50120130406014

International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-6367(Print),

ISSN 0976 - 6375(Online), Volume 4, Issue 6, November - December (2013), © IAEME

127

A TWO PHASE ALGORITHM FOR FACE RECOGNITION IN FREQUENCY

DOMAIN

Ms Archana H. Sable, Dr. Girish V. Chowdhary

School of Computational Sciences,

Swami Ramanand Teerth Marathwada University, Nanded(M.S.),India

ABSTRACT

Various changes in illumination, expression, viewpoint, and plane rotation present challenges

to face recognition. Low dimensional feature representation with enhanced discrimination power is

of paramount importance to face recognition system. In this paper, we propose a two-phase

algorithm for face recognition method in frequency domain using discrete cosine transform (DCT)

and discrete Fourier transform (DFT). The absolute values of DCT coefficients or DFT amplitude

spectrums are used to represent the face image, i.e. the transformed image. Then a two-phase face

classification method is applied to the transformed images. The algorithm works in two phases: its

first phase uses the Euclidean distance formula to calculate the distance between a test sample and

each sample in the training sets, and then exploits the Euclidean distance of each training sample to

determine K nearest neighbors for the test sample. Its second phase represents the test sample as a

linear combination of the determined K nearest neighbors and uses the representation result to

perform classification. The experimental results using FERET, ORL(case-I), and ORL(case-II)

databases are also presented and compared the two-phase face recognition method based on space

domain of face images.

Keyword: Face Recognition, DCT, DFT.

1. INTRODUCTION

Face recognition technology has a variety of potential applications such as security access

control, personal identification to human-computer communication, intelligent human machine

interface, and so on. In the last few years, a number of face recognition and speech recognition

methods have been proposed using transform domain such as principal component analysis(PCA)

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[1],[2],[3],[4], linear discriminant analysis(LDA) [5][6], locality preserving projection (LPP) [7], [8],

DCT[9], DFT[10] and discrete wavelet transforms(DWT) [11], [12].

A good many of DCT-based and DFT-based face recognition methods have been proposed.

In [13], Jiang et al. investigated that a certain number of DCT coefficients are removed, the

corresponding facial image description by the remaining DCT coefficients are robust to lighting

changes and scale variations. Such good properties would be very useful for applications of face

recognition, video object tracking, object segmentation and visual content processing. In general,

there are two kinds of face recognition methods based on DCT and DFT. One only uses part of DCT

coefficients or DFT amplitude spectrums for face recognition. For example, Sanderson et al.[14]

used the DCT coefficients of neighboring blocks to generate an efficient feature for face recognition.

Ghanbari [17] proposed an efficient feature extraction method based on DCT pyramid for face

recognition. And the other based on DCT and DFT face recognition methods is holistic and uses all

features of DCT or DFT to perform classification. For instance, Er. et al. [15] demonstrated an

efficient method for high-speed face recognition based on DCT and radial basis function (RBF)

neural networks. In [16], they presented a technique for recognition of frontal human faces on gray

scale images. In this technique, the distance between the DCT of the face under evaluation and all

the DCTs of the faces database are computed. Jadhao.et at[18] used Radon transform and Fourier

transform for face recognition on ORL database and achieved a good performance. Furthermore,

more face recognition algorithms focusing on selection of efficient features from DFT or DCT can

be found in [19], [20], [21], [22], [23]. Specifically, 3D face recognition techniques based on 3D-

DCT features and 3D frequency-domain representation can be found in [24], [25],[26]. Theoretically,

transform-based approaches have a number of practical advantages. First, they have been proven to

be very efficient with face images of different features and illumination. Second, they have been

proven to be good with face images of different scales, poses and rotated images. Third, they may be

more efficient than in the pixel domain.

Recently, a method that addresses classification problems from a novel viewpoint has been

proposed. This method uses a two-phase test sample representation method to perform face

recognition [27]. In this method, the first phase represents a test sample as a linear combination of all

the training samples, and exploits the representation ability of each training sample to determine the

K nearest neighbors for the test sample. The second phase represents the test sample as a linear

combination of all the K nearest neighbors and uses the representation result to perform

classification. We note that the above method is a successful 2 norms based sparse representation

method. Though it obtains a very high accuracy, it is computationally more efficient than the naïve 1

norm-based sparse representation method proposed in[28]. Moreover, the 2 norms based sparse

representation methods not only can perform well in face recognition [29], [30], [31], [32], but also

achieve a good performance in palm print recognition [33] and bimodal biometrics [34].

Furthermore, the 2 norms based sparse representation methods have been extended into the feature

space [35].

