction Using High-Frequency Details](https://mlsanity.com/paper/2206.07850/) (2022)
- [Analytic-Splatting: Anti-Aliased 3D Gaussian Splatting via Analytic Integration](https://mlsanity.com/paper/2403.11056/) (2024)
- [Multi-View Photometric Stereo: A Robust Solution and Benchmark Dataset for Spatially Varying Isotropic Materials](https://mlsanity.com/paper/2001.06659/) (2020)
- [PET-NeuS: Positional Encoding Tri-Planes for Neural Surfaces](https://mlsanity.com/paper/2305.05594/) (2023)
- [Uncertainty-Aware Deep Multi-View Photometric Stereo](https://mlsanity.com/paper/2202.13071/) (2022)
- [Scalable, Detailed and Mask-Free Universal Photometric Stereo](https://mlsanity.com/paper/2303.15724/) (2023)
- [Anti-Aliased Neural Implicit Surfaces with Encoding Level of Detail](https://mlsanity.com/paper/2309.10336/) (2023)
- [Rip-NeRF: Anti-aliasing Radiance Fields with Ripmap-Encoded Platonic Solids](https://mlsanity.com/paper/2405.02386/) (2024)
- [Normal Integration: A Survey](https://mlsanity.com/paper/1709.05940/) (2017)
- [SuperNormal: Neural Surface Reconstruction via Multi-View Normal Integration](https://mlsanity.com/paper/2312.04803/) (2023)
- [RNb-NeuS: Reflectance and Normal-based Multi-View 3D Reconstruction](https://mlsanity.com/paper/2312.01215/) (2023)
- [Gaussian Splatting with Discretized SDF for Relightable Assets](https://mlsanity.com/paper/2507.15629/) (2025)
- [An Adaptive Screen-Space Meshing Approach for Normal Integration](https://mlsanity.com/paper/2409.16907/) (2024)
- [GS-Octree: Octree-based 3D Gaussian Splatting for Robust Object-level 3D Reconstruction Under Strong Lighting](https://mlsanity.com/paper/2406.18199/) (2024)
- [Multiview Geometric Regularization of Gaussian Splatting for Accurate Radiance Fields](https://mlsanity.com/paper/2506.13508/) (2025)
- [RING-NeRF : Rethinking Inductive Biases for Versatile and Efficient Neural Fields](https://mlsanity.com/paper/2312.03357/) (2023)
- [Feature-Preserving Mesh Decimation for Normal Integration](https://mlsanity.com/paper/2504.00867/) (2025)
- [PMNI: Pose-free Multi-view Normal Integration for Reflective and Textureless Surface Reconstruction](https://mlsanity.com/paper/2504.08410/) (2025)

## Abstract (arXiv)

Previous multi-view normal integration methods typically sample a single ray per pixel, without considering the spatial area covered by each pixel, which varies with camera intrinsics and the camera-to-object distance. Consequently, when the target object is captured at different distances, the normals at corresponding pixels may differ across views. This multi-view surface normal inconsistency results in the blurring of high-frequency details in the reconstructed surface. To address this issue, we propose a scale-encoded neural surface representation that incorporates the pixel coverage area into the neural representation. By associating each 3D point with a spatial scale and calculating its normal from a hybrid grid-based encoding, our method effectively represents multi-scale surface normals captured at varying distances. Furthermore, to enable scale-aware surface reconstruction, we introduce a mesh extraction module that assigns an optimal local scale to each vertex based on the training observations. Experimental results demonstrate that our approach consistently yields high-fidelity surface reconstruction from normals observed at varying distances, outperforming existing multi-view normal integration methods.