# Novel Iris Biometric Watermarking Based on Singular Value Decomposition and Discrete Cosine Transform

Authors: Jinyu Lu; Tao Qu; Hamid Reza Karimi
Journal: Mathematical Problems in Engineering
 (2014)

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## Abstract

A novel iris biometric watermarking scheme is proposed focusing on iris recognition instead of the traditional watermark for increasing the security of the digital products. The preprocess of iris image is to be done firstly, which generates the iris biometric template from person's eye images. And then the templates are to be on discrete cosine transform; the value of the discrete cosine is encoded to BCH error control coding. The host image is divided into four areas equally correspondingly. The BCH codes are embedded in the singular values of each host image's coefficients which are obtained through discrete cosine transform (DCT). Numerical results reveal that proposed method can extract the watermark effectively and illustrate its security and robustness.


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## Body

## 1. Introduction

With the internet age coming, amount of digital products have swarmed into our living. Especially the digital products are inevitable for being copy-free. Therefore, the security of these products is presented over the past few decades. A typical solution is the digital watermarking technology which has been widely applied to information security, such as copyright protection and authentication. Watermarking can be classified into visible and invisible. Visible watermarking is attacked even more than invisible because visible watermarking is disclosed [1]. In contrast, invisible watermarking is more prevalent. Invisible watermarking could be done in the spatial domain or in the transform domain according to human visual system (HVS). However, transform-domain-based watermarking techniques present advantages in terms of perceptibility and robustness more than the spatial domain, so more researchers pay attention to the transform domain. Researchers frequently used the transform domain including the Fourier transform, discrete cosine transform (DCT), discrete wavelet transform (DWT), and many more.In biometrics feature recognition, iris has become focus and emphasis which has unique, stability, be-collected, non-invasion, and so forth as an important characteristic of authentication. Daugman has made many contributions to iris-based biometrics [2, 3]. Wildes et al. have proposed an automated iris recognition [4]. Wildes et al. [4, 5], Boles and Boashash [6] have obtained some research on the iris recognition. More and more research institutes and companies have been added to the field of iris recognition [7, 8]; iris-based authentication technology is paid attention to by academia and business. A lot of standard databases have been generated by various institutes to work in this field [9, 10]. Lots of organizations are focusing on the issue, such as Chinese Academy of Sciences-Institute of Automation (CASIA) [11], Lion’s Eye Institute (LEI) [12], Universities of Bath, and Carnegie Mellon University, and we use the database from University of Bath. Similar method is discussed in [13–20].To sum up, we focus on the iris biometric database, a novel iris biometric watermarking based on singular value decomposition (SVD), and DCT is proposed.The preprocess of iris image is to be done firstly, which generates the iris biometric template from person’s eye images. And then the templates are to be on discrete cosine transform; the value of the discrete cosine is converted to BCH-based coding. The host image is divided into four areas equally correspondingly. The DCT coefficients of each area are applied with the SVD [21, 22]. The DCT coefficients of each area are modified by the singular vectors and the BCH-based error control coding watermark to embed the watermark image. Embedding intensities depends on the key. The algorithm is robust under popular attacks.


## 2. Iris Image Technology Normalization and Coding

We use the database of eye images from University of Bath. In addition to iris, there are pupil, sclera, and eyelid in any eye image. It is necessary to normalize to remove these adverse factors from eye image prior to coding. We apply a minimum bounded isothetic rectangle (MBIR) format to eye image for eliminating these factors. Thus, we obtain rectangular iris templates which are normalized to a size of120×200 pixels by MBIR format [23, 24]. The normalized 120×200 iris image is applied with column-wise, 1D DCT and retaining of DC value of each column, to obtain a 1×200 set of pixels [23, 25, 26]. Then, these 1×200 DC values are encoded to binary string, which is 8×200 bits format with BCH-based error control coding (Figure 1).Figure 1
Iris biometric normalization and coding.


