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Integrate the original face image and its mirror image for face recognition

Integrate the original face image and its mirror image for face recognition
Integrate the original face image and its mirror image for face recognition

Integrate the original face image and its mirror image

for face recognition

Yong Xu a,b,Xuelong Li c,n,Jian Yang d,David Zhang e

a Bio-Computing Research Center,Shenzhen Graduate School,Harbin Institute of Technology,Shenzhen518055,Guangdong,P.R.China

b Key Laboratory of Network Oriented Intelligent Computation,Shenzhen518055,Guangdong,P.R.China

c Center for OPTical IMagery Analysis an

d Learning(OPTIMAL),Stat

e Key Laboratory o

f Transient Optics and Photonics,Xi'an Institute of Optics and Precision

Mechanics,Chinese Academy of Sciences,Xi'an710119,Shaanxi,P.R.China

d Colleg

e o

f Computer Science and Technology,Nanjin

g University of Science and Technology,Nanjing,210094,China

e Biometrics Research Center,The Hong Kong Polytechnic University,Hong Kong

a r t i c l e i n f o

Article history:

Received3June2013

Received in revised form

21September2013

Accepted22October2013

Communicated by D.Zhang

Keywords:

Pattern recognition

Biometrics

Face recognition

Mirror image

Sparse representation

a b s t r a c t

The face almost always has an axis-symmetrical structure.However,as the face usually does not have an

absolutely frontal pose when it is imaged,the majority of face images are not symmetrical images.These

facts inspire us that the mirror image of the face image might be viewed as a representation of the face

with a possible pose opposite to that of the original face image.In this paper we propose a scheme to

produce the mirror image of the face and integrate the original face image and its mirror image for

representation-based face recognition.This scheme is simple and computationally ef?cient.Almost all

the representation-based classi?cation methods can be improved by this scheme.The underlying

rationales of the scheme are as follows:?rst,the use of the mirror image can somewhat overcome the

misalignment problem of the face image in face recognition.Second,it is able to somewhat eliminate the

side-effect of the variation of the pose and illumination of the original face image.The experiments show

that the proposed scheme can greatly improve the accuracy of the representation-based classi?cation

methods.The proposed scheme might be also helpful for improving other face recognition methods.

&2013Elsevier B.V.All rights reserved.

1.Introduction

As we know,the main challenges of face recognition are that

the face image might severely vary with the various poses,facial

expression and illumination[1–3].A face recognition method

greatly suffers from these challenges.In order to address these

challenges,people have made many efforts.For example,Jian et al.

proposed the illumination compensation method for face recogni-

tion[4].Sharma et al.proposed pose invariant virtual classi?ers

for face recognition[5].We also note that if the available training

samples of a face can suf?ciently show possible variations of the

pose,facial expression and illumination,it will be possible to

obtain a high accuracy.Unfortunately,in real-world applications

a face usually has only a very small number of training samples,

which cannot convey many variations of the face[6–10].In order

to overcome the problem that the training samples of a face do not

convey suf?cient variations of the face,previous literatures

have proposed some approaches to generate new(i.e.virtual or

synthesized)face images and to enlarge the size of the set of the

training samples.

It is known that both the facial structure and the facial expression

are symmetrical[11].Previous literatures have successfully exploited

the symmetrical structure of the face for face detection[11–14].

However,it should be pointed out that in real-world face recognition

applications,a large number of face images are not symmetrical

images due to non-frontal and non-neutral pose[15].Xu et al.

proposed an approach to generate“symmetrical”face images and

exploited both the original and“symmetrical”face images to

recognize the subject[15].As the“symmetrical”face image is

generated with the assumption that the facial structure is symme-

trical,it is an axis-symmetrical image.However,as shown later,the

“symmetrical”face images obtained in[15]is not a natural face

image and even appear to be strange.

A real-world face recognition application also often suffers

from the misalignment problem of the face image.This problem

certainly makes the face image not symmetrical and is advanta-

geous for correctly recognizing the face.Fig.3presented later

shows an example of misalignment of the face image.

