Pattern Recognition Letters 31 (2010) 1453–1460

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Pattern Recognition Letters

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Improving face recognition by combination of natural and Gabor faces q

Christian Tenllado *, José Ignacio Gómez, Javier Setoain, Darío Mora, Manuel PrietoDpto. Arquitectura de Computadores y Automática, Universidad Complutense de Madrid, Avd. Complutense s/n, 28040 Madrid, Spain

a r t i c l e i n f o

Article history:Received 21 September 2009Available online 20 March 2010Communicated by H. Wechsler

Keywords:Face recognitionGabor image representationFace recognition grand challengeKernelGaborPCA

0167-8655/$ - see front matter � 2010 Elsevier B.V. Adoi:10.1016/j.patrec.2010.03.011

q This work has been partially supported by the4153065 and by the Spanish government through the2008/00508 and MEC Consolider Ingenio 2010 ESP00

* Corresponding author. Fax: +34 913944687.E-mail addresses: tenllado@dacya.ucm.es (C. Tenl

(J.I. Gómez), jsetoain@fdi.ucm.es (J. Setoain), dariompmatias@dacya.ucm.es (M. Prieto).

a b s t r a c t

Different approaches have been proposed over the last few years for improving holistic methods for facerecognition. Some of them include color processing, different face representations and image processingtechniques to increase robustness against illumination changes. One of the most successful strategies hasshown to be the use of Gabor representation of the images. There has been also some research about thecombination of different recognition methods, both at the feature and score levels. In this paper, we pro-pose an effective combination scheme that is able to improve a single holistic method by fusing the rec-ognition scores obtained from both natural face images and their Gabor representations. We haveevaluated this scheme using some of the best known holistic approaches in the context of the Face Rec-ognition Grand Challenge (FRGC). Results show at least 10% improvements in all cases. Moreover, thisscheme also works when the scores are obtained from two different methods whenever one of them usesnatural images and the other their Gabor representation. These results suggest that some complementa-riness exists between both representations, which can be easily exploited by fusion at the score level.

� 2010 Elsevier B.V. All rights reserved.

1. Introduction

Over the last few years, the increasing concern on security haspromoted research in different biometric technologies for humanidentity assessment. Among these techniques Face Recognitionhas captured the interest of both public and private institutionsdue to its non-intrusive nature, becoming a very active research to-pic (Chellappa et al., 1995; Zhao et al., 2003). For instance, auto-matic face recognition systems are currently being used to helphuman operators in border control facilities. These systems canaccomplish two different tasks: face recognition and face verifica-tion. In the former a face is analyzed to find out if the correspond-ing person is in the list of N previously known faces. In the latter,two new face pictures are analyzed to see whether they are fromthe same person or not. In this paper we focus on systems designedfor recognition or verification from 2D still images of frontal faces.

Most face recognition and verification algorithms are designedas classifiers. The classifier is trained on a set of face images takenfrom a database, looking for some discriminant features to repre-sent these faces. This training process is usually performed off-line.Once trained, the classifier can be used to enroll a new image pre-

ll rights reserved.

private contract UCM art83/research contracts CYCIT TIN

C-07-20811.

lado), jigomez@dacya.ucm.es.mora@fis.ucm.es (D. Mora),

sented to the system, i.e. to extract the discriminant features fromthe new face. Faces are then compared by their set of features.

The algorithms for feature extraction can be broadly classifiedinto holistic and local (also known as feature-based) methods(Zhao et al., 2003). Holistic methods use the whole face region asthe raw input to a recognition system. In general these systemsproject the faces onto a dimensional reduced space where recogni-tion is performed. Well known holistic techniques are Eigenfaces(Turk and Pentland, 1991) and Fisherfaces (Belhumeur et al.,1997). On the other hand, local methods try to recognize facesusing the information gathered from some well defined positions,like eyes, nose or mouth. Some examples of local methods are Elas-tic Bunch Graph Matching (Wiskott et al., 1997) and Hidden Mar-kov Models (Nefian and Hayes, 1998). There is still active researchon both holistic and local methods (Zhao et al., 2003; Tolba et al.,2005).

Since Daugman (1980), Daugman et al. (1985) show that theGabor wavelets model the receptive fields profiles of cortical sim-ple cells, this transform is being incorporated in all kind of com-puter vision algorithms. Indeed, it is at the heart of the ElasticBunch Graph Matching (Wiskott et al., 1997) and many variationsof well-known holistic methods (Liu and Wechsler, 2001, 2002;Liu, 2004, 2006). The Gabor transform analyzes the spatial fre-quency distribution of the texture on different scales, positionsand orientations. When fed into a holistic classifier, the featuresextracted differ from those extracted from natural faces, usuallypresenting better accuracy. However, it might also be possible thatsome information, relevant for verification, is lost when usingGabor faces.

