# Variational Uncalibrated Photometric Stereo under General Lighting

arXiv: https://arxiv.org/abs/1904.03942 · HTML: https://mlsanity.com/paper/1904.03942/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Apr 2019.

## Built on by (most cited first, 14 of 14)

- [Shape and Material Capture at Home](https://mlsanity.com/paper/2104.06397/) (2021)
- [Scalable, Detailed and Mask-Free Universal Photometric Stereo](https://mlsanity.com/paper/2303.15724/) (2023)
- [Universal Photometric Stereo Network using Global Lighting Contexts](https://mlsanity.com/paper/2206.02452/) (2022)
- [Self-calibrating Photometric Stereo by Neural Inverse Rendering](https://mlsanity.com/paper/2207.07815/) (2022)
- [Fast Light-Weight Near-Field Photometric Stereo](https://mlsanity.com/paper/2203.16515/) (2022)
- [Light of Normals: Unified Feature Representation for Universal Photometric Stereo](https://mlsanity.com/paper/2506.18882/) (2025)
- [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)
- [MS-PS: A Multi-Scale Network for Photometric Stereo With a New Comprehensive Training Dataset](https://mlsanity.com/paper/2211.14118/) (2022)
- [Lifting the Convex Conjugate in Lagrangian Relaxations: A Tractable Approach for Continuous Markov Random Fields](https://mlsanity.com/paper/2107.06028/) (2021)
- [Spin-UP: Spin Light for Natural Light Uncalibrated Photometric Stereo](https://mlsanity.com/paper/2404.01612/) (2024)
- [Polarimetric Multi-View Inverse Rendering](https://mlsanity.com/paper/2212.12721/) (2022)
- [MoAngelo: Motion-Aware Neural Surface Reconstruction for Dynamic Scenes](https://mlsanity.com/paper/2509.15892/) (2025)

## Abstract (arXiv)

Photometric stereo (PS) techniques nowadays remain constrained to an ideal laboratory setup where modeling and calibration of lighting is amenable. To eliminate such restrictions, we propose an efficient principled variational approach to uncalibrated PS under general illumination. To this end, the Lambertian reflectance model is approximated through a spherical harmonic expansion, which preserves the spatial invariance of the lighting. The joint recovery of shape, reflectance and illumination is then formulated as a single variational problem. There the shape estimation is carried out directly in terms of the underlying perspective depth map, thus implicitly ensuring integrability and bypassing the need for a subsequent normal integration. To tackle the resulting nonconvex problem numerically, we undertake a two-phase procedure to initialize a balloon-like perspective depth map, followed by a "lagged" block coordinate descent scheme. The experiments validate efficiency and robustness of this approach. Across a variety of evaluations, we are able to reduce the mean angular error consistently by a factor of 2-3 compared to the state-of-the-art.