Journal of Computer Sciences and Applications, 2015, Vol. 3, No. 3, 67-72 Available online at http://pubs.sciepub.com/jcsa/3/3/2 © Science and Education Publishing DOI:10.12691/jcsa-3-3-2 Three Dimensional Face Surfaces Analysis using Geodesic Distance Rachid AHDID * , Said SAFI, Bouzid MANAUT Interdisciplinary Laboratory of Research in Sciences and Technologies (LIRST), Sultan Moulay Slimane University, Beni Mellal, Morocco *Corresponding author: r.ahdid@usms.ma Received March 04, 2015; Revised April 16, 2015; Accepted May 06, 2015 Abstract In this paper, we present an automatic 3D face recognition system based on the computation of the geodesic distance between the reference point and the other points in the 3D face surface. To compute a geodesic distance, we use the Fast Marching algorithm for solving the Eikonal equation. For space reduction, we apply Principal Component Analysis (PCA) and Fisher Linear Discriminant Analysis (LDA). Quantitative measures of similarity are obtained and then used as inputs to several classification methods. 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). Keywords: 3D face recognition, geodesic distance, reference point, Principal Components Analysis, Linear Discriminant Analysis, fast marching, eikonal equation Cite This Article: Rachid AHDID, Said SAFI, and Bouzid MANAUT, “Three Dimensional Face Surfaces Analysis using Geodesic Distance.” Journal of Computer Sciences and Applications, vol. 3, no. 3 (2015): 67-72. doi: 10.12691/jcsa-3-3-2. 1. Introduction The task of recognizing human face with the help of a machine has been has attracted more attention in recent years. Biometric face recognition technology has received significant attention in the past several years due to its potential in different applications. Automated human face recognition was applied in different fields including automated secured access to machines and buildings, automatic surveillance, forensic analysis, fast retrieval of records from databases in police departments, automatic identification of patients in hospitals, checking for fraud or identity theft, and human-computer interaction [27]. In a face recognition system, the individual is subject to a varied contrast and brightness lighting background. This three-dimensional shape when it is part of a two- dimensional surface as is the case of an image can lead to significant variations [3]. The human face is an object of three-dimensional nature. This object may be subject of various rotations, not only flat but also space and also subject to deformations due to facial expressions. The shape and characteristics of this object also change over time [13]. Automatic face recognition based on the 2D images processing is well developed this last years, and several techniques have been proposed [4]. There are a methods of 3D face recognition based on the use of three- dimensional information of the human face in the 3D space. Existing approaches that address the problem of 3D face recognition can be classified into several categories of approaches: Geometric or Local approaches 3D, Bronstein et al [1,2] propose a new representation based on the isometric nature of the facial surface, Samir et al [3,4] use 2D and 3D facial curves for analyzing the facial surface; Holistic approaches, Heseltine et al [5] have developed two approaches to applying the representations PCA Three-dimensional face, Cook et al [6] present a robust method for facial expressions based on Log-Gabor models from images of deep and some approaches are based on face segmentation can be found in [7-12]. The objective of this paper is to perform an automatic 3D face recognition system based on geodesic distance computing using Eikonal equation. For this we take the following steps: • Detection of 3D face where the nose end is a reference point. • Compute of geodetic distance between the reference point and the other points of the 3D facial surface using the Fast Marching algorithm as a solution of the Eikonal equation. • Reduction of geodesic distances space matrices by Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA) algorithms. The rest of this paper is organized as follows: Section 2 describes the methodology of the proposed method with its stages: reference point detection, geodesic distance computing, Principal Component Analysis (PCA), Fisher Linear Discriminant Analysis (LDA) and classification algorithms (NN, KPPV and SVM). Section 3 includes the simulation results and method analysis. Section 4 draws the conclusion of this work and possible points for future work.