Blind Watermarking using QIM and the Quantized SVD Domain based

on the q-Logarithm Function

Ta Minh Thanh

1,2

and Keisuke Tanaka

1,3

Dept. of Computer Science, Tokyo Institute of Technology, Tokyo, 152-8552, Japan

Dept. of Network Security, Le Quy Don Technical University, 236 Hoang Quoc Viet, Cau Giay, Ha Noi, Vietnam

CREST, JST., Tokyo, Japan

Keywords:

q-Logarithm SVD (q-SVD), Image Watermarking, Quantization Index Modulation (QIM).

Abstract:

We propose new image blind watermarking by using both the quantization index modulation (QIM) technique

and the quantized singular value decomposition (SVD) domain based on the q-logarithm function. In order to

reduce the distortion of the embedded image, we employ the q-logarithm transform on the Y component of the

original image after performing the SVD domain. We call this domain the q-SVD domain. In our proposed

method, the tradeoff of robustness and quality can be controlled by a predeﬁned quantization coefﬁcient Q of

QIM and a parameter q of the q-SVD domain. Several experiments are conducted to show the robustness of

our proposed method against processing attacks and geometric attacks.

1 INTRODUCTION

1.1 Background

Due to the advance of computer and network tech-

niques, e-business of digital contents has become the

most popular market for various types of digital con-

tents such as picture, audio, movie, and so on. How-

ever, since network applications have become very

popular, everyone can easily copy, alter, or even steal

digital content via network. Therefore, the protection

of digital content in e-business has become one of the

most important issue.

Digital watermarking is a promising technique in

order to protect the digital content by embedding the

watermark directly into digital content. The embed-

ded watermark can be extracted later for authentica-

tion, copyright protection, and traitor detection (Shih,

2008; Yeung, 1998; Nikolaidis and Pitas, 2003; Bao

and Ma, 2005; Liu and Tan, 2002).

In general, the invisibility, robustness, and capac-

ity of the watermark are important requirements for

the proposed watermarking. The watermark should

not make visible changes on digital content in order

to remain the quality of the original image. Addi-

tionally, the watermark must be robust against the im-

age attacks/distortions applied to the embedded con-

tent. Finally, the watermark must be easily extracted

to prove ownership and to detect the traitor.

There are two types of the digital watermarking

methods, the spatial domain watermarking and the

transform domain watermarking.

In the spatial domain watermarking, the water-

mark information is embedded directly into the com-

ponents of the original content, for example, an RGB

component by altering its values (Yeung, 1998). The

spatial watermarking domain has advantages such as

low complexity and simple implementation. How-

ever, the spatial domain watermarking methods are

not robust against image processing attacks, and geo-

metric attacks.

The transform domain watermarking methods em-

bed the watermark by modifying the magnitude of

coefﬁcients in transform domain such as discrete

Fourier transformation (DFT), discrete cosine trans-

form (DCT), discrete wavelet transform (DWT), and

singular value decomposition (SVD) (Nikolaidis and

Pitas, 2003; Bao and Ma, 2005; Liu and Tan, 2002).

Also, there have been a lot of proposals of watermark-

ing methods that use the mixed domain. For instance,

the combination of DCT and SVD (Liu and Liu, 2008;

Lu et al., 2007; Yavuz and Telatar, 2006), that of SVD

and DWT (Cao et al., 2009; Yavuz and Telatar, 2007;

Zhang and Li, 2009), that of DWT and DCT (Deb et

al., 2012; Feng et al., 2010; Bei et al., 2011) are em-

ployed to embed the watermark into the digital con-

Thanh T. and Tanaka K..

Blind Watermarking using QIM and the Quantized SVD Domain based on the q-Logarithm Function.

DOI: 10.5220/0005291900140025

In Proceedings of the 10th International Conference on Computer Vision Theory and Applications (VISAPP-2015), pages 14-25

ISBN: 978-989-758-091-8

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

tent. Embedding on transform domain seems more

robust but rather complicated to compute because of

its high computation cost. Additionally, the previous

methods only focused on the robustness of the water-

mark by sacriﬁcing the quality of the embedded con-

tent.

In particular, the SVD-based technique is used to

efﬁciently extract algebraic features from an image.

Based on the feature of SVD transform, the stable

SVD matrices feature of image can be easily obtained.