1454 C. Tenllado et al. / Pattern Recognition Letters 31 (2010) 1453–1460

In this paper we study if the accuracy of representative holisticmethods can be improved by combining scores obtained from twoclassifiers, one of them trained on natural face images and theother on their Gabor representations. The proposed combinationscheme has been evaluated in the context of the Face RecognitionGrand Challenge (FRGC) (Phillips et al., 2005), which is one of themost relevant databases for face recognition from 2D still images.Our results show that the proposed fusion of scores improves theaccuracy of all the holistic methods under study.

The rest of the paper is organized as follows. Sections 2 and 3discuss the related work and provide some background on Gaborimage representation respectively. In Sections 4 and 5 we brieflyintroduce the holistic verification algorithms considered in ourwork, and the strategy used to combine the independent scores. Fi-nally, Sections 6 and 7 provide the evaluation, summarize our find-ings and give some hints about our future research.

Table 1Parameters selected for the Gabor wavelets for 128� 128 images.

kmax f r l m

p=2ffiffiffi2p

2p [0, . . . ,7] [0, . . . ,4]

2. Related work

The Gabor transform has been used to improve the accuracy ofmost holistic methods. In (Liu and Wechsler, 2001; Liu and Wechs-ler, 2002), Liu and Wechsler proposed a modification of the Eigen-faces (PCA) and Fisherfaces (LDA) methods using Gabor faces asinputs to these classifiers, showing around 30% improvements onthe FERET database. The same strategy was latter used by Liu onthe respective kernel versions Liu (2004), Liu (2006), showingone of the best performances in the FRGC.

A different holistic approach is KCFA, proposed by Xie et al.(2005,b). This method computes a 2D correlation filter for eachperson in the training set. On verification the new image is corre-lated with each filter and the center of the correlation planes aretaken as features to represent the face. This correlation can becomenon-linear using the kernel trick Xie et al. (2005). In this paper weslightly modify the original method by applying Gabor wavelets tothe input images.

The combination of different recognition systems has gainedincreasing attention in biometric research. Broadly speaking, thecombination can be applied at two different levels: fusion of fea-tures and fusion of scores. The former usually involves a selectionof the most discriminant features, which requires an additionaltraining stage. For instance Zhao et al. (2004) proposed a combina-tion of different feature extractors working on the same input inwhich the final score is determined by a Neural Network Commit-tee. Another interesting combination scheme is presented in (Tanand Triggs, 2007), where PCA-features of different representationsof the image (Gabor and LBP) are concatenated. Then, most dis-criminant features are extracted using Kernel Discriminative Com-mon Vectors (KDCV).

On the other hand, Jain et al. (2005) performed a deep study onthe alternatives of combining different biometric recognition sys-tems at the score level. For each identity verification, a globalmatching score is obtained by combining (addition, multiplication,min or max) the scores from the different biometric systems. Weshould remark that this scheme does not require any additionaltraining stage and is easier to generalize than the feature levelcounterpart. Good results are obtained when the information han-dled by the different systems is, at least partially, complementary.

In this paper we analyze the effects of combining scores ob-tained by two instances of the same face recognition method,one trained on natural images and the other on their Gabor repre-sentation, using the scheme that Jain proposed for multimodal sys-tems (Jain et al., 2005). Notice that we do not search for the mostdiscriminant features from the set of concatenated features; werather compute our score based on the combination of the individ-ual scores. The experimental results obtained on the FRGC data sets

show that this simple fusion scheme improves the accuracy of allthe holistic methods considered in this study.

3. Gabor face representation

The Gabor image representation is obtained by computing theconvolution of the original image with several Gabor wavelets,which can be defined as follows (Lee, 1996; Lades et al., 1993;Liu, 2006):

wl;mð~rÞ ¼k~kl;mk2

r2 e�k~kl;m �~rk2

2r2 ei~kl;m �~r � e�r22

h i; ð1Þ

where ~kl;m ¼ kmðcos/l; sin/lÞ and ~r ¼ ðx; yÞ. For image representa-tion it shows to be effective to select wavelets spaced logarithmi-cally in the frequency domain (Lades et al., 1993). For thispurpose it is convenient to express km ¼ kmax

f m and /l ¼ pl=8, wherekmax is the maximum frequency, and f is the spacing factor betweenkernels in the frequency domain. The choice of these parametersdepends on both the number of samples of the images to be pro-cessed and the discrete frequencies we want to consider. Table 1shows an effective set for 128� 128 images Lades et al. (1993).

