[Paper Review] Facial Surface Analysis using Iso-Geodesic Curves in Three Dimensional Face Recognition System

Rachid Ahdid, El Mahdi Barrah+2 more|arXiv (Cornell University)|Aug 31, 2016

Face recognition and analysis23 references3 citations

TL;DR

This paper proposes a 3D face recognition system that represents facial surfaces as collections of iso-geodesic curves (IGCs) using the 3D Fast Marching algorithm to compute geodesic distances via Riemannian geometry. The method achieves a 98.9% recognition rate on the SHREC2008 database using SVM classification, outperforming prior methods.

ABSTRACT

In this paper, we present an automatic 3D face recognition system. This system is based on the representation of human faces surfaces as collections of Iso-Geodesic Curves (IGC) using 3D Fast Marching algorithm. To compare two facial surfaces, we compute a geodesic distance between a pair of facial curves using a Riemannian geometry. In the classifying step, we use: Neural Networks (NN), K-Nearest Neighbor (KNN) and Support Vector Machines (SVM). To test this method and evaluate its performance, a simulation series of experiments were performed on 3D Shape REtrieval Contest 2008 database (SHREC2008).

Motivation & Objective

• To develop an automatic 3D face recognition system that is robust to pose variations, lighting, and facial expressions.
• To represent 3D facial surfaces using iso-geodesic curves extracted via the Fast Marching algorithm.
• To compute geodesic distances between facial curves using Riemannian geometry for improved discriminative power.
• To evaluate the system’s performance using the SHREC2008 database and compare it with existing 3D face recognition methods.
• To demonstrate the superiority of the proposed method through classification using NN, KNN, and SVM.

Proposed method

• The reference point (nose tip) is manually detected as the starting point for geodesic distance computation.
• The 3D Fast Marching algorithm solves the Eikonal equation to compute geodesic distances from the reference point to all other points on the facial surface.
• Iso-geodesic curves are extracted at regular geodesic distance intervals from the reference point, forming a hierarchical representation of the facial surface.
• Geodesic distances between corresponding iso-geodesic curves of two faces are computed using Riemannian metric formulas to form feature vectors.
• Classification is performed using three algorithms: Neural Networks (NN), K-Nearest Neighbor (KNN), and Support Vector Machines (SVM).
• The feature vector dimension equals the number of iso-geodesic curves used (five curves in experiments), with geodesic distances as input features.

Experimental results

Research questions

• RQ1 Can a 3D face recognition system based on iso-geodesic curves achieve higher accuracy than existing methods?
• RQ2 How effective is the use of Riemannian geodesic distance for comparing facial surface curves in 3D face recognition?
• RQ3 Does the combination of iso-geodesic curve representation and SVM classification outperform other classifiers and prior approaches?
• RQ4 To what extent does the method remain robust under facial expression variations and pose changes?
• RQ5 How does the number of iso-geodesic curves affect recognition performance?

Key findings

• The proposed method achieved a recognition rate of 98.9% on the SHREC2008 database using the SVM classifier, significantly outperforming previous methods.
• The SVM classifier yielded the highest recognition rate among the three tested algorithms (NN, KNN, SVM), demonstrating its effectiveness for this feature space.
• Using five iso-geodesic curves provided a strong balance between feature richness and computational efficiency, with recognition rate stabilizing at this number.
• The method outperformed prior approaches, including those based on facial contour curves, integral invariants, and elastic deformations, which reported recognition rates between 91.1% and 95.3%.
• The use of Riemannian geometry for geodesic distance computation enabled robust and accurate comparison of facial surface curves across different expressions and poses.
• The system demonstrated high performance across diverse conditions in the SHREC2008 database, including frontal, look-up, look-down, and expression variations.