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

2026-07-08

AI Summary

Existing 3D morphable face models (3DMMs) exhibit shape biases due to limited training data, compromising their generalization and fairness across diverse populations. This work proposes the first evaluation framework integrating curvature-aware and spectral geometric analysis, leveraging the Laplace–Beltrami operator to generate high-resolution curvature error maps that enable precise localization, quantification, and visualization of reconstruction biases. Experimental results demonstrate that the proposed error metric aligns closely with human perception and significantly outperforms conventional Euclidean distance measures. Systematic evaluation across multiple state-of-the-art 3DMMs reveals pronounced reconstruction biases correlated with age, gender, and ethnicity, with age-related discrepancies being particularly substantial.

Abstract

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.

Problem

• 3D face reconstruction
• geometric bias
• 3D Morphable Models
• demographic fairness
• surface curvature

Innovation

• curvature-aware
• Laplace-Beltrami Operator
• 3D face reconstruction
• geometric bias
• fairness evaluation