Let Iðx; yÞ be the gray-level distribution of an image, the convo-lution of image I and a Gabor kernel wl;m is defined as follows:

Ol;mðx; yÞ ¼ Iðx; yÞ � wl;mðx; yÞ; ð2Þ

where � denotes the convolution operator, and Ol;mðx; yÞ is the con-volution result corresponding to the Gabor kernel at orientation land scale m. Although this representation is complex valued, weonly use the complex modulus, which has shown a better behaviourin the presence of edges (Lades et al., 1993). In addition, we downs-ample each Ol;mðx; yÞ by a factor q ¼ 64 (a factor 8 by both rows andcolumns) so that the final dimension does not exceed that of theoriginal images.

Let OðqÞl;mðx; yÞ represent the column vector obtained by down-sampling Ol;mðx; yÞ by a factor q, concatenating each row to forma column vector and normalizing the result to zero mean and unitvariance. Then the final Gabor representation of the image I is,

X ¼ OðqÞ0;0

t;OðqÞ0;1

t; . . . ;OðqÞ4;7

t� �tð3Þ

where t is the transpose operator. The augmented Gabor featurevector thus encompasses all the elements (downsampled and nor-malized) of the Gabor wavelet representation set, S ¼ fOl;mðx; yÞ :

l 2 f0; . . . ;7g; m 2 f0; . . . ;4gg, as important discriminating informa-tion. As an example, for 128 � 128 pixels images the size of this vec-tor is 10240 (40 � 16 � 16).

4. Verification algorithms

Fig. 1 represents a block diagram of a typical holistic recognitionor verification system. Assuming preprocessed images, a trainingdatabase is used to design a classifier which is used as featureextractor. This process is performed off-line. Then, when twonew images are presented to the system for verification (on-line),their features are extracted and a distance between their featurevectors is measured. The verification result is obtained by thres-holding this distance based on the desired False Acceptance Rate(FAR) for the system. Commonly used similarity measures includeManhattan ðL1Þ, Euclidean ðL2Þ, cosine ðdcosÞ and the MahalanobisðdMdÞ distances.

In this paper we have considered four representative featureextractors: PCA, LDA, KDA and KCFA, which are described in moredetail in the rest of this section. In all cases we consider an imageas a two-dimensional array of N intensity values. When conve-nient, the image is interpreted as a vector Xi in RN by row-wisescanning the array. We assume a training set Xi 2 RN : i ¼0; . . . ;M � 1, that can be classified in classes xk : k ¼ 0; . . . ; L� 1(images from L different individuals). We denote by Mk the numberof images for class xk.

4.1. Principal Component Analysis

Principal Component Analysis (PCA) uses the eigenvectors ofthe covariance matrix as projection directions for feature extrac-tion. The covariance is estimated from the training set. Formally:

S ¼ 1M � 1

XM�1

i¼0

ðXi � lÞðXi � lÞT ; ð4Þ

where l ¼ 1M

PMi¼1Xi. Let U ¼ ½U0;U1; . . . ;Ur�1� be the matrix with the

r eigenvectors of S with largest eigenvalues as columns. The corre-sponding PCA-based features F for a new test image Y are computedby projecting it onto the eigenface space:

F ¼ UT Y: ð5Þ

4.2. Linear Discriminant Analysis

The PCA method described above is unsupervised, in the sensethat no information is given to the algorithm to classify the images.The Linear Discriminant Analysis (LDA), also known as Fisher Lin-ear Discriminant (FLD), uses previous knowledge about correctclassification to find out the directions that maximize the ratio of

the between-class scatter matrix and the within-class scatter ma-trix. These directions are then used for projection in order to ex-tract features for a new image.

The between-class scatter matrix for the training set is:

SB ¼XL�1

k¼0

Mkðlk � lÞðlk � lÞT ; ð6Þ

while the within-class scatter matrix is:

SW ¼XL�1

k¼0

XXi2xk

ðXi � lkÞðXi � lkÞT ; ð7Þ

where again l ¼ 1M

PMi¼1Xi is the mean image of the whole training

set and lk ¼ 1Mk

PXi2xk Xi is the mean image of the kth class.

The LDA method seeks for the L� 1 directions v that maximizethe relation:

J ¼ vT SBvvT SWv : ð8Þ

It is well known that the directions v that maximize J are the solu-tions to the following generalized eigenproblem:

SBv ¼ kS B

1456 C. Tenllado et al. / Pattern Recognition Letters 31 (2010) 1453–1460

among faces might be non-linear. The Kernel Discriminant Analysis(KDA) exploits the kernel trick to obtain a non-linear version of theLDA.

