# Local Shape Spectrum Analysis for 3D Facial Expression Recognition

## TL;DR

This paper introduces Graph Laplacian Features (GLF), a spectral surface representation method for 3D facial expression recognition, demonstrating improved accuracy and efficiency over previous curve-based and Shape-DNA methods.

## Contribution

The paper extends 3D facial analysis to a spectral surface representation using Graph Laplacian eigenspaces, enhancing recognition performance and computational efficiency.

## Key findings

- GLF achieves higher recognition rates than curve-based methods.
- GLF outperforms Shape-DNA in stability and accuracy.
- The spectral approach reduces computational complexity.

## Abstract

We investigate the problem of facial expression recognition using 3D data. Building from one of the most successful frameworks for facial analysis using exclusively 3D geometry, we extend the analysis from a curve-based representation into a spectral representation, which allows a complete description of the underlying surface that can be further tuned to the desired level of detail. Spectral representations are based on the decomposition of the geometry in its spatial frequency components, much like a Fourier transform, which are related to intrinsic characteristics of the surface. In this work, we propose the use of Graph Laplacian Features (GLF), which results from the projection of local surface patches into a common basis obtained from the Graph Laplacian eigenspace. We test the proposed approach in the BU-3DFE database in terms of expressions and Action Units recognition. Our results confirm that the proposed GLF produces consistently higher recognition rates than the curves-based approach, thanks to a more complete description of the surface, while requiring a lower computational complexity. We also show that the GLF outperform the most popular alternative approach for spectral representation, Shape- DNA, which is based on the Laplace Beltrami Operator and cannot provide a stable basis that guarantee that the extracted signatures for the different patches are directly comparable.