# Normal Integration: A Survey

arXiv: https://arxiv.org/abs/1709.05940 · HTML: https://mlsanity.com/paper/1709.05940/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Sep 2017.

## Built on by (most cited first, 21 of 21)

- [ECON: Explicit Clothed humans Optimized via Normal integration](https://mlsanity.com/paper/2212.07422/) (2022)
- [MatFusion: A Generative Diffusion Model for SVBRDF Capture](https://mlsanity.com/paper/2406.06539/) (2024)
- [Chupa: Carving 3D Clothed Humans from Skinned Shape Priors using 2D Diffusion Probabilistic Models](https://mlsanity.com/paper/2305.11870/) (2023)
- [LUCES: A Dataset for Near-Field Point Light Source Photometric Stereo](https://mlsanity.com/paper/2104.13135/) (2021)
- [Fast Light-Weight Near-Field Photometric Stereo](https://mlsanity.com/paper/2203.16515/) (2022)
- [An Adaptive Screen-Space Meshing Approach for Normal Integration](https://mlsanity.com/paper/2409.16907/) (2024)
- [Edge-preserving Near-light Photometric Stereo with Neural Surfaces](https://mlsanity.com/paper/2207.04622/) (2022)
- [Multi-view Surface Reconstruction Using Normal and Reflectance Cues](https://mlsanity.com/paper/2506.04115/) (2025)
- [Discontinuity-preserving Normal Integration with Auxiliary Edges](https://mlsanity.com/paper/2404.03138/) (2024)
- [Deflectometry for specular surfaces: an overview](https://mlsanity.com/paper/2204.11592/) (2022)
- [Feature-Preserving Mesh Decimation for Normal Integration](https://mlsanity.com/paper/2504.00867/) (2025)
- [Discontinuity-aware Normal Integration for Generic Central Camera Models](https://mlsanity.com/paper/2507.06075/) (2025)
- [On the Regularising Levenberg-Marquardt Method for Blinn-Phong Photometric Stereo](https://mlsanity.com/paper/2302.08765/) (2023)
- [An overview of some mathematical techniques and problems linking 3D vision to 3D printing](https://mlsanity.com/paper/2309.10549/) (2023)
- [Towards Fast and Scalable Normal Integration using Continuous Components](https://mlsanity.com/paper/2510.11508/) (2025)
- [Near-Light Color Photometric Stereo for Mono-Chromatic Non-Lambertian Surfaces](https://mlsanity.com/paper/2601.12666/) (2026)
- [Perspective-aware fusion of incomplete depth maps and surface normals for accurate 3D reconstruction](https://mlsanity.com/paper/2602.07444/) (2026)
- [Near-light Photometric Stereo with Symmetric Lights](https://mlsanity.com/paper/2603.16404/) (2026)
- [High-fidelity Multi-view Normal Integration with Scale-encoded Neural Surface Representation](https://mlsanity.com/paper/2603.20337/) (2026)
- [Calibration-Free Surface Normals Estimation in Vision-Based Tactile Sensing using Universal Photometric Stereo](https://mlsanity.com/paper/2609.31754/) (2026)
- [Texture Space Material Diffusion](https://mlsanity.com/paper/2609.37654/) (2026)

## Abstract (arXiv)

The need for efficient normal integration methods is driven by several computer vision tasks such as shape-from-shading, photometric stereo, deflectometry, etc. In the first part of this survey, we select the most important properties that one may expect from a normal integration method, based on a thorough study of two pioneering works by Horn and Brooks [28] and by Frankot and Chellappa [19]. Apart from accuracy, an integration method should at least be fast and robust to a noisy normal field. In addition, it should be able to handle several types of boundary condition, including the case of a free boundary, and a reconstruction domain of any shape i.e., which is not necessarily rectangular. It is also much appreciated that a minimum number of parameters have to be tuned, or even no parameter at all. Finally, it should preserve the depth discontinuities. In the second part of this survey, we review most of the existing methods in view of this analysis, and conclude that none of them satisfies all of the required properties. This work is complemented by a companion paper entitled Variational Methods for Normal Integration, in which we focus on the problem of normal integration in the presence of depth discontinuities, a problem which occurs as soon as there are occlusions.