Elsevier

Neurocomputing

Volume 147, 5 January 2015, Pages 307-314
Neurocomputing

Noise-free representation based classification and face recognition experiments

https://doi.org/10.1016/j.neucom.2014.06.058Get rights and content

Abstract

The representation based classification has achieved promising performance in high-dimensional pattern classification problems. As we know, in real-world applications the samples are usually corrupted by noise. However, representation based classification can take only noise in the test sample into account and is not able to deal with noise in the training sample, which causes side-effect on the classification result. In order to make the representation based classification more suitable for real-world applications such as face recognition, we propose a new representation based classification method in this paper. This method can effectively and simultaneously reduce noise in the test and training samples. Moreover, the proposed method can reduce noise in both the original and virtual training samples and then exploits them to determine the label of the test sample. The virtual training sample is generated from the original face image and shows possible variation of the face in scale, facial pose and expression. The experimental results show that the proposed method performs very well in face recognition.

Introduction

As we know, noise extensively exists in the data [1]. In order to better model, predict and classify the data, we should well deal with noise. For pattern classification problems, it is significant to devise a way to resist noise and to improve the robustness of the classifier [2], [3], [4].

As shown in literature [5], noise has great influence on the face recognition accuracy. Moreover, the image of a face usually varies with the illumination, pose and facial expression [6], [7], [8], [9], [10], [11]. This is indeed a great challenging problem in face recognition. We can treat the difference between the images of the same face as generalized noise. For pattern classification problems, if we can identify and reduce noise, a better result can be obtained. A number of methods have been proposed for noise-free face recognition. For example, it is conceived that not-necessarily orthogonal basis which may reconstruct the data is better than principal component analysis (PCA) in the presence of noise and independent component analysis (ICA) is proposed for face recognition in the presence of noise [12]. A unified framework of subspace is proposed for robust face recognition [13]. The enhanced fisher linear discriminant (EFLD) model is also proposed for overcoming noise in face images [14]. In recent years, the low-rank decomposition is also applied to eliminate noise [15], [16], [17].

The recently proposed representation based classification has performed very well in high-dimensional pattern classification problems. Especially, the representation based classification proposed by Wright et al. [18], [19], i.e. sparse representation classification (SRC) is viewed as a breakthrough of face recognition. Besides SRC, there have also been a number of other representation based classification methods. For example, representation based classification with the l2 norm minimization constraint on the solution vector is not only able to obtain a high accuracy but also computationally very efficient. For example, collaborative representation [20], the two-phase test sample representation (TPTSR) method [21], the feature space representation method [22], [23], [24] have achieved satisfactory results in face recognition. The recently proposed linear regression classification (LRC) is also a representation based classification with the l2 norm minimization constraint [25], [26]. LRC is closely related with the previously proposed nearest intra-class space (NICS) method [27]. The pattern recognition community has paid much attention to the theoretical foundation of representation based classification and to design new representation based classification algorithms [28], [29], [30].

Rationales of representation based classification have been demonstrated from different aspects. Wright et al. considers that the “sparsity” of the representation is very helpful for achieving the high classification accuracy [18], [19]. However, Zhang et al. claimed that for representation based classification it is not the “sparsity” but the way to represent and classify the test sample, i.e. collaborative representation that contributes the most to the face recognition performance [20]. Moreover, Yang et al. considered that for SRC “locality” is more significant than “sparsity” because in representation based classification “locality” always leads to “sparsity” but not vice visa [28]. Our studies on representation based classification with the l2 norm minimization constraint show that the “sparsity” can be achieved by using a simple scheme which is very helpful for identifying the class that the test sample is truly from [21], [31], [32]. The idea of representation based classification has been applied to improve various methods such as tensor discriminant analysis and eigen-subspace methods [30], [33], [34], [35]. A number of studies on manifold learning also made notable contributions in designing methods that preserve localities of samples. For example, Laplacian faces [36], semisupervised multiview distance metric learning [37], elastic manifold embedding [38] and adaptive hypergraph learning [39] all address the problem of preserving locality structures of samples from different viewpoints. These methods can be applied to various issues such as object correspondence construction in animation [40] and Cartoon character retrieval [41]. Sparse representation was also integrated with other methods such as the wavelet decomposition for face recognition [42].

It seems that it is crucial to properly model noise in data [43]. Though noise exists in both the training and test samples, the algorithm of conventional representation based classification is established on the basis of the conventional least squares algorithm and it cannot take noise in the training samples into account. This will cause side-effect to the classification accuracy. For face recognition, besides noise from the acquisition stage, the variation of the facial pose and expression [44], [45] of the same face can also be viewed as generalized noise.

In this paper, we use the following scheme to improve the representation based classification: we first perform matrix decomposition for the matrix consisting of all the training samples and obtain the approximations of all the training samples, referred to as approximation training samples (ATRS). Then we exploit the ATRS to obtain an approximation of the test sample, referred to as approximation test sample (ATES). Finally, conventional representation based classification (CRBC) is applied to ATES and ATRS and the classification result of the test sample is obtained. Moreover, motivated by the fact the face usually has an axis-symmetrical structure, the proposed method also exploits the original face images to generate virtual symmetrical face images, which are helpful for showing possible variation of the face in scale and pose. Simply speaking, an original face image will generate two virtual symmetrical face images. The left half of the first virtual symmetrical face image is the same as the left half of the original face image and the right half of the first virtual symmetrical face image is just the mirror image of its left half. The right half of the second virtual symmetrical face image is the same as the right half of the original face image and the left half of the second virtual symmetrical face image is just the mirror image of its right half. The proposed method uses both the original and virtual training samples to represent and classify the test sample and outperforms the state-of-art face recognition methods. The main contributions of this work are as follows: (1) it proposes a simple and reasonable way to simultaneously reduce noise in the training and test samples. (2) The designed algorithm can lead to very accurate recognition of faces by properly integrating the original and virtual training samples.