It should be pointed out that though previous literatures have

made many efforts in making virtual or synthesized face images

which re?ect the variation of the face as much as possible,almost

Contents lists available at ScienceDirect

journal homepage:https://www.doczj.com/doc/4f5619375.html,/locate/neucom

Neurocomputing

0925-2312/$-see front matter&2013Elsevier B.V.All rights reserved.

https://www.doczj.com/doc/4f5619375.html,/10.1016/j.neucom.2013.10.025

n Corresponding author.

E-mail addresses:yongxu@https://www.doczj.com/doc/4f5619375.html,(Y.Xu),xuelong_li@https://www.doczj.com/doc/4f5619375.html,(X.Li),

csjianyang@https://www.doczj.com/doc/4f5619375.html,(J.Yang),csdzhang@https://www.doczj.com/doc/4f5619375.html,.hk(D.Zhang).

Neurocomputing?(????)???–???

no literature generated virtual or synthesized face images by exploiting the special nature of the face i.e.the symmetry of the structure.This motivates us to exploit the symmetrical structure of the face to improve previous face recognition methods.

In this paper,we propose a novel scheme to improve the face recognition method.The proposed scheme ?rst generates the mirror image of the original face image and then applies a representation-based classi ?cation (RBC)method to both the origi-nal face image and its mirror image to perform face recognition.We also refer to the mirror image of the original face image as face mirror image.The rationales of the proposed scheme are as follows:?rst,the face mirror image re ?ects some possible change in pose and illumination of the original face image.For example,if two original face images of a same subject have a left tilt pose and right tilt pose,then the difference between them will be great in terms of the distance metric.If these two face images from the same face are used as training and test samples,then the test sample will be hard to be correctly classi ?ed.The example shown in Fig.1clearly illustrates this.As a consequence,the face recognition method using only the original face images will be very hard to obtain satisfactory accuracy.However,the difference between either of the two original face images and the mirror image of the other original face image might be very little in terms of the distance metric.As a result,the use of the face mirror image will be very useful for correctly classifying the test sample.For detailed demonstration,refer to Section 5.Second,the face mirror image is very useful to overcome the possible misalignment problem of the original face image (for detail refer to Section 5).The results of various experi-ments on face recognition also show that the proposed scheme is quite feasible and can improve the state-of-the-art representation-based classi ?cation methods.

This paper has the following main contributions.First,it proposes the scheme to integrate the original face images and their mirror images for representation-based face recognition.It also describes the rationale of the proposed scheme.Second,it shows that a number of representation-based classi ?cation methods can be improved by using the proposed scheme.

The remainder of the paper is organized as follows.Section 2presents related works.Section 3presents representation based classi ?cation methods.Section 4describes our proposed scheme.Section 5describes the rationales of the proposed scheme.Section 6shows the experimental results and Section 7offers the conclusion.

2.Related works

Because our proposed scheme is based on representation-based classi ?cation (RBC)methods and the generated virtual face images,this section mainly reviews the literatures of generating virtual or synthesized face images and those literatures on RBC

methods.A number of previous works focus on generating virtual or synthesized face images and on enlarging the size of the set of the training samples.For example,Tang et al.[16]obtained “virtual ”facial expression by exploiting the prototype faces and optic ?ow.Jung et al.[17]obtained new samples of the face by using the noise.Thian et al.[18]used simple geometric transfor-mations to make virtual samples.Ryu et al.[19]exploited the distribution of the training samples to produce virtual training samples of the face.Sharma et al.[5]extended training samples by generating multiple virtual views of a person under different poses and illumination from a single face image.Beymer et al.[6]and Vetter et al.[7]also addressed this issue by generating new samples with virtual views.

Among a variety of face recognition methods,the representation-based classi ?cation (RBC)method can achieve a very high accuracy and has received much attention [20–23].The conventional RBC method is also referred to as sparse representation classi ?cation (SRC)method [20–22].RBC including SRC assumes that the test sample can be well represented by a linear combination of all the training samples.SRC obtains its solution using the constraint of the ?1norm minimization.In other words,SRC achieves its solution with the sparsity constraint which assumes that a number of the coef ?cients of the linear combination are equal or close to zeroes.We also say that SRC uses a sparse linear combination of all the training samples to represent the test sample.

