8/13/2019 2008 - Comparative Study of Dimension Reduction and Recognition Algorithms of DCT and 2DPCA
1/4
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
407
8/13/2019 2008 - Comparative Study of Dimension Reduction and Recognition Algorithms of DCT and 2DPCA
2/4
Proceedings of the Seventh International Conference on Machine Learning and Cybernetics, Kunming, 12-15 July 2008
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
408
8/13/2019 2008 - Comparative Study of Dimension Reduction and Recognition Algorithms of DCT and 2DPCA
3/4
Proceedings of the Seventh International Conference on Machine Learning and Cybernetics, Kunming, 12-15 July 2008
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
409
8/13/2019 2008 - Comparative Study of Dimension Reduction and Recognition Algorithms of DCT and 2DPCA
4/4
Proceedings of the Seventh International Conference on Machine Learning and Cybernetics, Kunming, 12-15 July 2008
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.
410