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Palmprint Identification Based on Non-separable Wavelet Filter Banks Jie Wu1 , Xinge You2 , Yuan Yan Tang2,3 , Yiu-ming Cheung2 1

2

Faculty of Mathematics and Computer Science, Hubei University, Wuhan, China Department of Electronics and Information Engineering, Huazhong University of Science and Technology, Wuhan, China 3 Department of Computer Science, Hong Kong Baptist University, Hong Kong E-Mail: [email protected], [email protected]

Abstract Creases, as a special salient feature of palmprint, are large in number and distributed at all directions. It changes slowly in a person’s whole life, which qualifies themselves as features in palmprint identification. In this paper, we devised a new algorithm of crease extraction by using non-separable bivariate wavelet filter banks with linear phase. Compared with the traditional wavelet, our research demonstrates that the three high frequency sub-images generated by Non-separable Discrete Wavelet Transform (NDWT) can extract more creases and no longer extensively focus on the three special directions. As a consequence, we proposed a new method by combining NDWT and Support Vector Machines (SVM) for palmprint identification. Tested by our experiment, this method achieves a satisfied identification result and computational efficiency as well. Keywords: Palmprint identification; NDWT

1. Introduction Biometrics-based personal identification is regarded as a reliable method for automatically recognizing during the last few years [8]. Lots of interesting and meaningful research results have been achieved at the same time. As a new research area of this technology, the palmprint identification has been greatly emphasized recently because of its advantages such as low cost and stable structure feature. Therefore, the investigation and development in palmprint identification become particularly valuable. Generally speaking, the previous work on palmprint recognition focused on two aspects: first, extracting the textural characteristics of palmprints (principle lines and creases) in spatial domain [1], [5]; second, transforming the palmprint images into the frequency domain to obtain the

energy distribution feature [2], [3], [4]. However, in the first method, the three types of basic creases: principal lines, wrinkles and ridges are difficult to extract directly from a palmprint image. In the second approach, the singular information which obtained from the 2-D Wavelet Transform (WT ) are extensively focusing on the three special directions (vertical, horizontal and diagonal), an enormous amount of singular information in other directions can not be revealed in the high frequency components. Thus, the problem with these two approaches suggest that new methods are required for palmprint identification. The non-separable wavelet, is one of the filter banks, which constructed by using the centrally symmetric orthogonal matrices. It is also holding the ability of multiresolution analysis and low computational complexity as traditional wavelet. Our investigation demonstrates that the high frequency components from NDWT can capture more singular information than traditional wavelets. Moreover, when we select different parameters, we could obtain different filter banks which emphasize different directional feature. Therefore, it motivates us to apply an approach based on the non-separable wavelet to extract the features. The paper is organized as follows: Section 2 describes the non-separable wavelet filter banks. Section 3 shows the algorithm of feature extraction. Section 4 provides experimental results. Section 5 gives a conclusion.

2. The Non-separable Wavelet Filter Banks In digital images processing, multivariate filter banks are especially important. A commonly used method to build multivariate filter banks is the tensor products of univariate filters. Nevertheless, this construction of multivariate filter banks focuses extensively on the coordinate direction. In this paper, we give a general description on how to construct the non-separable wavelet filter banks by using cen-

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trally symmetric matrices. The further theory of construction is presented in our previous work [6], [7]. In this section, we firstly consider the following 4 × 4 centrally symmetric orthogonal matrix H(θ,η) :    cosθ + cosη −sinθ + sinη −sinθ − sinη cosθ − cosη   sinθ − sinη cosθ + cosη cosθ − cosη sinθ + sinη   sinθ + sinη cosθ − cosη cosθ + cosη sinθ − sinη  (1)   cosθ − cosη

−sinθ − sinη

−sinθ + sinη

 N   1 Y 2 2 T m j (z1 , z2 ) = (1, z1 , z2 , z1 z2 )  H(θx ,ηx ) D(z1 , z2 )H(θx ,ηx )  V j 4 k=1

let z1 = e−iξ , z2 = e−iη , ∂D = {z : |z| = 1}   0   1 0 0   0 z 0 0  1  , (z , z ) ∈ ∂D × ∂D D(z1 , z2 ) =  0  1 2  0 0 z2 0 0 0 z1 z2 V0 = (1, 1, 1, 1)T ; V1 = (1, −1, 1, −1)T V2 = (1, 1, −1, −1)T ; V3 = (1, −1, −1, 1)T

−0.0173

0.0410

0.3125

0.2081

0.0352 −0.0092 −0.0071 −0.0273

0.0273 0.0071 0.0092 −0.0352

−0.2081 0.0543 −0.0700 −0.2679

−0.2679

0.0273 −0.0071 0.0092 0.0352

−0.0352 −0.0092 0.0071 −0.0273

0.2679 −0.0700 −0.0543 −0.2081

−0.3125

0.0173 −0.0045 0.0107 0.0410

0.0410 0.0107 −0.0045 0.0173

−0.3125 0.0816 0.0345 0.1319

  0.2081  0.0543 m2 =   0.0700   0.1319  0.0345 m3 =   0.0816

(a) separable wavelet (db4)