Besides SRC,RBC can be also implemented by using the constraint of the ?2norm minimization [24–26].The corresponding method can be referred to as RBC with the ?2norm minimization constraint.It seems that the algorithm of RBC with the ?2norm minimization constraint is simpler and easier to implement than that of SRC.There are two kinds of RBC with the ?2norm minimization constraint.The ?rst kind exploits the training samples from all the classes to represent the test sample and uses the representation result to perform classi ?cation [24–26].The sparsity constraint is imposed on only a few methods of this kind.For example,the methods proposed by Shi et al.[23]and by Zhang et al.[25]have no sparsity constraint.In other words,these two methods do not require that the coef ?cients of the linear combination to represent the test sample are equal or close to zeroes.On the other hand,the sparsity constraint is imposed on the method proposed in [26]in a special way.The second kind exploits the training samples from each class to represent the test sample and the classi ?cation is also performed in terms of the representation result [27,28].The sparsity constraint is also not imposed on this kind of method.Specially,this kind of method usually assumes that the test sample can be respectively approximately represented by a linear combination of the training samples of every class and no any constraint sparsity is imposed on the coef ?cients of the linear combination.A typical example of this kind of method is linear regression classi ?cation (LRC)[27].The sparse representation has also been used to other problems such as sparse graph based image annotation [29],super-resolution reconstruction [30],image alignment [31]and image de-noising [32].The sparsity has also been used to modify discriminant analysis [33,34]and locality preserving projection [35,36].The sparse graph is also used in video semantic annotation [36]and representative image selection [37,38].For recent advances and more applications of RBC,refer to literatures [39–41].

3.Representation based classi ?cation (RBC)

In this section,we introduce representation based classi ?cation (RBC)brie ?y.Because LRC has a distinct characteristic,we describe it in Section 3.1and present other RBCs in Section 3.2.We assume that there are c classes and each class has n training samples in the form of column vectors.Let x 1;…;x N be all the N training samples in the form of column vectors (N ?cn ).Column vector x ei à1Tn t

k

Fig.1.An original face image with a left tilt pose (a)and another original face image right tilt pose (b)of a same subject.It is clear that these two face images have great difference in terms of the distance metric.

Y.Xu et al./Neurocomputing ?(????)???–???

2

(k ?1;…;n )stands for the k -th training sample of the i -th subject,i ?1,2,…,c .Let column vector z stand for the test sample.3.1.LRC [27]

In this subsection we present the algorithm of LRC as follows.LRC establishes an equation for each class.The equation of the i -th class is z ?X i A i

e1T

where A i ??a i 1…a i

n ,X i ??x ei à1Tn n t1…x i n n .The solution of Eq.(1)is obtained using

^A i ?eX T i X i Tà1X T i

z e2T

The deviation between the i -th class and the test sample is de ?ned

as d i ?J z àX i ^A i J .If k ?arg min i d i

,then the test sample is assigned to the k -th class.

3.2.Brief introduction to other RBCs

For the representation based classi ?cation methods,all the methods except for LRC ?rst exploit a linear combination of all the training samples to represent the test sample.

RBC with the ?2norm minimization constraint can be brie ?y described as follows.We ?rst take collaborative representation classi-?cation (CRC)as an example to show the basic characteristics of this kind of method.CRC assumes that Eq.(3)is approximately satis ?ed z ?XB

e3T

where B ??b 1…b N T ,X ??x 1…x N .The solution of Eq.(3)is usually obtained using ^B

?eX T X tμI Tà1X T z e4T

μis a small positive constant and I is the identity matrix.Let

^B ??^b 1…^b N

T .Of course,if X T X is not singular,the solution of Eq.(3)can be also obtained using

^B

?eX T X Tà1X T z e5T

CRC calculates the residual of the test sample with respect to the i -th

class using r i ?J z àX i ^B i J where X i ??x ei à1Tn n t1…x i n n and ^B i ??^b ei à1Tn n t1…^b i n n T .If k ?arg min i r i ,then CRC assigns the test

sample to the k -th class.

