# Rethinking Directional Parameterization in Neural Implicit Surface Reconstruction

arXiv: https://arxiv.org/abs/2409.06923 · HTML: https://mlsanity.com/paper/2409.06923/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 39 references that are in the map.
- First posted on arXiv 11 Sep 2024.

## Builds on (most cited first, 30 of 31)

- [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)
- [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)
- [pixelNeRF: Neural Radiance Fields from One or Few Images](https://mlsanity.com/paper/2012.02190/) (2020)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [NeRF++: Analyzing and Improving Neural Radiance Fields](https://mlsanity.com/paper/2010.07492/) (2020)
- [Accelerating 3D Deep Learning with PyTorch3D](https://mlsanity.com/paper/2007.08501/) (2020)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (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)
- [Ref-NeRF: Structured View-Dependent Appearance for Neural Radiance Fields](https://mlsanity.com/paper/2112.03907/) (2021)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [NeRV: Neural Reflectance and Visibility Fields for Relighting and View Synthesis](https://mlsanity.com/paper/2012.03927/) (2020)
- [MonoSDF: Exploring Monocular Geometric Cues for Neural Implicit Surface Reconstruction](https://mlsanity.com/paper/2206.00665/) (2022)
- [Baking Neural Radiance Fields for Real-Time View Synthesis](https://mlsanity.com/paper/2103.14645/) (2021)
- [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)
- [Geo-Neus: Geometry-Consistent Neural Implicit Surfaces Learning for Multi-view Reconstruction](https://mlsanity.com/paper/2205.15848/) (2022)
- [Multi-view Supervision for Single-view Reconstruction via Differentiable Ray Consistency](https://mlsanity.com/paper/1704.06254/) (2017)
- [SparseNeuS: Fast Generalizable Neural Surface Reconstruction from Sparse Views](https://mlsanity.com/paper/2206.05737/) (2022)
- [NeRO: Neural Geometry and BRDF Reconstruction of Reflective Objects from Multiview Images](https://mlsanity.com/paper/2305.17398/) (2023)
- [Improving neural implicit surfaces geometry with patch warping](https://mlsanity.com/paper/2112.09648/) (2021)
- [Differentiable Rendering: A Survey](https://mlsanity.com/paper/2006.12057/) (2020)
- [Perspective Transformer Nets: Learning Single-View 3D Object Reconstruction without 3D Supervision](https://mlsanity.com/paper/1612.00814/) (2016)
- [Voxurf: Voxel-based Efficient and Accurate Neural Surface Reconstruction](https://mlsanity.com/paper/2208.12697/) (2022)
- [NeILF++: Inter-Reflectable Light Fields for Geometry and Material Estimation](https://mlsanity.com/paper/2303.17147/) (2023)
- [Ref-NeuS: Ambiguity-Reduced Neural Implicit Surface Learning for Multi-View Reconstruction with Reflection](https://mlsanity.com/paper/2303.10840/) (2023)
- [ENVIDR: Implicit Differentiable Renderer with Neural Environment Lighting](https://mlsanity.com/paper/2303.13022/) (2023)

## Built on by (most cited first, 3 of 3)

- [HiMoR: Monocular Deformable Gaussian Reconstruction with Hierarchical Motion Representation](https://mlsanity.com/paper/2504.06210/) (2025)
- [TextureSplat: Per-Primitive Texture Mapping for Reflective Gaussian Splatting](https://mlsanity.com/paper/2506.13348/) (2025)
- [A Mixed-Primitive-based Gaussian Splatting Method for Surface Reconstruction](https://mlsanity.com/paper/2507.11321/) (2025)

## Abstract (arXiv)

Multi-view 3D surface reconstruction using neural implicit representations has made notable progress by modeling the geometry and view-dependent radiance fields within a unified framework. However, their effectiveness in reconstructing objects with specular or complex surfaces is typically biased by the directional parameterization used in their view-dependent radiance network. it Viewing direction and it reflection direction are the two most commonly used directional parameterizations but have their own limitations. Typically, utilizing the viewing direction usually struggles to correctly decouple the geometry and appearance of objects with highly specular surfaces, while using the reflection direction tends to yield overly smooth reconstructions for concave or complex structures. In this paper, we analyze their failed cases in detail and propose a novel hybrid directional parameterization to address their limitations in a unified form. Extensive experiments demonstrate the proposed hybrid directional parameterization consistently delivered satisfactory results in reconstructing objects with a wide variety of materials, geometry and appearance, whereas using other directional parameterizations faces challenges in reconstructing certain objects. Moreover, the proposed hybrid directional parameterization is nearly parameter-free and can be effortlessly applied in any existing neural surface reconstruction method.