# Discovering Geometric Biases in 3D Face Reconstruction: A Curvature-Aware Spectral Framework for Fairness Evaluation

arXiv: https://arxiv.org/abs/2607.07486 · HTML: https://mlsanity.com/paper/2607.07486/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 39 references that are in the map.
- First posted on arXiv 8 Jul 2026.

## Builds on (most cited first, 17 of 17)

- [Face2Face: Real-time Face Capture and Reenactment of RGB Videos](https://mlsanity.com/paper/2007.14808/) (2020)
- [Accurate 3D Face Reconstruction with Weakly-Supervised Learning: From Single Image to Image Set](https://mlsanity.com/paper/1903.08527/) (2019)
- [Learning an Animatable Detailed 3D Face Model from In-The-Wild Images](https://mlsanity.com/paper/2012.04012/) (2020)
- [3D Morphable Face Models -- Past, Present and Future](https://mlsanity.com/paper/1909.01815/) (2019)
- [Learning to Regress 3D Face Shape and Expression from an Image without 3D Supervision](https://mlsanity.com/paper/1905.06817/) (2019)
- [Towards Metrical Reconstruction of Human Faces](https://mlsanity.com/paper/2204.06607/) (2022)
- [Deep Appearance Models for Face Rendering](https://mlsanity.com/paper/1808.00362/) (2018)
- [Self-Supervised Monocular 3D Face Reconstruction by Occlusion-Aware Multi-view Geometry Consistency](https://mlsanity.com/paper/2007.12494/) (2020)
- [3D Face Reconstruction with the Geometric Guidance of Facial Part Segmentation](https://mlsanity.com/paper/2312.00311/) (2023)
- [A survey of bias in Machine Learning through the prism of Statistical Parity for the Adult Data Set](https://mlsanity.com/paper/2003.14263/) (2020)
- [REALY: Rethinking the Evaluation of 3D Face Reconstruction](https://mlsanity.com/paper/2203.09729/) (2022)
- [Evaluation of Dense 3D Reconstruction from 2D Face Images in the Wild](https://mlsanity.com/paper/1803.05536/) (2018)
- [Arc2Avatar: Generating Expressive 3D Avatars from a Single Image via ID Guidance](https://mlsanity.com/paper/2501.05379/) (2025)
- [FaceVR: Real-Time Facial Reenactment and Eye Gaze Control in Virtual Reality](https://mlsanity.com/paper/1610.03151/) (2016)
- [Makeup Prior Models for 3D Facial Makeup Estimation and Applications](https://mlsanity.com/paper/2403.17761/) (2024)
- [Fairness-Aware Grouping for Continuous Sensitive Variables: Application for Debiasing Face Analysis with respect to Skin Tone](https://mlsanity.com/paper/2507.11247/) (2025)
- [3D Face Reconstruction Error Decomposed: A Modular Benchmark for Fair and Fast Method Evaluation](https://mlsanity.com/paper/2505.18025/) (2025)

## Abstract (arXiv)

3D Morphable Models (3DMMs) remain the standard parametric shape priors for many state-of-the-art 3D face reconstruction algorithms. However, as these models are derived from a finite number of 3D face samples, they inherit the morphological biases of their training data, potentially limiting their generalizability across diverse global populations. In this paper, we propose a novel framework to analyze 3DMM reconstructions through the lens of surface curvature, with the objective to discover, quantify and visualize biases. While standard evaluation metrics often rely on Euclidean distances, our reconstruction error captures subtle surface nuances such as local topology or undulations. To do so, we leverage the Laplace-Beltrami Operator (LBO) to generate high-resolution curvature error maps, providing a localized and geometrically meaningful visualization of discrepancies between ground truth faces and reconstructed meshes. We derive from it an error metric that we validated through a user study, observing a significantly higher correlation to human perception compared to traditional methods. Furthermore, we conduct extensive experiments across several 3DMM bases and fitting algorithms, uncovering systematic age-related biases and providing preliminary evidence of biases associated with gender and ethnicity. Our findings highlight the necessity of adopting curvature-aware evaluation protocols to ensure demographic fairness and geometric precision in future 3D face reconstruction research.