The main difference between CRC and the other RBCs with the ?2norm minimization constraint is that other RBCs might have extra constraints or steps.For example,the improvement to the nearest neighbor classi ?er (INNC)[42]has the same equation and solution scheme as CRC but uses a simpler classi ?er.The two-phase sparse representation (TPSR)method [24]has the same ?rst step as CRC but exploits an extra step to obtain a sparse linear combination of all the training samples to represent the test sample.

SRC,i.e.RBC with the ?1norm minimization constraint can be brie ?y described as follows.SRC attempts to solve the following problem:min B

J B J 1;

s :t :J z àXB J 2r ε

e6T

where ε40is a constant.SRC has no closed solution and should be iteratively solved.The original SRC algorithm is very computa-tionally inef ?cient and recently some ef ?cient algorithms for SRC have been proposed [43,44].

4.The proposed scheme

The main motivation of our proposed scheme is to use a simple way to obtain more training samples and to improve the face recognition accuracy.Though the used mirror image is simply

generated from the original face image,it also appears to be a

natural image and properly re ?ects possible variation of the original face image in pose and illumination.Moreover,the mirror image is also suf ?ciently different from the original face image in terms of the distance metric,so the use of the mirror image does enable the face recognition method to exploit more available information of the face.In this section we describe the proposed scheme in detail.The proposed scheme works as follows.It ?rst generates the mirror image of each original face image for training.It then exploits both the original face image of a face for training and the corresponding mirror image as training samples of this face.As a result,a face has 2n training samples in total.For the i -th face,we use y 0ei à1Tn tk ek ?1;…;n Tto denote the mirror image of original face image

x 0ei à1Tn tk ,respectively.x 0

ei à1Tn tk represents the original face image matrix corresponding to column vector x ei à1Tn tk .The algorithm of the proposed scheme can be presented as follows:

Step 1:Suppose that the original face image matrix has P rows

and Q columns.The mirror image of an original face image has the same size.For the i -th face,mirror image

y 0ei à1Tn tk ek ?1;…;n Tis generated using y 0

ei à1Tn tk ep ;q T?

x 0ei à1Tn tk ep ;Q àq t1T,p ?1,…,P ,q ?1,…,Q .x 0

ei à1Tn tk ep ;q Tand y 0ei à1Tn tk ep ;q Tdenote the pixels located in the p -th row and q -th column of x 0ei à1Tn tk and y 0ei à1Tn tk ,respec-tively.y 0ei à1Tn tk is then converted into a column vector and is denoted by y ei à1Tn tk .As all x ei à1Tn tk and y ei à1Tn tk act as training samples,we say that there are 2cn training samples in total.

Step 2:For the i -th face ei ?1;…;c T,let X i ??x ei à1Tn n t1…x i n n

y ei à1Tn t1…y i n n .Actually,X 1;…;X c are respectively the matrices consisting of all training samples including the original face images and mirror images of the ?rst to the i -th faces.x ei à1Tn n t1…x i n n and y ei à1Tn n t1…y i n n are all column vectors.c stands for the number of the faces i.e.number of the subjects.Then X is de ?ned as X ??X 1…X c .A RBC method (LRC or an ordinary RBC method)is applied to each test sample and corresponding training samples.For an ordinary RBC method,the equation on test sample

z is expressed as z ?XB and the solution is denoted by ^B

.If the applied method is LRC,then test sample z has c equations and the i -th equation is expressed as z ?X i A i .

Let ^A i denote the solution of z ?X i A i

.Step 3:For LRC,after solutions ^A 1;…;^A c are obtained,the devia-tion between the test sample and the i -th subject is

calculated using d i ?J z àX i ^A i J .If k ?arg min i d i

,then LRC assigns the test sample to the k -th class.For other

RBC methods,solution ^B

is a vector and has 2cn entries.It is clear that each entry of ^B

is associated with one column of X (i.e.one training sample).We refer to an entry of ^B as coef ?cient of the corresponding training sample.Let ^B

i be the vector consisting of 2n entries of ^B

i.e.the coef ?cients of x ei à1Tn n t1;…;x i n n ,y ei à1Tn n t1;…;y i n n .In other words,^B

i is associated with the i -th subject.The residual of the test sample with respect to the i -th class is calculated using

r i ?J z àX i ^B

i J .If j ?arg min i r i ,then test sample z is assigned to the j -th subject.