Let /ðXÞ : RN ! F be a non-linear mapping from the inputspace to a high dimensional feature space F . The KDA uses as pro-jection vectors the solutions to Eq. (9) in F , thus using:

SB ¼XL�1

k¼0

Mk l/k � l/

� �l/

k � l/� �T

; ð11Þ

SW ¼XL�1

k¼0

XXi2xk

/ðXiÞ � l/k

� �/ðXiÞ � l/

k

� �T; ð12Þ

where l/k ¼ 1=Mk

PXi2xk /ðXiÞ and l/ ¼ 1=M

PM�1i¼0 /ðXiÞ, are the

means for each class and the global mean in F .To simplify the equations, let for the moment assume that data

are centered in Fðl/ ¼ 0Þ, and define the matrix:

D ¼ ½/ðX0Þ;/ðX1Þ; . . . ;/ðXM�1Þ�: ð13Þ

Then, using D we can express Eqs. (11) and (12) as (He et al., 2005):

SB ¼ �DðI�WÞDT þ DDT ; ð14ÞSW ¼ DðI�WÞDT ; ð15Þ

where I is the M �M identity matrix and W 2 RM�M is the blockdiagonal matrix W ¼ diagfW0;W1; . . . ;WL�1g, with Wk 2 RMk�Mk , aMk �Mk matrix with elements all equal to 1=Mk.

Plugging Eqs. (14) and (15) in (9) we obtain:

DðI�WÞDTv ¼ k0DDTv; ð16Þ

where k0 ¼ 1=ð1þ kÞ. From the theory of reproducing kernels, thesolutions to (16) must lie in the span of the images in F :

v ¼XM�1

i¼0

ci/ðXiÞ ¼ Da; ð17Þ

where a ¼ ½c0; c1; . . . ; cM�1�T 2 RM . Replacing v in (16) with thisexpression and multiplying from the left by DT we get:

KðI�WÞKa ¼ k0KKa; ð18Þ

where K ¼ DT D is the kernel matrix of the training data:

Kij ¼ /ðXiÞ � /ðXjÞ: ð19Þ

Notice that, using the kernel trick, we never perform the explicitmapping /, as it only appears in our equations as dot products,which can be computed using the associated kernel function onthe original data: Kij ¼ kðXi;XjÞ.

If the original data are not centered in F the above equationsare valid on the following transformed data:bD ¼ ½/ðX0Þ � l/;/ðX1Þ � l/; . . . ;/ðXM�1Þ � l/� ð20Þ

transforming Eqs. (17) and (18) into:

v ¼XM�1

i¼0

cið/ðXiÞ � l/Þ ¼ bDa ¼ Dð1� 1MÞa; ð21Þ

bK ðI�WÞbK Ta ¼ k0 bK bK Ta; ð22Þ

where bK ¼ ðI� IMÞKðI� IMÞ is the kernel matrix of the originalimages centered in F , with IM 2 RM�M being a matrix with all ele-ments equal to 1=M.

Finally, Eq. (22) may be rewritten as:bK W bK Ta ¼ k00 bK bK Ta; ð23Þ

with k00 ¼ 1� k0 ¼ k=ð1þ kÞ. The solutions to (23) with largest k00

correspond to the solutions in F to (9) with largest k.Let A ¼ ½a0;a1; . . . ;an�1� 2 RM�n be the matrix with the

n : n 6 L� 1 solutions to (23) with largest eigenvalues, normalized

such that kvk2 ¼ abKat ¼ 1. To extract the features for a set of testimages Yj : j ¼ 0; . . . ; t � 1, we must project them onto the eigen-vectors v in F :

Fj ¼Xn�1

i¼0

v i � ð/ðYjÞ � l/Þ: ð24Þ

Defining Dtest ¼ ½/ðY0Þ;/ðY1Þ; . . . ;/ðYt�1Þ�, the feature matrix asF ¼ ½F0; F1; . . . ; Ft�1� and using Eq. (24) we arrive at:

F ¼ ATðKtest � IMKtest � KIM þ IMKIMÞ ¼ AT bK test; ð25Þ

where Ktest ¼ DT Dtest 2 RM�t is the test kernel matrix whose ele-ments are Ktestði; jÞ ¼ /ðXiÞ � /ðYjÞ, and bK test the corresponding cen-tered version.

