Elsevier

Computational Geometry

Volume 97, August 2021, 101758
Computational Geometry

An efficient three-dimensional face recognition system based random forest and geodesic curves

https://doi.org/10.1016/j.comgeo.2021.101758Get rights and content

Abstract

3D Face recognition is being extensively recognized as a biometric performance refers to its non-intrusive environment. In spite of large research on 2-D face recognition, it suffers from low recognition rate due to illumination variations, pose changes, poor image quality, occlusions and facial expression variations, while 3D face models are insensitive to all these conditions. In this paper, we present an efficient 3D face recognition approach based on Geodesic Distance (GD) of Riemannian geometry and Random Forest (RF), named GD-FM+RF. Therefore, to compute the geodesic distance between the specified pairs of the points of 3D faces, we applied Fast Marching (FM) algorithm, in order to solve the Eikonal equation. Then, these extracted features presented by the geodesic facial curves are used by Principal Component Analysis (PCA) algorithm to analyze class separability. Afterwards, these features were utilized as input of RF classifier. In order to test our approach and assess its effectiveness, simulated series of tests were implemented on 3D SHape REtrieval Contest 2008 database (SHREC'08). As a result, our proposed approach enhances the recognition rate and achieves promising results compared to state of the art methods, getting 99.11% in terms of recognition rate.

Introduction

Recently, 3D face recognition has become one of the hottest research topics for its wide range of applications [1]. Among the primary modules in face recognition system is the classification process and the feature extraction, which have an important impact on the whole system performance.

In the last decades, many approaches have been proposed to fulfill the task of 3D face recognition. In [2], the authors proposed an automatic 3D occlusion detection and restoration system by using 3D geometry-based face recognition in presence of eye and mouth occlusion. In the work presented by Gilani et al. [3], the authors proposed a Deep CNN model designed specifically for 3D face recognition. In [4], the authors developed an improved deep convolutional neural network (DCNN) combined with softmax classifier to identify faces, based on two Deep CNNs for feature extraction, the first one is 2D images converted to gray scale and the second one is 3D grid models. In [5], the authors proposed deep learning framework based on geodesic moments for robust 3D shape classification by using two-layer stacked sparse autoencoder in order to learn deep features. Cai et al. used three techniques: fast 3D scan preprocessing, multiple data augmentation, and a deep learning method by using facial component patches for 3D face recognition [6]. In [7] the authors combined 3D Principal Component Analysis (PCA) and Support Vector Machine (SVM) for 3D face recognition under various expressions based on Bosphorus 3D face database. Shi et al. proposed an efficient 3D face recognition approach based Frenet feature that is derived from the 3D facial iso-geodesic curves [9]. Lei et al. [12] presented a robust 3D face recognition approach, using a new feature algorithm named Angular Radial Signature (ARS), which was extracted from the semi-rigid region of the face, followed by the SVM classifier to perform 3D face recognition. In [37], the authors proposed a deep 3D face recognition approach by using a deep convolutional neural network (DCNN) and a 3D augmentation algorithm. Cardia et al. were used the Deep Learning based on Convolutional Neural Networks (CNN) and low-level 3D local features (3DLBP) for 3D Face Recognition [10]. Another work is presented by [11], which the authors used a geometry and local shape descriptor in a matching process for 3D face recognition to overcome the distortions caused by expressions in faces. Then, a survey of 3D face recognition techniques based on local features is presented in [8].

The improvement of 2D face recognition algorithms severely suffers owing to illumination variations, pose changes, poor image quality, occlusions, aging, makeup variation and facial expression variations [13], [14]. Moreover, the 3D face recognition has the potential to overcome all these points. For this reason, we proposed a 3D face recognition system, based on the computation of the geodesic distance between a set of starting points and arrival points. The Geodesic representation of the facial surface describes the invariant properties under isometric deformations, by using Riemannian framework based on the method of Fast Marching, in order to extract the features of 3D faces represented by the geodesic facial curves, then, we test our data by the PCA algorithm to analyze the separability between classes, followed by the classification process by applying the Random Forest classifier.

The paper is organized as follows: Section 2 gives a brief literature review of the used methods. Section 3 presents our proposed 3D Face Recognition system. Section 4 evaluates the classes inter-Connection based on PCA algorithm. Section 5 presents the experimental results and a comparative analysis of SHREC'08 3D facial database. Section 6 concludes the paper with possible points for future work.

Section snippets

Geodesic distance

Traditionally, the methods to calculate the geodesic path are classified into two categories [25], [24]. In the first one, we calculate the distance between a source vertex and all other vertices, and in the second one, we compute the distance between a pair of fixed vertices which called starting point and arrival point.

In the practice of our work, we used the second category, which we choose three starting points and three arrival points, each distance is the sum of geodesic distance on every

3D face representation

The Geometric meshes are a three-dimensional surface which consists of a set of points in 3D space connected in a graph structure. According to [15], the 3D mesh representation uses pre-computed and indexed local information about the 3D surface. It is more preferred as it is flexible and more suitable for 3D geometric transformations, like translation, rotations and scaling. In [15] the 3D mesh is expressed as a collection of mesh elements: vertices, edges and polygons. Then, almost the 3D

Evaluation of classes inter-connection

To evaluate the class inter connection of 3D SHREC'08 database, we start by using PCA [21] to analyze the matrix representing the data. Thus, Fig. 4 presents the first six components. Therefore, the eigenvalues measure the amount of variance explained by each principal axis. They are large for the first axes and small for the following axes. In other words, the first axes correspond to the directions carrying the maximum amount of variation contained in the data set. Just by using two axes, we

Experimental results

Our experiments are investigated to evaluate the effect of geodesic distance combined with RF classifier for 3D face recognition system. We carried out experiments on a well-known 3D face database, SHREC'08 [28] 3D face database. Thus, SHREC'08 database comprises 427 3D facial scans belonging to 61 individuals (45 male and 16 females). For each individual, seven scans are taken that differ in the acquisition viewpoint and facial expressions. Specifically, two frontal scans are with neutral

Conclusions

In this paper, we proposed an efficient 3D face recognition approach named GD-FM+RF. First, we extract manually the specified points which represent almost the center of the pertinent characteristics in the mesh face. Second, we measure geodesic distances between the detected points (vertices and ridges) of the 3D face by using the Fast Marching algorithm in order to extract the geodesic facial curves. Third, we test our data presented by the geodesic features with PCA algorithm to verify the

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This research work is supported by the SAFEROAD project under contract No: 24/2017.

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