5.Rationales of the proposed scheme

5.1.Intuitive rationales of the proposed scheme

The proposed scheme has the following rationales:?rst,it is able to reduce the side-effect of the variation of the pose and

Y.Xu et al./Neurocomputing ?(????)???–???3

illumination of the original face image.Second,it can somewhat overcome the misalignment problem of the face image in face recognition.These rationales will be demonstrated in detail below.

We ?rst show an example in which the proposed scheme can somewhat overcome the misalignment problem of the face image.Fig.2shows photos of three faces with a homogeneous background from the SCface database [45,46].Fig.3shows test samples and training samples cropped from the photos shown in Fig.2as well as the mirror images of the training samples.They have the same size and are cropped from the same original photos.For the test and training samples in the same column,the face is the same but the test sample is a shift of the training sample.This means that there exists the misalignment problem of the face.We see from Table 1that the Euclidean distance between the original test and training samples of the same subject,referred to as original distance of the same subject,is relatively larger.However,as also shown in Table 1,the Euclidean distance between the test sample and the mirror image of the training sample of the same subject,referred to as mirror distance of the same subject,is smaller.For two face images x 0and y 0,we ?rst convert them into column vectors x and y and

calculate their Euclidean distance using

????????????????????????????

ex ày TT ex ày Tq .We also see

from Fig.3that for the same face the mirror image looks more similar with the test sample and will have a smaller distance from the test sample in comparison with the original training sample.This clearly illustrates that the use of the mirror image of the original face image is helpful for a “distance ”based classi ?er to correctly classify the test sample and is able to reduce the side-effect of the mis-alignment problem of the original face image.The following example shows that the proposed scheme can somewhat overcome the side-effect of the variation of the pose

of

Fig.2.Three photos with a homogeneous

background.

Fig.3.Test samples and training samples cropped from the photos shown in Fig.2as well as the mirror images of the training samples.The ?rst and second rows show the test samples and training samples,respectively.The third row shows the mirror images of the training samples.The images in the same column are generated from a same face.

Table 1

The original and mirror distances of the samples shown in Fig.3.Each sample has the size of 1400?1200.No.of the subject 123Original distance (?105) 1.97 2.01 2.23Mirror distance (?105)

1.91

1.95

1.95

Y.Xu et al./Neurocomputing ?(????)???–???

4

the original face image.Fig.4shows six test samples and six training samples from the SCface database [45,46]as well as the mirror images of these training samples.They have the same size but have different poses.Table 2shows the original and mirror distances of the same subject.We see that for the same face the mirror distance is greatly smaller than the original distance.This implies that the simultaneous use of both the original face image and the mirror image will enable us to more accurately classify the face image.

The following example shows that the proposed scheme can somewhat overcome the variation of the illumination of the original face image.Fig.5shows several test samples and training samples of the same face from the Yale B database shown in Section 6.3.They have the same size but different illuminations.For the test sample,the right face has stronger illumination than the left face.For the training sample,the right face has weaker illumination than the left face.Table 3shows the original and mirror distances on the samples shown in Fig.5.The mirror distance is also much smaller than the original distance.This again implies that the use of the mirror image is bene ?cial for correctly recognizing the face.

5.2.More analyses of the proposed scheme

In this section,we will give more interpretation of the pro-posed scheme.As we know,RBC exploits the deviation or residual of each class to classify the test sample.RBC assigns the test sample to the class with the minimum deviation or residual.The deviation and residual indeed somewhat re ?ect the ability,to well represent the test sample,of the training samples of a class.The smaller the deviation or residual is,the greater the ability to well represent the test sample the corresponding class has.

