2008 - Comparative Study of Dimension Reduction and Recognition Algorithms of DCT and 2DPCA

8/13/2019 2008 - Comparative Study of Dimension Reduction and Recognition Algorithms of DCT and 2DPCA

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Proceedings of the Seventh International Conference on Machine Learning and Cybernetics, Kunming, 12-15 July 2008

COMPARATIVE STUDY OF DIMENSION REDUCTION AND RECOGNITIONALGORITHMS OF DCT AND 2DPCA

BIN JIANG1, GUO-SHENG YANG

2, HUAN-LONG ZHANG

3

1Institute of Advanced Control and Intelligent Information Processing, Henan University, Kaifeng 475001, China2Information Engineering College,Central University for Nationalities, Beijing, 100081, China

3Department of Computer, Luoyang Institute of Science and Technology, Luoyang 471023, China

E-MAIL: [email protected],[email protected],[email protected]

Abstract:Based on the application of DCT discrete cosine

transformin the image compression, the feasibility of DCT tobe used in image feature dimension reduction is analyzed, and

the basic principle of the image feature dimension reduction

based on DCT is given in this paper. And then, taking the face

recognition and the facial expression recognition as the

research background, the theoretical analysis that DCT

algorithm has the higher recognition than 2DPCA

two-dimensional principal component analysis in the facerecognition and the facial expression recognition is given

under the condition that DCT and 2DPCA algorithms have

the approximate dimension reduction effect. At last, the

comparative simulation experiment is performed on DCT and2DPCA algorithms respectively by use of the AT&T face

database and JAFFE facial expression database.

Keywords:DCT; Image Compression; Feature Dimension Reduction;

Facial Recognition; Facial Expression Recognition

1. Introduction

In image pattern recognition, high dimension imagefeature always has heavy workload on computation andstorage, which exerts seriously negative effect on the real

time performance of the algorithm. So, image dimensionreduction is the key to solve the problem of image pattern

recognition. PCAPrincipal Component Analysisand

2DPCA are two common and useful approaches todimension reduction. They have obvious advantages indimension reduction, but it is to be further researched that

they have the same advantages in recognition.DCT is a common approach to image compression.

The nature of DCT is that much more information can bedenoted in less data by using DCT on image. The imagecompression is implemented in such the way so that thedestination of reducing data storage and speeding can beachieved. Viewing from this point, we can see there are

many similarities between the image compression andimage feature dimension reduction. It is based on this ideathat many researchers try to apply DCT in the image featuredimension reduction. Reference [1] expatiates the approachof face recognition based on DCT, reference [2] uses DCTto work on the local wavelet transform image, and achieve

the further feature extraction. The functions of DCTdecorrelation and dimension reduction are explained in bothreferences, but the basic principle of the image featuredimension reduction based on DCT is not given. It is in thereference [3] that the basic principle of the image featuredimension reduction based on DCT is given.

Based on above-mentioned, the paper explicit thebasic principal of feature dimension reduction by use ofDCT. And then taking the face recognition and facialexpression recognition as the research background, weanalyze DCT and 2DPCA algorithm of feature dimension

reduction theoretically, and get the reason why the twoalgorithms have different recognition rate under theapproximate level of feature dimension reduction. Finally,the simulation result shows the validation of theoreticalanalysis.

The paper is organized as follows: Section 2 gives the

principal of DCT feature dimension reduction. Section 3explains the reason why DCT and 2DPCA algorithms have

different recognition rate under the approximate level offeature dimension reduction. Section 4 gives thecomparative simulation result and some analysis. And theconclusion is given in Section 5.

2. Feature dimension reduction based on DCT

2.1. The basic principal of DCT image compression

Given that ( , )f m n represent an image with the size

of , be the coefficients obtained from the

two-dimension DCT of the image, then

N N ( , )C u v[4]:

978-1-4244-2096-4/08/$25.00 2008 IEEE

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1 1

0 0

( , ) { ( , ) ( ) ( )

cos[(2 1) 2 ]

cos[(2 1) 2 ]}

1 , 0( )

2 , 1, 2, .... 1

1 , 0( )

2 , 1, 2, .... 1

, 0,1, 2... 1

N N

m n

C u v f m n u v

m u N

m v N

N uu

N u N

N vv

N v N

u v N

= =

=

+

+ = = = = = =

=

(1)

From equation (1), it can be seen that the workload of

computing is increased as the image size is

increased. So in actual application, we use the approach ofimage blocking to divide the image matrix with size

of into

( , )C u v

N N )()( 2 NhhN image blocks

i (2)(,,2,1 hNi = ) with size of . DCT is

performed on each

hh

i, which results in:

'

i iD TM T= (2)

Where is the transform matrix derived

from equation (1), and the elements of are defined asfollows:

}{ kitTT =

T

1,2,1

1,,2,1,2

,0,1

=

=

==

Nk

NiN

iNtki

(3)

According to the requirement of image quality andcompression rate

[5], we can select the quantization matrix

which is performed on equation (2). The quantized matrixcontains many zero elements which represent noinformation. Accordingly, we can use a few non-zeroelements to represent an image to realize the image

compression.

