Elsevier

Neurocomputing

Volume 72, Issues 16–18, October 2009, Pages 3930-3934
Neurocomputing

Median MSD-based method for face recognition

https://doi.org/10.1016/j.neucom.2009.04.013Get rights and content

Abstract

An improved maximum scatter difference (MSD) criterion is proposed in this paper. A weakness of existing MSD model is that the class mean vector in the expressions of within-class scatter matrix and between-class scatter matrix is estimated by class sample average. Under the non-ideal conditions such as variations of expression, illumination, pose, and so on, there will be some outliers in the sample set, so the class sample average is not sufficient to provide an accurate estimate of the class mean using a few of given samples. As a result, the recognition performance of traditional MSD model will decrease. To address this problem, also to render MSD model rather robust, within-class median vector rather than within-class mean vector is used in the original MSD method. The results of experiments conducted on CAS-PEAL and FERET face database indicate the effectiveness of the proposed approach.

Introduction

Face recognition has been an important issue in image processing and pattern recognition over the last several decades. It plays an important role in many applications such as card identification, access control, mug shot searching, security monitoring and surveillance.

Much progress has been made towards recognizing faces under controlled conditions as described in [1], [2], [3], [4], [5]. Eigenfaces [6] method introduced by Turk and Pentland and linear discriminant analysis (LDA) [7] are two popular approaches used in face recognition. As we all know, eigenfaces is a effective method to represent the face image, while it is not the best method to be used to classify because this approach dose not make full use of classification information.

LDA has better recognition performance than eigenfaces due to the fact that its basic idea is trying to find optimal projection vectors by maximizing the ratio between between-class scatter matrix and within-class scatter matrix, which can be obtained by maximizing the Fisher discriminant criterion:J(w)=wTSbwwTSww

However, due to the high-dimensional and small sample size problem encountered in face recognition, the classical LDA cannot be used directly in that the within-class scatter matrix is always singular. To overcome this problem, some corresponding techniques were proposed [8], [9], [10], [11], [12]. A common weakness of all these methods is that the inverse matrix of within-class scatter matrix must be calculated when we use them, however. This is a complex procedure.

In addition, Song et al. [13] proposed a method, called maximum scatter difference (MSD), which adopts the difference of both between-class scatter and within-class scatter as discriminant criterion, due to the inverse matrix is need not constructed, so the small sample size problem occurred in traditional Fisher discriminant analysis is avoided in nature.

There is a important problem in applying MSD method should be mentioned, however. In the existing MSD models, class mean vector is always estimated by the class average. In small sample size problems such as face recognition, the class sample average is not sufficient to provide an accurate estimate of the class mean based on a few of given samples, particularly when there are outliers in the sample set (for example, the images with noise, occlusion, etc.) [14]. To address this problem, we apply the within-class median vector to estimate the class mean vector in MSD model. Thus, the median-based MSD model should be more robust than the current sample average based MSD models. We will demonstrate this by our experiments using two popular face databases such as CAS-PEAL and FERET.

The paper of the rest is organized as follows: Section 2 introduces the existing MSD model. Section 3 introduces the concept of median. Ours proposed method is introduced in Section 4. The last two sections give experiment results and conclusions.

Section snippets

Maximum scatter difference criterion

Suppose there are c known pattern classes, the between-class scatter matrix and within-class scatter matrix can be denoted asSb=1Mi=1cMi(mi-m0)(mi-m0)T,Sw=1Mi=1cj=1Mi(xij-mi)(xij-mi)T,where Mi is the number of training samples in class i and M the total number of training samples. xij denotes the jth training sample in class i, the mean vector of training samples in class i is denoted by mi and the mean vector of all training samples is m0.

From the classical LDA method, the samples can be

Concept of median [14]

In a finite list of numbers, the median is the middle value, so above and below which lie an equal number of values. This states that 12 of the population will have values less than or equal to the median and 12 of the population will have values equal to or greater than the median.

The first step we should take is to sort the list in increasing order when we find the median of a finite list of numbers. Subsequently, we pick the middle entry value if there are an odd number of observations.

Proposed method (median MSD)

The main idea of MSD is to make the distance between the within-class samples minimum, while that of between-class samples maximum, so all samples can be partitioned easily. This objective can be achieved by selecting optimal eigenvectors w1,w2,,wk corresponding to k largest eigenvalues of Sb-B·Sw.

As we all know, in existing MSD models, the definitions of Sw and Sb applies class mean matrix which is generally estimated by the class sample averages. Therefore, the role that class sample average

Experiment results

In this section, several experiments were designed to demonstrate the effectiveness of our proposed method. In order to show the recognition performance in an all-round way, we compare the proposed method with common MSD and other popular methods such as PCA and LDA .The first experiment is conducted on a subset of FERET database, and the second one is conducted on the CAS-PEAL database.

Conclusions

A novel feature extraction method, i.e., median maximum scatter difference is proposed in this paper. In MMSD method, the original within-class mean is substituted by within-class median. The within-class median not only preserves useful details in the sample images but also is robust to outliers that exist in training sample set, so the proposed method is more robust than common MSD. The experiments are conducted on two popular data sets (subsets of CAS-PEAL database and FERET database) with

Acknowledgment

This work is support by the National Science Foundation of China under Grant no.60574006.

Xiaodong Li was born in Shandong, PR China, 1974. He received his M.S. degree in Control Theory and Control Engineering from Qufu Normal University, PR China in 2004. He is currently pursuing the Ph.D. degree at College of Automation, Southeast University, China. The main research interests include pattern recognition and digital image processing.

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Xiaodong Li was born in Shandong, PR China, 1974. He received his M.S. degree in Control Theory and Control Engineering from Qufu Normal University, PR China in 2004. He is currently pursuing the Ph.D. degree at College of Automation, Southeast University, China. The main research interests include pattern recognition and digital image processing.

Shumin Fei received the M.S. degree in Mathematics from Anhui University in 1985. He received the Ph.D. of Engineering from Beijing University of Aeronautics and Astronautics in 1995. From 1995 to 1997, he did research work as a post doctoral in the automation institute of Southeast University. Now he is a professor in the College of Automation in Southeast University. His research interests are in the design and colligation of nonlinear control system, robust control, adaptive control, pattern recognition intelligence system.

Tao Zhang was born in Shandong, PR China, 1981. He received the B.S. and M.S. degree from Qingdao University of Science and Technology, PR China in 2002 and 2006, respectively. He is currently pursuing the Ph.D. degree at College of Automation, Southeast University. His main research interests include computer vision, pattern recognition and image processing.

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