Fig.6shows the deviations between a test sample and all the classes of the ORL face database.The deviations obtained using both LRC and the improvement to LRC (i.e.the integration of our proposed scheme and LRC)are shown in Fig.6.This test sample is from the ?fth class.From Fig.6,we see that LRC will lead to erroneous classi ?cation of the test sample,since the correspond-ing deviation between the test sample and the ?fth class is not the smallest.However,the improvement to LRC will obtain the correct classi ?cation result,because the corresponding deviation between the test sample and the ?fth class is the smallest.Fig.6also implies that the improvement to LRC has stronger ability to represent the test sample than LRC.

Fig.7shows the deviations between a test sample and all the classes of the FERET face database.This test sample is from the nineteenth class.From Fig.7,we see that LRC will lead to erroneous classi ?cation for this test sample,but the improvement to LRC will obtain the correct classi ?cation result.Shan et al.[8]also exploited the mirror image of the face image in recognizing the face,but the performance of his method is associated with the size of the blocks generated from the original face image.

The rationale of the proposed scheme can also be presented from the viewpoint of numerical analysis.For simplicity of presentation,we just take LRC and the improvement to LRC as an example.Suppose that test sample is from the i -th class.As the improvement to LRC has more available training samples than LRC,it is easy to know that the deviation between the i -th class and the test sample obtained using the improvement to LRC is usually smaller than that obtained using LRC.

https://www.doczj.com/doc/4f5619375.html,parison of our scheme with the one proposed in [15]In this subsection,we show the difference between our scheme and the scheme proposed in [15].The scheme proposed in [15]is able to obtain a virtual axis-symmetrical face image.As shown in [15],these virtual face images can somewhat re ?ect possible variation in pose and scale of the face.However,the “symmetrical ”face images obtained in [15]have the following shortcoming:they are not natural face images and even appear to be strange.Figs.8and 9show some reasonable and unreasonable “symmetrical ”face images obtained in [15].From Fig.9,we see that unreasonable “symmetrical ”face images do appear not to be natural face

images.

Fig.4.Six test samples and six training samples from the SCface database as well as the mirror images of these training samples.The ?rst and second rows show six test samples and six training samples,respectively.The third row shows the mirror images of the six training samples shown in the second row.The images in the same column are generated from a same face.

Table 2

The original and mirror distances of the samples shown in Fig.4.Each sample has the size of 75?75.No.of the subject 123456Original distance (?103)9.948.338.728.619.908.82Mirror distance (?103)

4.05

6.62

3.57

4.08

4.47

4.01

Y.Xu et al./Neurocomputing ?(????)???–???5

For example,some unreasonable “symmetrical ”face images have a very big or small nose,which not only makes the “symmetrical ”face image far from the original true face image but also looks ugly.

Differing from the virtual face image obtained using the scheme proposed in [15],the virtual face image i.e.mirror image of the original face image generated from our scheme always looks like a true face image.Another difference between the scheme proposed in [15]and our scheme is as follows.The “symmetrical ”face images obtained in [15]indeed contains much redundant information,because it is a strictly axis-symmetrical face image,the left face of which is the mirror image of the right face.In other words,one half of the pixels in the “symmetrical ”face image seem to be redundant.However,the virtual face image generated from our scheme is not an axis-symmetrical face image and does not have the same kind of redundant information as the “symmetrical ”face images obtained in [15].In addition,because our scheme generates only one virtual face image for an original face image and the scheme proposed in [15]obtains two virtual face images for an original face image,our scheme is simpler and easier to implement.