Therefore, when the image is degraded by several

image processing attacks, its singular values (SVs)

do not change signiﬁcantly (Liu and Tan, 2002; Lai,

2011; Zhou and Chen, 2004). This feature is normally

used to embed the user’s information into the image

with less degradation.

As shown in the papers (Liu and Tan, 2002;

Lai, 2011; Zhou and Chen, 2004; Bhatnagar and

Raman, 2009), SVD-based watermarking algorithms

were proposed. In order to achieve the robustness,

Liu and Tan (Liu and Tan, 2002) presented a water-

mark method which embeds the watermark into the

SVD domain. They added the watermark bits into the

singular values of matrix S. Three matrices U

,S, and

are saved as the secret key. These matrices are

required in the watermark extraction. In order to ex-

tend the method of (Liu and Tan, 2002), Lai et al.

(Lai, 2011) demonstrated a watermarking technique

using SVD and a tiny genetic algorithm to achieve

the robustness of the watermark information. Un-

fortunately, both algorithms of (Liu and Tan, 2002)

and (Lai, 2011) are fundamentally ﬂawed as men-

tioned in (Loukhaoukha, 2013). This bug of these

algorithms causes false positive detection even if the

attacker uses a different embedded watermark or the

secret key. In the method of Chandra et al. (Chandra,

2002), not only the original image is required but also

the original watermark during the watermark extrac-

tion process. Hence, their method is not suitable for

real applications. Bao (Bao and Ma, 2005) utilized

the quantization parameter for enhancing the quality

of the watermarked image. In the extraction process,

the quantization parameter is required as the private

key. However, the original image must to be trans-

formed to the wavelet and SVD domain. It requires

high computation cost.

As mentioned above, the previous SVD-based wa-

termarking techniques mainly focused on the robust-

ness of embedding methods but did not the quality of

the watermarked images.

1.2 Our Contributions

We consider that it is very important to improve the

quality of the embedded content, while maintaining

the robustness of watermarking methods.

We extend the original SVD domain to the q-

logarithm SVD domain in order to improve the qual-

ity of image and to retain the robustness of water-

marking method. In particular, we make the following

contributions in this paper:

(1) Inspired by the motivation of (Tsallis, 1998),

we present the novel frequency domain, called q-

logarithm SVD domain (q-SVD), for the image wa-

termarking that is not proposed before. – See Section

(2) We investigate the efﬁciency of the combina-

tions of both parameters Q and q for our method. We

ﬁnd out the appropriate values for Q and q suitable

for watermark embedding. By these combinations,

the tradeoff of the robustness and the quality can be

controlled by a predeﬁned quantization coefﬁcient Q

of QIM and a parameter q of the q-SVD transform. –

See Section 4.2.

(3) Various simulation experiments are conducted

to demonstrate the performance of our proposed

method. Experimental results show that the proposed

method has stronger robustness against most com-

mon attacks such as the JPEG compression, cropping,

swirl, and so on. – See Section 4.3.

Therefore, by using our method, we simultane-

ously improve the quality of embedded image also

achieve the robustness of the watermark.

1.3 Roadmap

The rest of this paper is organized as follows. The

proposed q-SVD domain is described in Section 2 and

we will explain why the q-SVD domain is suitable for

our watermarking method. Section 3 describes our

proposed watermarking method using QIM on the q-

SVD domain. Our simulation results are shown in

Section 4. Section 5 concludes our paper.

2 QUANTIZED SVD DOMAIN

BASED ON q-Logarithm

FUNCTION

2.1 q-Logarithm and q-Exponential

Function

q-logarithm and its inverse, q-exponential, are the

concept of non-extensive statistics which is intro-

BlindWatermarkingusingQIMandtheQuantizedSVDDomainbasedontheq-LogarithmFunction

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Figure 1: The comparison of SVD and q-SVD.

duced by Tsallis (Tsallis, 1998), a theory of non-

extensive statistics. The q-logarithm function is de-

ﬁned as follows:

log

(x) =

1−q

− 1

1 − q

(1)

and its converse, q-exponential is deﬁned as:

exp

(x) = (1 + (1 − q)x)

1−q

, (2)

where the parameter q is a real number that is prede-

termined and x is also a real number. In our work,

x can be a pixel of image or a coefﬁcient of the fre-

quency domain.

Inspired by the theory of non-extensive statistics, we

propose q-SVD domain to provide a novel frequency

domain, which is very ﬂexible by randomly choos-

ing q parameter to control the quality of image af-

ter inverse transform. We employ the feature of q-

logarithm and q-exponential in Eq. (1) and Eq. (2) to

construct q-SVD for image processing.