(2)

(3)

(4)

For any given positive integer N, the arbitrary real number pairs (θk , ηk ), k = 1, 2, · · · , N (the (θk , ηk ) may equal to (θ j , η j ) while k , j ) can generate different filter banks. For example, when the N = 1, θ = 0.386, η = 0.125, the filter banks can be represented in matrix form as follows:   0.0410 −0.0173 0.1319   0.3125  0.0816 −0.0107 −0.0045 −0.0345  m0 =    −0.0345 −0.0045 −0.0107 0.0816  0.1319

As we known, the traditional two-dimension WT has four orthogonal sub-images which corresponding to LL, LH, HL and HH at each level of decomposition.

cosθ + cosη

where (θ, η) is the arbitrary real number pair. By using the above matrix H(θ,η) we will construct the following Nonseparable bivariate wavelet filter banks. According to MRA, the designed orthogonal FIR and QMF filter banks: m0 , m1 , m2 , m3 should satisfy the following conditions: (a): The low-pass filter m0 satisfying the orthogonal condition; (b): The matrix generated from four filters m0 , m1 , m2 , m3 is unitary. By using the previous matrix H(θ,η) on the viewpoint of polyphase. The four filters m j (z1 , z2 ), j = 0, 1, 2, 3 are defined as follows:

  0.2679  0.0700 m1 =   −0.0543

3. Feature Extraction and Algorithm

              

(b) non−separable wavelet

Figure 1. Wavelet decomposition Similarly, the previous non-separable wavelet filter banks also can generate four orthogonal sub-images which corresponding to the filters m0 , m1 , m2 and m3 at each level of decomposition. Here the sub-image corresponding to the filter m0 carries low frequency information as coarse as possible. The other three parts capture high frequency information of the image in different directions. As Figure 1 shown, the three high frequency components could capture more singular information than tensor products WT , and the approximation of original image is much coarser than the low frequency component from the tensor products WT . Feature vector, which represents the original palmprint, should well distinguish the palmprints from different person.It is obvious that, the sub-image cropped from the central of palmprint contains an enormous of creases in different directions. As a consequence, it is reasonable for us to apply a method based on MRA to represent the multi-scale

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feature. Here, we will describe the general construction of NDWF by using the above non-separable wavelet. Our previous studies showed that the three high frequency components obtain from NDWT can capture more singular information than traditional wavelets. However, as we have mentioned above, the crease in high frequency components is vital to our identification. Thus, it benefits us from the viewpoint of NDWT to construct the feature vector. When the palmprint decomposed by NDWT in the I-th level, the original palmprint G can be represented by 3I + 1 decomposed sub-images: [AI , {Hi , Vi , Di }i=1,2...,I ], where AI is the low frequency sub-image of original palmprint, {Hi , Vi , Di }i=1,2,··· ,I are the high frequency sub-images. For each high frequency sub-image, we extract the statistical feature: mean, which defined as follows: 1 XX |Hi (x, y)| m ∗ n x=1 y=1 m

Mi =

original palmprint G

Divide

3×4×n×n high frequency components

n×n sub-images

ĂĂĂ

4-th NDWT

ĂĂĂĂĂĂ compute the mean of each high frequency components

NDWF

Figure 2. Construction of NDWF

n

(5)

where Hi (x, y) corresponds to the coefficient of high frequency sub-images at i-th level, while m, n denote it width and height. The mean reflects the distribution of palmprint’s details in different direction at each non-separable wavelet decompose level. Hence, the vector (6) constituted by the means of all high frequency sub-images could describe the statistical intensity of original palmprint efficiently. (6) T d = (M1 , M2 , · · · , MI )d where I is the total decomposition level. d refers to the three high frequency sub-images from NDWT . Nevertheless, the feature vector we obtain only by computing the mean from high frequency sub-images is a global feature of palmprint. It fails to preserve the information concerning the spatial location of different details. To deal with this problem, we divide the original palmprint G into n × n non-overlap blocks equally. For each blocks we apply 4-th non-separable wavelet transform, and 3 × 4 × n × n high frequency sub-images are obtained consequently. Then we use the means of all high frequency sub-images which computed from (5) to form a vector F, here we called as NDWF (see Figure 2). F = ( f1 , f2 , · · · , fn×n ) (7)   where fk = T 1d , T 2d , · · · , T Id k=1,2,··· ,n×n

The feature matching is based on measuring the similarity between two NDWF s F1 and F2 . As a conventional classifier, Nearest Neighbor algorithm (NN) is commonly adopted in palmprint identification. However, in recent research work, the S V M classifier has demonstrated better performance than NN. In this paper, the S V M is applied to final classification. To sum up, our method is composed of the two factors, which could simply termed as NDWT + S V M. The general procedures can be summarized as below:

step 1 Divide original palmprint into 4 × 4 non-overlap blocks; step 2 Decompose the sub-images by non-separable wavelet to 4th level; step 3 For all the high frequency components, compute the means and construct the NDWF; step 4 Use the S V M to compute the correctness.