The method proposed in this paper is holistic and uses all the DCT coefficients or the DFT

amplitude spectrums to generate the transformed images. Firstly, we apply the Euclidean distance

formula to measure the distance between a test sample and each sample in the training sets, and then

exploit the Euclidean distance of each training sample to determine K nearest neighbors for the test

sample. Then, we represent the test sample as a linear combination of the determined K nearest

neighbors and use the representation result to perform classification. In addition, we use various

numbers of DCT coefficients and DFT amplitude spectrums to test the effect on performance of our

algorithms. The experimental results demonstrate that our proposed algorithms are very competitive.



129

This paper is organized as follows. Section 2 describes the structure of the proposed method

for face recognition. Experimental results are presented and discussed in Section 3. Finally,

conclusions are drawn in Section 4.

2. THE PROPOSED ALGORITHM

The proposed method is divided into four stages: feature selection, the first phase of test

sample representation, the second phase of test sample representation and classification.

In feature selection stage, all the samples are converted into feature matrices by implying

DCT or DFT. Then, we extract the absolute values of DCT coefficients or DFT amplitude spectrums.

Furthermore, we convert each feature matrix into a matrix with the same size as the matrices of the

original images, which formed transformed images.

a b

Fig.1. Result of DCT on a sample from the ORL database

(a) original image, (b) DCT image

Fig.2. Result of DFT on a sample from the ORL database

(a) original image, (b) DFT image.

Figs.1 and 2 show the application of the DCT and DFT on one of the face images obtained

from the ORL database. Fig.1.a and Fig.2.a display the original image. Fig.1.b and Fig.2.b display

the result of applying the DCT and DFT on the original image, respectively.

In the following sections, we assume that there are L classes and n training samples x1,…, xn.

If a sample is from the j th class j =1,2,…,L, we take j as the class label of the training sample. In the

first phase of the test sample representation, first of all, we use the Euclidean distance formula to

measure the distance between a test sample and all the training samples. The Euclidean formula for

distance in d dimensions is:

(1)

Where, a andb are the column vectors of samples.

Secondly, the Euclidean distance between a test sample y and the i th training sample will be

D( y, xi)(i=1,…, n) . A smaller D( y, xi) means that the i th training sample is more similar to the test

sample than other training samples, and which has a great contribution in representing the test

sample. Furthermore, we exploit D( y, xi)(i=1,…, n) to identify the K training samples that have the

K minimal distances, and denote them by x1…,xk . The test sample can be represented by x1…,xk. And

these samples are considered as the K nearest neighbors of the test sample. In addition, let

( ) ( )

−∑

=

=d

nnn

baD ba1

2.

2/1



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C ={ c1…,cd}, a set of some numbers, stand for the set of class labels of the K nearest neighbors. C

are one subset of set={ 1,…,L}In the second phase of the test sample representation, firstly, we

represent the test sample as a linear combination of the determined K nearest neighbors.

Accordingly, we assume that the following equation is approximately satisfied:

(2)

Where ~

ix (i=1,..,K) are the identified K nearest neighbors, and bi (i=1,…,K) are the coefficients.

Equation (2) shows that the K nearest neighbors of test sample makes their own contribution to

representing the test sample, which are the best representing of the test sample. If the dimensions of ~

ix (i=1,..,K) are d , the time complexity of Equation (2) will be O(d3 ) . Secondly, according to the

neighbors might be from different classes, all the neighbors from the r th ( r єc ) class are ~~

,..., ts xx ,

then the sum of the contributions to represent the test sample of the r th class will be

(3)

In classification stage, first, we convert a test image into a transformed image ty by using the

features selection method, and then we calculate the deviation of gr from ty by using

(4)

A smaller deviation Dr means a greater contribution to representing the test sample. Thus, we

classify ty into the class that produces the smallest deviation.

As a result, we use the Euclidean distance formula instead of the linear combination to

determine the K nearest neighbors of the test sample in the first stage. Thus, our proposed algorithms

have a lower time complexity than TPTSR.

3. EXPERIMENTAL RESULTS

In order to test the efficiency of our algorithms presented above, we perform a series of

experiments using the ORL [36] and the FERET [37], [38] face databases. The ORL face database

contains 400 images of 40 persons (10 images per person). The resolution of ORL images is 46×56.

The FERET face database contains 1400 images of 200 persons (7 images per person). The

resolution of FERET images is 40×40. Both of these databases, the images that belong to the same

person usually present variations in expression and illumination. Sample images from the two

databases are displayed in Figs 3 and 4.

Fig.3. Some Face Images of a Person from the ORL Database

~~

... ttssr xbxbg ++=

crgtD ryr ∈−= ,|||| 2

~~

11 ... KK xbxby ++=



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Fig.4 Some Face Images of a Person from the FERET Database

If s samples of the n samples per class are used for training and the remaining samples are

used for testing, there are

possible combinations. As a result, there are s

nC training sets and s

nC test sets. For the ORL database,

we test different algorithms in two cases. In the first case, we use five images of each person as the

training samples and there are 252 training and test sample sets. In the second case, we use six

images of each person as the training samples and there are 210 training and test sample sets. For the

FERET database, we use four images of each person as the training samples and take the remaining

images as test samples. As a result, we test different methods by using 35 training and test sample

sets from the FERET database. When implementing our method, we solve B by using

YXIXXBTT ~

)~~ 1−

+= γ . In order to eliminate the influence of the negative values, we use the absolute

values of DCT coefficients or DFT amplitude spectrums. Beyond that, γ is set to 0.001.