2.2 Proposed q-SVD Domain

Suppose that the image I with size N × N is divided

into non-overlapping blocks. Each block is a matrix,

called A, with size 8 × 8.

In general, the real matrix A can be decomposed

into three matrices SV D(A) = USV

, where U and V

are orthogonal matrices, such that UU

= E, VV

E and S = diag(λ

,λ

,···). Here, the singular values

,λ

,··· of matrices A are sorted decreasingly, and

E is the unit matrix.

There are the following advantages when using

SVD in digital image processing:

(1) It is not necessary to ﬁx the size of the matrix A

beforehand. Its size is x × x or x ×y for some x, y.

Therefore, we can choose the size of A suitable

for that of the watermark image.

(2) SVs of a digital image are less affected under the

general image processing such as blurring, noise

addition, slight rotation. Therefore the quality of

the watermarked image can be kept after embed-

ding.

Inspired by the theory of non-extensive statistics

(Tsallis, 1998), we propose the q-SVD domain, which

is very ﬂexible by arbitrary choosing the parameter q

to control the quality of image. We employ the fea-

ture of q-logarithm and q-exponential (Tsallis, 1998)

to construct the q-SVD for image processing.

Suppose an image I is given. First, I is trans-

formed into q-logarithm as follows:

(i, j) = log

{I(i, j)} =

{I(i, j)}

1−q

− 1

1 − q

, (3)

where I(i, j) and I

(i, j) represent the pixel (coefﬁ-

cient) at coordinate (i, j) of the spatial domain and the

q-logarithm domain, respectively. The matrix A

from

can be transformed to q-SVD using the original

SVD. The q-SVD domain of I is deﬁned as SV D(A

We call the resulting U, S, and V

as q-SVD domain.

After performing the SVD, we adjust the values of

U, S, or V

to control the quality of image. In order

to reconstruct the image I

, we apply SVD again to

obtain I

based on the adjusted values of U, S, and

. Finally, we perform the q-exponential function:

(i, j) = exp

(i, j)) = (1 + (1 − q)I

(i, j))

1−q

(4)

Since the values of image pixels are slightly

changed after applying the q-logarithm transform, the

low-frequency of q-SVD domain is considered to be

very suitable for the image watermarking method.

Therefore, the watermarking based on q-SVD can be

expected not only to improve the quality of the em-

bedded image, but also to keep the robustness of the

watermark information.

2.3 Advantage of the q-SVD

In the previous watermarking researches, the water-

mark is directly added into the coefﬁcient of the fre-

quency domain. Therefore, it causes the distortion

in quality of the embedded digital content. In our

proposed frequency domain, q-SVD, the coefﬁcient

of the classical frequency domain is then quantized

by q-logarithm transformation. The modiﬁcation of

(a) (b) (c)

Figure 2: Permuted watermark by the Torus permutation

after p times, where a) p=20, b) p=60, c) p=96.

VISAPP2015-InternationalConferenceonComputerVisionTheoryandApplications

Original Image

RGB=>YCbCr

Conversion

Blocking

Y-component

SVD

q-logarithm

QIM

embedding

Watermark

Torus

permutation

q-exponential

Inverse

SVD

YCbCr=>RGB

Conversion

Last block?

Next block

Watermarked Image

CbCr-component

q-SVD

Figure 3: Embedding based on q-SVD.

the coefﬁcient in q-SVD after watermark embedding

does not affect to the value of the coefﬁcient of the

classical frequency domain after applying the inverse

transform of the q-logarithm transform. Based on this

feature, when the parameter q is changed, the loga-

rithm transformed coefﬁcients are slightly changed.

Hence, the quality of the digital content can be con-

trolled ﬂexibly.

To show the property of quality controlling based

on q-SVD, we employ the Lena image to implement

the classical frequency domain and our q-SVD. In

order to compare the quality of image after inverse

transform, we choose 100 coefﬁcients of S(0,0) from

the same number of coefﬁcients of SVs of the SVD

domain and q-SVD domain. The comparison of the

quality of image after inverse transformation is shown

in Figure 1.

As described in Figure 1, if we change the param-

eters q, its frequency coefﬁcients are also changed.

