# A Differential Volumetric Approach to Multi-View Photometric Stereo

arXiv: https://arxiv.org/abs/1811.01984 · HTML: https://mlsanity.com/paper/1811.01984/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Nov 2018.

## Built on by (most cited first, 24 of 24)

- [Uncertainty-Aware Deep Multi-View Photometric Stereo](https://mlsanity.com/paper/2202.13071/) (2022)
- [Neural Radiance Fields Approach to Deep Multi-View Photometric Stereo](https://mlsanity.com/paper/2110.05594/) (2021)
- [WildLight: In-the-wild Inverse Rendering with a Flashlight](https://mlsanity.com/paper/2303.14190/) (2023)
- [Multi-view 3D Reconstruction of a Texture-less Smooth Surface of Unknown Generic Reflectance](https://mlsanity.com/paper/2105.11599/) (2021)
- [Multi-View Azimuth Stereo via Tangent Space Consistency](https://mlsanity.com/paper/2303.16447/) (2023)
- [LUCES: A Dataset for Near-Field Point Light Source Photometric Stereo](https://mlsanity.com/paper/2104.13135/) (2021)
- [Leveraging Near-Field Lighting for Monocular Depth Estimation from Endoscopy Videos](https://mlsanity.com/paper/2403.17915/) (2024)
- [RNb-NeuS: Reflectance and Normal-based Multi-View 3D Reconstruction](https://mlsanity.com/paper/2312.01215/) (2023)
- [A CNN Based Approach for the Point-Light Photometric Stereo Problem](https://mlsanity.com/paper/2210.04655/) (2022)
- [Normal-guided Detail-Preserving Neural Implicit Function for High-Fidelity 3D Surface Reconstruction](https://mlsanity.com/paper/2406.04861/) (2024)
- [Sparse Views, Near Light: A Practical Paradigm for Uncalibrated Point-light Photometric Stereo](https://mlsanity.com/paper/2404.00098/) (2024)
- [High-Quality RGB-D Reconstruction via Multi-View Uncalibrated Photometric Stereo and Gradient-SDF](https://mlsanity.com/paper/2210.12202/) (2022)
- [Multi-view Surface Reconstruction Using Normal and Reflectance Cues](https://mlsanity.com/paper/2506.04115/) (2025)
- [NPLMV-PS: Neural Point-Light Multi-View Photometric Stereo](https://mlsanity.com/paper/2405.12057/) (2024)
- [One Ring to Rule Them All: a simple solution to multi-view 3D-Reconstruction of shapes with unknown BRDF via a small Recurrent ResNet](https://mlsanity.com/paper/2104.05014/) (2021)
- [Towards Scalable Multi-View Reconstruction of Geometry and Materials](https://mlsanity.com/paper/2306.03747/) (2023)
- [A Neural Height-Map Approach for the Binocular Photometric Stereo Problem](https://mlsanity.com/paper/2311.05958/) (2023)
- [Learning Efficient Photometric Feature Transform for Multi-view Stereo](https://mlsanity.com/paper/2103.14794/) (2021)
- [LUCES-MV: A Multi-View Dataset for Near-Field Point Light Source Photometric Stereo](https://mlsanity.com/paper/2412.16737/) (2024)
- [Keypoint-based Stereophotoclinometry for Characterizing and Navigating Small Bodies: A Factor Graph Approach](https://mlsanity.com/paper/2312.06865/) (2023)
- [Stereophotoclinometry Revisited](https://mlsanity.com/paper/2504.08252/) (2025)
- [PS-GS: Gaussian Splatting for Multi-View Photometric Stereo](https://mlsanity.com/paper/2507.18231/) (2025)
- [Learning Photometric Feature Transform for Free-form Object Scan](https://mlsanity.com/paper/2308.03492/) (2023)
- [Neural Multi-View Self-Calibrated Photometric Stereo without Photometric Stereo Cues](https://mlsanity.com/paper/2507.23162/) (2025)

## Abstract (arXiv)

Highly accurate 3D volumetric reconstruction is still an open research topic where the main difficulty is usually related to merging some rough estimations with high frequency details. One of the most promising methods is the fusion between multi-view stereo and photometric stereo images. Beside the intrinsic difficulties that multi-view stereo and photometric stereo in order to work reliably, supplementary problems arise when considered together. In this work, we present a volumetric approach to the multi-view photometric stereo problem. The key point of our method is the signed distance field parameterisation and its relation to the surface normal. This is exploited in order to obtain a linear partial differential equation which is solved in a variational framework, that combines multiple images from multiple points of view in a single system. In addition, the volumetric approach is naturally implemented on an octree, which allows for fast ray-tracing that reliably alleviates occlusions and cast shadows. Our approach is evaluated on synthetic and real data-sets and achieves state-of-the-art results.