## 3. Watermarking Methodology

Discrete cosine transform is correlated with Fourier transform, which is similar to the discrete Fourier transform and only use real parts. 2D DCT transformation is commonly used in video compression conversion. In the compression process, the image is divided into many small pieces of8×8 format. A signal x(i,j) is converted into frequency domain as follows:
(1)y(k,m)=α(k)·α(m)∑i=0N-1∑j=0N-1{·cos⁡[(2j+1)mπ2N]x(i,j)×cos⁡[(2i+1)kπ2N]·cos⁡[(2j+1)mπ2N]},x(i,j)=∑i=0N-1∑j=0N-1{×cos⁡[(2j+1)mπ2N]α(k)·α(m)y(k,m)×cos⁡[(2i+1)kπ2N]×cos⁡[(2j+1)mπ2N]},
where N=8. Then the watermark-embedding process is discussed in the following steps.Step 1.
The host imageI is divided into four blocks equally Ij, which block is applied with DCT IDj,   j=1,2,3,4.
SVD is an important matrix factorization in linear algebra which has some important application in signal processing, statistics, and other fields.
SupposeM is a m×m matrix, the elements of which all belong to K domain, that is, real domain or complex domain. Thus, it exists a decomposition such that:
(2)M=U∑VT,
where U is m×m unitary matrix and VT is the conjugate transpose of V which also is m×m unitary matrix. We choose special orthonormal bases: v1,…,vm for the row space and u1,…,um for the column space. ∑ is positive semidefinite matrix of m×m and is the singular value of M:
(3)∑=diag⁡(λ1,λ2,…,λm),M=U1λ1V1+⋯+UmλmVm.Step 2.
I
D
j is implemented by SVD for each block:
(4)IDj=UDjSDjVDjT,UDjSDjVDjT=SVD(IDj),j=1,2,3,4.Step 3.
Iris image is normalized and encoded to binary string. Here iris image is converted to8×200 bits binary, which is divided into four sections equally and each section is 400 bits binary. The 400 bits binary change into 403 bits added with 3 zero values at the end of the 400 bits. The 403 bits binary is converted to BCH(511,403), where n=511, k=403, and t=12. The watermark consists of these four sections.Step 4.
Watermark is embedded into the singular values of the DCT-transformed host image on each block:(5)SD′j=SDj+αIw.Step 5.
The DCT coefficients of watermarked image are modified in each block:(6)ID′j=UD′jSD′jVD′jT.Step 6.
The watermarked image is performed inverse DCT (IDCT) onID′j.For illustrating the watermark embedded process, the description figure is presented as shown in Figure2.Figure 2
Watermark embedded process.For the watermark-extraction process, we consider that the received image is corrupted version of the watermarked image. And the description of the watermark extraction process is presented in Figure3.Figure 3
Watermark extraction process.Step 1.
In this step of the extraction process, the corrupted imageI′′ is divided into four areas I′′j(j=1,2,3,4) equally.Step 2.
I
′′
j is applied with DCT:
(7)ID′′j=DCT(I′′j).Step 3.
SVD operation is implemented onID′′j:
(8)ID′′j=UD′jSD′′jVD′jT,UD′jSD′′jVD′jT=SVD(ID′′j).Step 4.
Watermark is hidden in the singular value ofID′′j, so watermark Iw′j is expressed by the following:
(9)Iw′j=1αj(UT(ID′′j-IDj)V).Step 5.
I
w
′
j is divided into four sections equally; then, each section is processed error correction decoding, as Iw′j is binary BCH coding. The result of the decoding is that Iw*j is 1600 bits binary format.Step 6.
Perform mod 2 operation onIw*j:
(10)Aij=Iw*i⊕Iw*j,i,j=1,2,3,4,
where Aii=0, Aij=Aji, Aij={a1ij,a2ij,…,a1600ij}, and Aij is vector.Step 7.
Do a summation of the elements inAij:
(11)Mij=∑r=11600arij,i≠j.Step 8.
Take the minimum ofMij as Iw*:
(12)Iw*=Iw*iorIw*j.Step 9.
This is done conversion of the binary formatIw* into the DC values.Step 10.
The obtained set of DC coefficients is contrasted with the standard sets of DC coefficients stored for each person and judged to belong to who in the database.