Section snippets

The proposed method

In this section we describe the proposed method in detail. Suppose that there are C classes and each class has n training samples. Let x1,x2,,xN(n=nC) be all the training samples from the first, second,…, and C-th classes, respectively. In other words, x1,x2,,xn are the n training samples from the first class. xn(i1)+1,xn(i1)+2,,xni are the n training samples from the i-th class. Let y be the test sample. x1,x2,,xN and y are all M dimensional column vector. The following context describes

Analysis on the method

In complex real-world applications, it seems that both the training and test samples contain noise. As a result, to reduce noise in both the training samples and test sample will be beneficial for recognition of faces. However, the conventional representation based classification (CRBC) is based on the conventional least squares and can take only noise in the test sample into account. Specifically, CRBC assumes that the true test sample can be approximated by a weighted sum of all the training

Experimental results

We used the ORL and AR face databases as well as a subset of the FERET face database to test our method. We also tested collaborative representation classification (CRC) in [20], coarse to fine face recognition (CFFR) in [32], the improvement to the nearest neighbor classifier (INNC) in [46] and coarse to fine k nearest neighbor classifier (CFKNNC) in [47], feature space-based human face image representation and recognition (FSHFRR) in [24]. When we implemented CFKNNC, we set its parameters n

Conclusions

The proposed method uses a simple and feasible way to reduce noise in the test and training samples and exploits the obtained “uncontaminated” samples to perform representation based classification. The proposed method is very suitable for complex real-world applications such as face recognition, in which it is almost impossible for conventional representation based classification to completely eliminate the side-effect on classification of noise. However, the proposed method simultaneously

Acknowledgments

This article is partly supported by NSFC under Grant nos. 61370163, 61300032 and 61332011, as well as the Shenzhen Municipal Science and Technology Innovation Council (Nos. JC201005260122A, CXZZ20120613141657279, JCYJ20120613153352732, JCYJ20130329151843309 and JCYJ20130401152508661).

Yong Xu received his B.S. and M.S. degrees at Air Force Institute of Meteorology (China) in 1994 and 1997, respectively. He then received his Ph.D. degree in pattern recognition and intelligence system at the Nanjing University of Science and Technology (NUST) in 2005.

From May 2005 to April 2007, he worked at Shenzhen graduate school, Harbin Institute of Technology (HIT) as a postdoctoral research fellow. Now he is a professor at Shenzhen graduate school, HIT. He also acts as a research

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  • Cited by (0)

    Yong Xu received his B.S. and M.S. degrees at Air Force Institute of Meteorology (China) in 1994 and 1997, respectively. He then received his Ph.D. degree in pattern recognition and intelligence system at the Nanjing University of Science and Technology (NUST) in 2005.

    From May 2005 to April 2007, he worked at Shenzhen graduate school, Harbin Institute of Technology (HIT) as a postdoctoral research fellow. Now he is a professor at Shenzhen graduate school, HIT. He also acts as a research assistant researcher at the HongKong Polytechnic University from August 2007 to June 2008. His current interests include pattern recognition, biometrics, and machine learning. He has published more than 40 scientific papers.

    Xiaozhao Fang received the M.S. degree in computer science from Guangdong University of Technology, Guangzhou, China, in 2008. He is currently pursuing the Ph.D. degree in computer science and technology at Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, China.

    He has published more than 9 journal papers. His current research interests include pattern recognition and machine learning.

    Jane You obtained her B.Eng. in Electronic Engineering from Xi׳an Jiao tong University in 1986 and Ph.D. in Computer Science from La Trobe University, Australia in 1992.

    She was a lecturer at the University of South Australia and senior lecturer at Griffith University from 1993 till 2002. Currently she is a professor at the Hong Kong Polytechnic University. Her research interests include image processing, pattern recognition, medical imaging, biometrics computing, multimedia systems and data mining.

    Yan Chen received her B.E. and M.E. degree in computer science from Northeastern University, China in 1997 and 2000 respectively, and her Ph.D. in 2010 from University of Technology, Sydney (UTS), Australian. Currently, she is a Post-Doctoral Researcher with Harbin Institute of Technology (HIT) at Shenzhen, China. Her research interests include computer vision and pattern recognition.

    Hong Liu received Bachelor degree in computer science in 1990, Master degree in computer science in 1993 and Doctor degree in electrical control and automation engineering in 1996, post-doctoral in computer science and technology in 1996. Professor Liu is currently the supervisor of doctoral students, the director of Research Department of Shenzhen Graduate School and director of Intelligent Robot Laboratory of Peking University. He is also an IEEE member, an executive director and vice secretary – Intelligent Automation Committee of Chinese Automation Association (IACAA). His expertise is in the areas of image processing and pattern recognition, intelligent robots and computer vision, intelligent micro-systems hardware and software co-design. He has published more than 100 papers in the important scholarly journals and international conferences, and access to subsidized Korean Academy of Jung-geun Awards, Department of Space Science and Technology Progress Award, and Peking University Teaching Excellence Award, Aetna award and candidates of Peking University Top Ten Teachers. He has done exchange visits in many famous universities and research institutions in several countries and regions, including the United States, Canada, France, the Netherlands, Japan, Korea, Singapore, Hong Kong and so on.

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