6.Experimental results

6.1.Experiments on the FERET face database

We ?rst used a subset of the FERET face database to test our method.This subset consists of 1400images from 200subjects each providing seven images [47].This subset was composed of images whose names are marked with two-character strings:‘ba ’,‘bj ’,‘bk ’,‘be ’,‘bf ’,‘bd ’,and ‘bg ’.We resized each image to a 40?40image using the down-sampling algorithm.We took the ?rst 1,2,3and 4face images of each subject as original training samples and treated the remaining face images as test samples.Table 4shows the rates of classi ?cation errors of different methods.We see that our proposed scheme can improve LRC,CRC,SRC,INNC and coarse to ?ne k nearest neighbor classi ?er (CFKNNC)[48].Hereafter,the integrations of our proposed scheme and LRC,CRC,SRC,INNC as well as KNNC are referred to as the improvements

to

Fig.5.Six test samples and six training samples from the Yale B database as well as the mirror images of these training samples.The ?rst and second rows show six test samples and six training samples,respectively.The third row shows the mirror images of the six training samples shown in the second row.The images in the same column are generated from a same face.

Table 3

The original and mirror distances on the samples shown in Fig.5.No.of the column 123456Original distance (?104) 2.47 2.16 3.23 2.30 2.07 1.36Mirror distance (?104)

2.34

2.01

3.10

2.15

1.95

1.21

Fig.6.The deviations between a test sample and all the classes of the ORL face database.The deviations are obtained by using LRC and the improvement to LRC.The test sample is from the ?fth

class.

Fig.7.The deviations between a test sample and all the classes of the FERET face database.The deviations are obtained by using LRC and the improvement to LRC.The test sample is from the nineteenth class.

Y.Xu et al./Neurocomputing ?(????)???–???

6

Fig.8.Some original face images from the FERET face database and the corresponding “symmetrical ”face images.The ?rst row shows the original face images.The second and third rows respectively show the ?rst and second symmetrical face images,of the original face images,obtained using the scheme proposed in [15].Because these “symmetrical ”face images appear to be natural face images,we refer to them as reasonable “symmetrical ”face

images.

Fig.9.Some original training samples from the AR face database and the corresponding symmetrical face images.The ?rst row shows the original face images.The second Y.Xu et al./Neurocomputing ?(????)???–???7

LRC,CRC,SRC,INNC as well as KNNC,respectively.When each subject provided two training samples,the rates of classi?cation errors of LRC,CRC,INNC and CFKNNC are35.9%,41.6%,41.7%and 36.70%,respectively.However,the rates of classi?cation errors of the improvements to LRC,CRC,INNC and CFKNNC are22.4%,34.5%, 33.5%,and27.70%,respectively.When CFKNNC and improvement to CFKNNC were implemented,we set parameter n and K to n?N/4and K?1.N stands for the number of all the original training samples.K?1means that the nearest neighbor classi?cation is indeed performed.

6.2.Experiments on the ORL face database

The ORL database[49]includes400face images taken from40 subjects each providing10face images.For some subjects,the images were taken at different times,with varying lighting,facial expressions(open/closed eyes,smiling/not smiling),and facial details(glasses/no glasses).Each image was also resized to a56 by46image matrix by using the down-sampling algorithm.We took the?rst1,2,3and4face images of each subject as original training samples and treated the remaining face images as test samples.The experimental results were shown in Table5.We see again that proposed scheme can improve all the methods.

6.3.Experiments on the Yale B face database

In this subsection we use the Yale B[50]and the Extended Yale B[51]face databases to conduct experiments.There are10 subjects in the Yale B database,and28subjects in the extended Yale B database.Each subject has64images under different illumination conditions.The facial portion of each original image was cropped to a192?168image.We resized the cropped image to a96by84matrix.In order to computationally ef?ciently perform improvement to CFKNNC and CFKNNC,we did as follows. Before improvement to CFKNNC and CFKNNC were implemented, the face image was further resized to48by42.We took the?rst 16,20and24face images of each subject as original training samples and treated the remaining face images as test samples. Table6shows the rates of classi?cation errors(%)of different methods on the Yale B database.The experimental results show again that our proposed scheme can improve all the methods. 7.Conclusions

Our this paper clearly demonstrates that the mirror image of the face image can be exploited to simulate possible variation of the face image and is able to reduce the side-effect of the pose and illumination difference between the training and test samples of the same face.The proposed scheme can also overcome the misalignment problem of the face image,which usually reduces the accuracy of face recognition.The proposed scheme is very simple and computationally very ef?cient and improves RBCs at a low computational cost.The analyses and experimental results suf?ciently show the rationales of the proposed scheme.As the proposed scheme provides a good way to exploit the special nature of the face and is helpful for achieving better recognition results,it can be also applied to other face recognition methods. Acknowledgments