## 4. Experiment Results and Discussion

Because the iris biometric has the superiority of security, imperceptibility, the iris biometric is employed to realize embed watermark. Via the conclusions discussed in [27], the DC coefficients of different persons’ iris, which can be seen to be noncorrelated, has a non-self-similar characteristic as shown in [27]. However, the variation of DC coefficients of the same iris biometric has a self-similar characteristic as in [27] in diversification condition. In terms of iris characteristics, the DC coefficients of iris biometric are used as a watermark.The detected watermark is a binary string in our proposed scheme, so the detected watermark is divided into two types of situation. One type of situation is that the detected watermark could match up with someone’s iris biometric in the database, so it is the identification of the biometric. The embedded watermark and the detected watermark belong to the same iris, that is, correct detection, or the embedded watermark and the detected watermark do not belong to the same iris, that is, false acceptance. Another type of situation is that the detected watermark could not match up with anyone’s iris biometric in the database, so it is false rejection. In the above types, we only pay attention to correct detection, for it is significant to identify the detected watermark. According to Figures1–3, the proposed scheme and the algorithm [23] are all viewed as digital communication system, it has greatly raised the correct-detection probability. Thus it is hard to measure the performance by traditional methods such as PSNR and ROC curve, it can be to measure the performance by the algorithm [23].In [27], there are 77 different attacks. In their results of experiment, both the identification 67 of the 77 attacks which has greater than 90% of correct detection and the identification 71 of the 77 attacks which has greater than 85% of correct detection have been successful. This algorithm [27] displays robustness when receiving most attacks by detection and identification except the “copy” attack. Some attacks like “scaling,” “MAP,” “up-down sampling,” and “bending” attacks are partially sustained. In this paper, the proposed algorithm almost has a good performance with the different attacks. There are 70 different attacks; the identification 60 of the 70 attacks which has greater than 95% of correct detection, the identification 61 of the 70 attacks which has greater than 90% of correct detection, and the identification 66 of the 70 attacks which has greater than 85% of correct detection have been successful, all shown in Table 1.Table 1
Major attack-wise total number of correct detections, false rejections, and false acceptances for70×400=28000 tests.
M
NM
W (%)
CD (%)
FR (%)
FA (%)
T
>95
>90
>85
95
90
85
95
90
85
95
90
85
1
Aspect ratio
30
29
29
30
11776
11835
11862
216
158
132
8
7
6
12000
2
Crop
6
5
5
6
2371
2380
2389
25
18
10
4
2
1
2400
3
JPEG
7
6
6
7
2724
2756
2767
73
42
31
3
2
2
2800
4
Scale
6
4
4
5
1905
1987
2093
448
382
285
47
31
22
2400
5
MAP
6
4
5
5
1396
1548
2173
935
810
200
69
42
27
2400
6
Up-down sample
4
2
2
3
1251
1385
1452
335
204
139
14
11
9
1600
7
Remodulation
4
4
4
4
1574
1582
1591
26
18
9
0
0
0
1600
8
Filtering
3
3
3
3
1189
1192
1197
10
7
3
1
1
0
1200
9
Bending
2
1
1
1
462
481
490
338
319
310
1
0
0
800
10
Copy
2
2
2
2
781
788
795
19
12
5
0
0
0
800
T
70
60
61
66
25429
25934
26809
2425
1970
1124
147
96
67
28000
Note. M: expresses major attack type, NM: expresses number of subattacks, W: expresses watermark detection cases, CD: expresses correct detection, F: expresses false rejection, FA: expresses false acceptance, and T:  expresses total.


## 5. Conclusion

In this paper, the DC coefficients of the same iris biometric have a self-similar characteristic to reduce complexity of implementation. BCH(511,403) codes have a 12 bits error-correction function. It has largely improved the correct-detection probability of extracted watermark in comparison with traditional watermark. Furthermore, four extracted watermarks are compared one by one so that the best one can be selected. This process also improves the correct-detection probability. A series of experiments have been conducted to validate the performance of the proposed SVD and DCT. The experimental results show that the proposed scheme has a more superior performance than the other methods under different kinds of attacks. The proposed algorithm based on SVD and DCT has robustness and imperceptibility.



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*Source: 926170-2014-02-16.xml*