3.1 Performance comparison This section compares our proposed algorithms performances, including the two-phase test

sample representation method based on DCT (TPTSR-DCT), the two-phase test sample

representation method based on DFT (TPTSR-DFT), two-phase face recognition method based on

DCT (TPFR-DCT), two-phase face recognition method based on DFT (TPFR-DFT), with four

existing algorithms, namely, TPTSR[27], SRC[28], PCA, LDA. The algorithms of TPTSR-DCT and

TPTSR-DFT use the linear combination of training samples to determine K neighbors. The

algorithms of TPFR-DCT and TPFR-DFT use the Euclidean distance between the test sample and

the training samples to determine the K neighbors.

Fig.5 Means of the rates of the classification errors (%) of our algorithms (TPTSR-DCT,TPFR-DCT,

TPTSR-DFT, TPFR-DFT), TPTSR on the ORL face database (the first case)

1)...1(

)1)...(1(

−

+−−=

ss

snnnC s

n



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Fig.6 Means of the rates of the classification errors of our algorithms (TPTSR-DCT,TPFR-DCT,

TPTSR-DFT, TPFR-DFT), TPTSR on the ORL face database (the second case)

Fig.7 Means of rates of the classification errors of our algorithms (TPTSR-DCT,TPFR-DCT,

TPTSR-DFT, TPFR-DFT), TPTSR on the FERET face database

Figs.5, 6 and 7 shows the means of rates of the classification errors (%) of our algorithms and

TPTSR for the ORL database (the first case), the ORL database (the second case) and FERET

database, respectively. Figs.5 and 6 clearly show that our proposed algorithms are always able to

obtain a much lower means of rates of the classification errors than TPTSR. Fig.7 shows the means

of rates of the classification errors of our proposed algorithms are lower than TPTSR in most cases.

But, the performances of TPTSR-DFT and TPFR-DFT are inferior to TPTSR when the number of K

is smaller certain values on FERET face database. In most cases, the performances of TPTSR-DCT

are better than TPFR-DCT on the ORL and FERET face databases. As for TPFR-DFT and TPTSR-

DFT, the performances of TPFR-DFT are better than TPTSR-DFT in most cases on ORL and

FERET face databases. Most important of all, those figures also show that our proposed algorithms

can achieve a better performance than TPTSR when they use a suitable K nearest neighbors training

samples to represent the test sample. Moreover, it can be observed than there is an increase in the

means of the rates of the classification errors as the numbers of K increase. But if we use a suitable K

nearest neighbors training samples to represent the test sample, the means of the rates of the

classification errors of our algorithms can achieve below 2% and 25% for ORL and FERET face

databases, respectively.



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Table.1. Mean of the rates of the classification errors (%) of Global version of our algorithms

(TPTSR-DCT, TPFR-DCT, TPTSR-DFT, TPFR-DFT), TPTSR, SRC, PCA, LDA

Table.1 shows the means of the rates of the classification errors of the global version of our

proposed algorithms, the global version of TPTSR, SRC, PCA and LDA in the ORL (the first case

and the second case) and FERET databases. The global version is the implementation of our

proposed algorithms in the case where K is equal of the total number of training samples. That is, in

the first stage of our algorithms, the test sample is represented by all the training samples. The global

version of K for the ORL and FERET face databases is 200 and 800, respectively. In

PCA algorithm, the rest of the feature vectors contain information account for 90% of total amount

of information. For the LDA algorithm, the transform axes of feature extraction on ORL database

and FERET database are 39 and 199, respectively.

Table.1demonstrates that the performances of our proposed algorithms are better than the

TPTSR, SRC, PCA and LDA. Moreover, TPTSR-DCT and TPFR-DCT achieve the best results on

the FERET database. The performances of TPTSR-DFT and TPFR-DFT are the best on the ORL

database (the second case). The reasons may be that the DCT coefficients and DFT amplitude

spectrums are more robust to lighting changes and scale variations than pixel gray values, which can

improve the face recognition performances. In addition, the test sample and its nearest neighbors

usually belong to the same class, so our algorithms provide a very reasonable way to determine the

class labels. Most important of all, our algorithms are an extended of TPTSR, which is a supervised

sparse representation method. Therefore, our algorithms have all the advantages of the SRC

algorithms, and achieve a better performance than the TPTSR, SRC, PCA and LDA.

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