This paper is partially supported by the National Basic Research Program of China(973Program)(Grant no.2012CB316400),the National Natural Science Foundation of China(Grant nos.61370163, 61233011,61203376,61332011,and61125106),Shenzhen Municipal Science and Technology Innovation Council(Nos.JC201005260122A, JCYJ20120613153352732and CXZZ20120613141657279),and the Shaanxi Key Innovation Team of Science and Technology(Grant no.: 2012KCT-04).

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Yong Xu was born in Sichuan,China,in1972.He

received his B.S.degree and M.S.degree at Air Force

Institute of Meteorology(China)in1994and1997,

respectively.He then received his Ph.D.degree in

Pattern recognition and Intelligence System at the

Nanjing University of Science and Technology(NUST)

in2005.From May2005to April2007,he worked at

Shenzhen Graduate School,Harbin Institute of Tech-

nology(HIT)as a Postdoctoral Research Fellow.Now he

is an Associate Professor at Shenzhen graduate school,

HIT.His current interests include Pattern Recognition,

Biometrics,Image Processing and Video Analysis. Xuelong Li is a Full Professor with the Center for OPTical IMagery Analysis and Learning(OPTIMAL),State Key Laboratory of Transient Optics and Photonics,Xi'an Institute of Optics and Precision Mechanics,Chinese Academy of Sciences,Xi'an 710119,Shaanxi,P.R.

China.

Jian Yang received the B.S.degree in Mathematics from

the Xuzhou Normal University in1995,the M.S.degree

in Applied Mathematics from the Changsha Railway

University in1998and the Ph.D.degree in Computer

Science from the Nanjing University of Science and

Technology(NUST)in2002.He was a Postdoctoral

Researcher at the University of Zaragozain2003.From

2004to2006,he was a Postdoctoral Fellow in Depart-

ment of Hong Kong Polytechnic University.From2006

to2007,he was a Postdoctoral Fellow in Department of

Computer Science of New Jersey Institute of Technol-

ogy.From2007,he has been a Professor in the School of

Computer Science and Technology of NUST.He is the author of more than50scienti?c papers in Pattern Recognition,Computer Vision and the related areas.His journal papers have been cited more than1100times in the ISI Web of Science,and2400times in the Web of Scholar Google.Currently,he is an Associate Editor of Pattern Recognition Letters and IEEE Transactions on Neural

Networks.

David Zhang graduated in Computer Science from

Peking University.He received his M.Sc.in Computer

Science in1982and his Ph.D.in1985from the Harbin

Institute of Technology(HIT).From1986to1988he

was a Postdoctoral Fellow at Tsinghua University and

then an Associate Professor at the Academia Sinica,

Beijing.In1994he received his second Ph.D.in Elec-

trical and Computer Engineering from the University of

Waterloo,Ontario,Canada.Currently,he is a Chair

Professor at the Hong Kong Polytechnic University

where he is the Founding Director of the Biometrics

Technology Centre(UGC/CRC)supported by the Hong

Kong SAR Government in1998.He also serves as Visiting Chair Professor in Tsinghua University,and Adjunct Professor in Shanghai Jiao Tong University,Peking University,Harbin Institute of Technology,and the University of Waterloo.He is the Founder and Editor-in-Chief,International Journal of Image and Graphics(IJIG);Book Editor,Springer International Series on Biometrics(KISB);Organizer,the?rst International Conference on Biometrics Authentication(ICBA);Associate Editor of more than ten international journals including IEEE Transactions and Pattern Recognition;Technical Committee Chair of IEEE CIS and the author of more than10books and200journal papers.Professor Zhang is a Croucher Senior Research Fellow,Distinguished Speaker of the IEEE Computer Society,and a Fellow of both IEEE and IAPR.

Y.Xu et al./Neurocomputing?(????)???–???9

五年级上册成语解释及近义词反义词和造句大全.doc

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