2.2. The principal of feature dimension reduction based

on DCT

As usual, the coefficient matrix obtained from thetwo-dimension DCT of the image can be used to describeimage features well. If the coefficient matrix is directlyused as a feature matrix, the rank of the feature matrix is

same to the image dimension, which leads to the highdimension of the feature matrix. But there are many zeroelements in the DCT coefficient matrix, and the coefficients

are small when coordinates of and v are big.

Moreover, the bigger coefficients are located in the left-top

of DCT coefficient matrix where and are small

),( vuDi u

u v [6]. Sothe left-top corner is taken as the useful information area,

and an area template is used to pick up bigger

coefficients by the dot multiply of and .

A

A ),( vuDi

=

==

0000000

000000

0000000

0000001

000001

00001100111

)/(,,2,1, 2

A

hNiDAH ii

(4)

Let p elements in the left-top corner be 1 in the area

template , and the remains are set to be zero.A p isdetermined by the image compression ratio. Rearrange

these coefficients in the format of a vector to realize thefeature dimension reduction. Then

1 2[ , , ,0,0, 0]

i i i ipH h h h= (5)

where . Because the zero

elements dont have any meaning for image feature,

non-zero elements are selected to form a new

vector

),2,1(,0 pqhiq =

][ 21 ipiii hhhH = . We can align these

vectors iH from the top to down to form a feature

matrixHwith the size is .phN 2)/(

=

=

phNhN

p

PhNhN hh

hh

H

H

H

222

2 )/(1)/(

111

)/()/(

1

(6)

3. Comparative analysis

Face recognition based on PCA is a simple, fast andeffective algorithm. But this algorithm needs to transform

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two-dimensional face image matrix into one-dimensionalvector at first, then constructs covariance matrix. As to the

face image with size of , the covariance matrix

dimension is if PCA is used to pick up feature. It

is difficult to compute the covariance matrix because of the

high dimension. Although we can use Singular ValueDecomposition to solve it, we cant avoid constructingcovariance matrix. Reference [7] proposals a methodnamed 2DPCA. 2DPCA is a straightforward imageprojection technique which does not need to transform theface image into a one-dimension vector. Instead an image

covariance matrix is constructed directly using the originalimage matrices. Compared with the conventional PCA,2DPCA has two important advantages over PCA. First, it iseasier to evaluate the covariance matrix accurately. Second,the sample number of image has less influence on featureextraction.

*N N2 *N N2

From the analysis mentioned as above, it can be seenthat the sample number of image has influence on thefeature dimensions of PCA and 2DPCA to some differentextents. But the DCT feature dimension has relations only

with the image dimension and the compression ratiop , and

has no relation with the sample number of the image. Andmoreover, DCT has the excellent performance ofde-correlation.

DCT can save the image feature in low frequency, andget rid of the correlation of image feature to achieve the

feature dimension reduction. Image feature in lowfrequency represent the facial features, for example themost of face apparatus, which change slowly. So DCTalgorithm can reserve the most information of human face,which results in that DCT algorithm has the higher

recognition than 2DPCA in the face recognition under thecondition that DCT and 2DPCA algorithms have theapproximate dimension reduction effect. Also in facialexpression recognition, DCT has a better recognition rate.The reason is that: first, DCT performs a excellentdecorrelation [8], so we can distinguish facial expression

feature easily; second, the major facial expression featureareas are eyes and mouth. These areas are the major area ofDCT feature extraction.

4. Experiment result and analysis

Taking the face recognition and facial expressionrecognition as the research background, the comparativesimulation study of DCT and 2DPCA algorithms of featuredimension reduction and recognition is done by use of

AT&T face database and JAFFE database. In the simulation,the accumulative contributions ratio of 2DPCA is 90%, anearest neighbor classifier is used for classification. The

simulation environment is Matlab 7.0 which runs on thepersonal computer with ACER P4, 2.6GHz. The results ofsimulation experiment are as follows, shown from table 1 to

table 3.