4. Experimental Results In this section, we compare the results of our method with some others which most of them are based on traditional WT , such as WT +NN, WT + S V M, NDWT + NN. Experiments are conducted by the PolyU Palmprint Database, which contains 600 palmprints captured from 100 different persons, six samples from each of them were collected. Three palmprints are chosen randomly in each person for training and the rest are for testing. Thus, a training samples set of 300 palmprints and a testing samples set with 300 palmprints are created. In this way, we run the system 10 times and obtain 10 different training and testing databases. For each time, we do the same procedures for WT method and compare the results of our method with others at two aspects: the identification accuracy and the computation time. The identification accuracy is decided by the top response rate achieved, and the computation time can be classified into two part: the first is defined as the seconds used for feature extraction of one palmprint, the second is the time used for classification of 300 palmprints. The experimental results for WT + NN, WT + S V M, NDWT + NN, NDWT + S V M are summarized in Table1. In the experiments, the blocks used for WT method are exactly the same as NDWT . It is obvious that the NDWT performs better than WT both in identification accuracy and

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computation time. The NDWT + S V M method achieves 99.67% accuracy which is 1.33 percent better than WT + S V M, and the computation time used for feature extraction of one palmprint is much lower. Moreover, when we choose the conventional classifier NN algorithm, the NDWT gives better performance than WT by 1.67 percent. Table 1. Comparisons of computational time and recognition rate among other methods method WT + NN NDWT + NN WT + S V M NDWT + S V M

computation time 0.234s+3.594s 0.062s+3.594s 0.234s+3.204s 0.062s+3.204s

accuracy 97.67% 99.33% 98.33% 99.67%

In order to test the reliability of our proposed method, we conduct the experiments of above four methods with decomposition level ranging from 1 to 4 for each palmprint. As Figure 3 shown, when we choose the same classifier, the methods based on NDWT are superior to the methods based on WT in each decomposition level. Moreover, the identification rate of NDWT is increasing as long as the decomposition level improving. When the palmprint is decomposed by NDWT to 4-th level, we could obtain the identification rate of 99.67% while WT reaches only 98.33%.

different directional information, which is suitable for extracting the irregular creases of palmprint. In order to reflect the distribution of creases in different directions at different resolutions, we decomposed the original palmprint to 4-th level by NDWT , and compute the means of each high frequency component to form a NDWF. To verify the reliability of our method, we conduct experiments to compare our method with some others under different decomposition levels. And it has been proved that the proposed method is superior to others in terms of identification accuracy and efficiency.

Acknowledgement This work is supported by the grant 607731871 from the NSFC, NCET-07-0338 from the Ministry of Education, and the grant 2006ABA023, 2007CA011 and 2007ABA036 from the Department of Science & Technology in Hubei province, China. Xinge You is the Corresponding author.

References [1] Duta N, Jain A K, and Mardia K V. ”Matching of Palmprint”, Journal; Pattern Recognition Letters, Vol 23, No. 4, pp. 477-485. 2001. [2] Li Wenxin, and David Zhang. ”Palmprint Identification by Fourier Transform”, Journal; International Journal of Pattern Recognition and Artificial Intelligence, Vol 16, No. 4, pp. 417-432. 2002.

100 99 98

Recognition rate

97

[3] Lu Guangming, David Zhang, W.K. Kong. ”Palmprint Identification by Fused Wavelet Characteristics”, Journal; Image Pattern Recognition, 2007.

96 95 94 93 NDWT+NN WT+NN WT+SVM NDWT+SVM

92 91 90

1

1.5

2

2.5 3 Decomposition level

3.5

4

Figure 3. Recognition rates versus the decomposition level

5. Conclusion In this paper, to overcome the drawbacks of feature extraction based on traditional WT , we propose a novel method by using non-separable wavelet filter banks. First of all, compared to the traditional WT , the non-separable wavelet filter banks could capture more singular information in three high frequency components. Secondly, when we choose different filter banks we could emphasize

[4] Wu Xiangqian, Wang Kuanquan, and David Zhang. ”Wavelet Energy Feature Extraction and Matching for Palmprint Recognition”, Journal; Journal of Computer Science and Technology, 2005. [5] Lu Guangming, David Zhang. ”Palmprint Recognition Using Eigenpalm Feature”, Journal; Pattern Recognition Letters, No. 24, pp. 1463-1467. 2003. [6] Xinge You, Dan Zhang, et al, ”Face Representation by Using Non-tensor Product Wavelets”, Proceedings of the 18th ICPR, Vol 1, pp. 503-506. 2006. [7] Xinge You, Qiuhui Chen et al, ”Construction of nontensor product wavelet and its application”, Technical Report, Department of Computer Science, Hong Kong Baptist University 2007. [8] Wu Xiangqian, David Zhang, and Wang Kuanquan, The Technology of Palmprint Recognition, Science press, Beijing, 2006.

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