In Face recognition there is usually a problem with Eq. (23). Itcan be shown that the rank of bK ðI�WÞbK is at most N � L (Heet al., 2005). Typically the number of images M is much lower thanthe number of pixels of the images N making bK ðI�WÞbK a singularmatrix. There are two common ways to tackle this problem: to adda regularization factor (Liu, 2006) or to perform a previous dimen-sionality reduction using PCA (Belhumeur et al., 1997). In this pa-per we use the former.

4.4. Kernel correlation feature analysis

The last holistic method considered in our work is the KernelCorrelation Feature Analysis (KCFA) (Xie et al., 2005). This methodproposes to design an Optimal Tradeoff Filter (OTF) (Refregier,1990) for each class in the training set. When a new image is pre-sented to the system it is correlated with all the filters, taking thecenters of the output correlation planes as the features for the newimage. In KCFA the correlation is performed in a high dimensionalfeature space F using the kernel trick.

The design of the OTF is performed in the frequency domain.This filter provides an optimal trade-off between the minimizationof the correlation output noise and the minimization of the averagecorrelation energy (Refregier, 1990). Defining D ¼

PM�1i¼0 Di, where

Di is a diagonal matrix whose elements Diðk; kÞ contain the powerspectra of Xi at frequency k;C as the diagonal matrix whose ele-ments Cðk; kÞ represent the noise power spectral density at fre-quency k and finally T as T ¼ aDþ bC, with 0 6 a; b 6 1; the OTFfor a given class is obtained as Xie et al. (2005), Refregier (1990):

hOTF ¼ T�1XðXþT�1XÞ�1c�; ð26Þ

where X ¼ ½X0;X1; . . . ;XM�1� is a N �M matrix, each X i is a Ndimensional vector constructed by row scanning the 2D Fouriertransform of i-th training image, and c� is a M � 1 column matrixwith elements ci equal to one if image i is in the class and zerootherwise.

Assuming that images are geometrically centered and normal-ized, the center of the correlation plain for a test image Y, with Fou-rier transform Y, correlated with the filter in Eq. (26), can bereplaced by the inner product:

cð0; 0Þ ¼ YþhOTF ¼ YþT�1XðXþT�1XÞ�1c�: ð27Þ

Since T is a diagonal matrix, it can be decomposed asT�1 ¼ T�1=2T�1=2, and (27) can be rewritten as:

cð0; 0Þ ¼ ðT�1=2YÞþðT�1=2XÞððT�1=2XÞþðT�1=2XÞÞ�1c�: ð28Þ

Eq. (28) shows that T�1=2 can be considered as a pre-filter for theimages. Denoting bX ¼ T�1=2X we can rewrite it as:

cð0; 0Þ ¼ bYþbXðbXþbXÞ�1c�: ð29Þ

As in the case of the KDA, let /ðXÞ : CN ! F be a non-linear map-ping from the frequency domain of the input space to a high dimen-sional feature space F . Eq. (29) on the transformed data is:

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

10-3 10-2 10-1 100

VR

FAR

KDA+LDA

LDAKDA

KDA+LDA

benefits of score fusion from different recognition methodologiesincrease when one of the systems is trained on natural face imageswhile the other is trained on their Gabor representations.

These results suggest that the holistic methods trained on nat-ural images find different discriminant information than whentrained on Gabor images; and by fusing the scores from the indi-vidual systems we can take advantage of all this information.

7. Conclusions

In this paper we have shown the benefits of combining, at thescore level, different holistic face recognition methods. More pre-cisely, we train two instances of the same method, one on naturalimages and the other on their Gabor representations, and finallycombine their individual scores. This novel analysis has been per-formed evaluating FRGC experiments for four representative holis-tic methods: PCA, LDA, KDA and KCFA. In all cases the score fusionhas provided around 10% improvements for a FAR of 0.001. Thiswork is also the first attempt to use KCFA on Gabor faces, for whichwe had to slightly modify the original method. In addition, weshow that the benefits of the proposed combination scheme persistacross methods, i.e. when scores from different methods are com-bined, one trained on natural images and the other on their Gaborrepresentations. These results suggest that there is some discrimi-nant information in the natural images that cannot be exploited bythe holistic methods studied in this work when Gabor transform isapplied; and that combining the score with a holistic methodtrained on natural images is a convenient way to exploit at leastpart of that information.

In future work we will extend this work including also localmethods and different combination strategies, both at the score

and the feature level. However, combination at the feature levelmay imply two training stages, one to train the feature extractionprocesses and other to train the fusion, increasing the difficulty tofind out a general combination strategy to improve recognitionperformance. The same situation appears if more complex score-fusion schemes are to be applied. For instance a neural networkcould be trained on the score space, requiring an additional train-ing set. The simplicity of the score-fusion scheme presented in thispaper highlights the relevance of our results.

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