# Incorporating Lambertian Priors into Surface Normals Measurement

arXiv: https://arxiv.org/abs/2107.07192 · HTML: https://mlsanity.com/paper/2107.07192/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 49 references that are in the map.
- First posted on arXiv 15 Jul 2021.

## Builds on (most cited first, 7 of 7)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PS-FCN: A Flexible Learning Framework for Photometric Stereo](https://mlsanity.com/paper/1807.08696/) (2018)
- [Self-calibrating Deep Photometric Stereo Networks](https://mlsanity.com/paper/1903.07366/) (2019)
- [CNN-PS: CNN-based Photometric Stereo for General Non-Convex Surfaces](https://mlsanity.com/paper/1808.10093/) (2018)
- [Neural Inverse Rendering for General Reflectance Photometric Stereo](https://mlsanity.com/paper/1802.10328/) (2018)
- [SPLINE-Net: Sparse Photometric Stereo through Lighting Interpolation and Normal Estimation Networks](https://mlsanity.com/paper/1905.04088/) (2019)
- [Shape and Spatially-Varying Reflectance Estimation From Virtual Exemplars](https://mlsanity.com/paper/1512.05278/) (2015)

## Built on by (most cited first, 4 of 4)

- [Prototype-Driven Structure Synergy Network for Remote Sensing Images Segmentation](https://mlsanity.com/paper/2508.04022/) (2025)
- [Deep Learning Methods for Calibrated Photometric Stereo and Beyond](https://mlsanity.com/paper/2212.08414/) (2022)
- [Credible Remote Sensing Scene Classification Using Evidential Fusion on Aerial-Ground Dual-view Images](https://mlsanity.com/paper/2301.00622/) (2023)
- [CMAWRNet: Multiple Adverse Weather Removal via a Unified Quaternion Neural Architecture](https://mlsanity.com/paper/2505.01882/) (2025)

## Abstract (arXiv)

The goal of photometric stereo is to measure the precise surface normal of a 3D object from observations with various shading cues. However, non-Lambertian surfaces influence the measurement accuracy due to irregular shading cues. Despite deep neural networks have been employed to simulate the performance of non-Lambertian surfaces, the error in specularities, shadows, and crinkle regions is hard to be reduced. In order to address this challenge, we here propose a photometric stereo network that incorporates Lambertian priors to better measure the surface normal. In this paper, we use the initial normal under the Lambertian assumption as the prior information to refine the normal measurement, instead of solely applying the observed shading cues to deriving the surface normal. Our method utilizes the Lambertian information to reparameterize the network weights and the powerful fitting ability of deep neural networks to correct these errors caused by general reflectance properties. Our explorations include: the Lambertian priors (1) reduce the learning hypothesis space, making our method learn the mapping in the same surface normal space and improving the accuracy of learning, and (2) provides the differential features learning, improving the surfaces reconstruction of details. Extensive experiments verify the effectiveness of the proposed Lambertian prior photometric stereo network in accurate surface normal measurement, on the challenging benchmark dataset.