Table 1 Comparison of DCT with 2DPCA in facerecognition

Method 2DPCA DCT

Size of Image 112*92 112*92

Size of Featurematrix

112*15 168*10

RecognitionRate

90% 92.86%

In Table 1, AT&T face database is used, 100 images of10 individuals (each person had 10 different images) areselected. The first 7 images of each person were used fortraining, and the remains were used for testing. The training

images were 70, and the testing images were 30.

Table 2 Comparison of DCT with 2DPCA in facialexpression recognition

Method 2DPCA DCT

Size of Image 124*124 124*124

Size of Featurematrix

124*17 156*10

Recognition

Rate 75.52% 79.30%

In Table 2, taking the facial expression recognition asthe research background, the comparative study of DCTand 2DPCA algorithms is done by using all 213 images of

10 individuals of the JAFFE Database. 70 images (includeall individuals) were used for training, and the remainswere used for testing. In order to remove the noise such asimage background or hairs, we follow the criterion ofreference [9] to cut the image by hand, and get the 124*124pure face images.

Table 3 Recognition accuracy of each facial expression

ExpressionMethod 2DPCA DCT

Angry 85% 85%

Disgust 73.68% 89.47%

Fear 72.73% 81.82%

Neutral 80% 95%

Sad 57.14% 57.14%

Table 3 shows the recognition ratios of the 5 facial

expressions including angry, disgust, fear, neutral and sad.From table 1 to table 3, we can see:

(1) From table 1 to table 2, we can see that DCT and2DPCA have the similar effect on feature dimensionreduction. The dimension reduction of DCT depends

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on the template size and the size ofp . When the sizeof template and p are fixed, the change of DCT

dimension is steady.(2) From table 1, it can be seen that the face recognition

ratio of 2DPCA is 90%, but the recognition ratio ofDCT is 92.86%, which is higher than 2DPCA. Fromtable 2, we find the facial expression recognition ratioof 2DPCA is 75.52%, and the recognition ratio of DCT

is 79.30%, which is also higher than 2DPCA. So, as awhole, DCT has higher recognition ratio than 2DPCA

in face recognition and facial expression recognition.(3) From table 3, it can be seen that DCT and 2DPCA have

the same recognition ratio for angry and sad expression,

but for the disgust, fear and neutral expression, DCThas higher recognition ratio than 2DPCA.

5. Conclusion

From theory and experiment, this paper analyzes thefeasibility of feature dimension reduction based on DCT.And taking the face recognition and facial expressionrecognition as the research background, two algorithms ofDCT and 2DPCA are studied. Compared to 2DPCA, DCTalgorithm has the higher recognition than 2DPCA in the

face recognition and the facial expression recognition underthe condition that DCT and 2DPCA algorithms have theapproximate dimension reduction effect. This has beendemonstrated by the simulation experiments. But DCTalgorithm of feature dimension reduction can be improvedin some aspects, for example, we can find different

templates to enhance the compression rate.

References

[1] Ning Fang, Jingzhi Li, and Guiming He, A FaceRecognition Based on DCT and Neural Network,

Computer Engineering, Vol 30, No.16, pp.53-54, Aug.2004.[2] Shufen Liang, Junning Gan, Face Recognition Based

on Local Wavelet Transform and Discrete Transform,Control&Automation, Vol 22, No.2, pp.206, 2006.

[3] Yankun Zhang, Chongqing Liu, Efficient facerecognition method based on DCT and LDA, Journalof Engineering and Electronics, Vol 15, No.2,pp.211-216, 2004.

[4] Rafael.C.Gonzalez, Digital Image Processing (secondedition), Publishing House of Electronics Industry,Beijing, 2004.

[5] K Cabeen, and P Gent, Image Compression and

Discrete Cosine Transform,http://online.redwoods.cc.ca.us/instruct/darnold/LAPR

OJ/Fall98/PKen/dct.pdf.[6] Jian Lu, and Hui Wang, Comparison between SVD

and DCT Feature Extraction Methods in FaceRecognition, Geomantics and Information Science ofWuhan University, Vol 30, No.2, pp.119, Feb.2006.

[7] Jian YangDavid ZhangAlejandro F Frangi et al.

Two- dimensional PCA A new approach to

appearance- based face representation andrecognition[J].IEEE Trans Patten Analysis and

Machine Intelligence2004261131-137.

[8] Syed Ali Khayam, The Discrete Cosine Transform

(DCT): Theory and Application,http://www.egr.msu.edu/waves/people/Ali_files/DCT_TR802.pdf

[9] Zhaoqi Bian, and Xuegong Zhang, PatternRecognition (second edition), Tsinghua University

Press, Beijing, 2000.

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