Fortunately, such kind of change just affects slightly

the quality of image. This feature is suitable for the

watermark embedding. This is the reason why we

propose the q-SVD for watermark embedding tech-

nique.

3 PROPOSED WATERMARKING

TECHNIQUE

In this section, we explain the proposed watermarking

method based on the q-SVD domain.

3.1 Watermark Permutation

Before embedding, we prepare watermark informa-

tion W of size L × L and obtain a binary sequence bits

from W denoted by w

∈ {0,1}, the i-th bit of the wa-

termark. In order to achieve more security, W should

be scrambled before embedding into the original im-

age.

We employ the Torus permutation (Voyatzis and

Pitas, 1996) to scramble W and obtain the scrambled

as follows:







1 1

k k + 1





mod L. (5)

Here, each pixel at coordinate (x, y) of W is moved

to (x

) of W

. W

is obtained by applying p times of

the Torus permutation to the watermark. k is chosen

from 1 to L−1. In our method, the choices of k and p

are unknown to the attackers. The Torus permutation

is periodic with period P which depends only upon

the parameters k ∈ [1,L − 1] and L. So, we set p ∈

[1,P]. Figure 2 shows the periodic property of the

Torus permutation where k = 1 and L = 64. It shows

that the period P of W is 96.

3.2 Watermark Embedding Algorithm

Figure 3 describes the detailed steps in our proposed

embedding method. The embedding process is de-

scribed in following.

Step 1. Convert the RGB image I to YCbCr color

space. Transform the Y-component by using the q-

logarithm transformation to obtain Y

. Divide Y

into

the non-overlapping blocks. The size of each block is

8 × 8.

Step 2. Perform SVD transformation on each

block A

divided from Y

to obtain the SVs in block S

of q-SVD domain.

Step 3. Embed the binary sequence {w

} from

into each SVs of S by QIM method (Chen and

Wornell, 2001) as:

BlindWatermarkingusingQIMandtheQuantizedSVDDomainbasedontheq-LogarithmFunction

(u,v)=



S(u,v)/Q×Q + sgn(S(u, v)) × 3Q/4ifw



= 1,

S(u,v)/Q×Q + sgn(S(u, v)) × Q/4ifw



= 0,

where S(u,v) and S

(u,v) are the SVs of the block S

in the q-SVD domain at the coordinate (u, v) of the

original image and the watermarked image, respec-

tively. sgn function equals to “+” if S(u,v) > 0, “−”

if S(u,v) < 0. b c denotes the ﬂoor function. Q de-

notes the embedding strength chosen to maintain the

quality of embedded image.

Step 4. Perform the SVD again to make the wa-

termarked matrix A and to obtain Y

Step 5. Apply the q-exponential function for Y

to obtain Y

. Include Cb, Cr component with Y

and

transform YCbCr space to RGB color for reconstruct-

ing the watermarked image I

According to the embedding process, we embed

the watermark W

into the q-SVD domain of the Y

component. Thus, we can control the quality of the

embedded image based on two parameters: the pa-

rameter q for q-SVD domain, and the parameter Q for

watermark strength. Therefore, our proposed method

is more ﬂexible than conventional methods using the

SVD domain.

3.3 Watermark Extraction Algorithm

The extraction is performed without using the origi-

nal image and those steps are described in following.

Basic steps involved in the watermarking extraction,

shown in Figure 4, are given as follows:

Step 1. Convert the RGB image I

∗

to YCbCr

color space. Transform Y

∗

component using the q-

logarithm transformation to obtain Y

∗

. Divide Y

∗

into

the non-overlapping blocks. The size of each block is

the size used in the embedding process.

Step 2. Perform SVD on each block A

∗

to obtain

the SVs of each block.

Step 3. Extract the binary sequence of the

watermark from matrices S

∗

based on the following

rule:

∗

(

1 if S

∗

(u,v) − bS

∗

(u,v)/Qc × Q ≥ sgn(S

∗

(u,v)) × Q/2,

0 if S

∗

(u,v) − bS

∗

(u,v)/Qc × Q < sgn(S

∗

(u,v)) × Q/2.

(6)

Step 4. From {w

∗

}, we can obtain the permuted

watermark W

∗

. Permute W

∗

with P − p times using

Torus permutation, we can obtain the extracted water-

mark W

Watermarked Image

RGB=>YCbCr

Conversion

Blocking

Y-component

DWT/SVD

q-logarithm

QIM

extraction

Torus

permutation

Last block?

Next block

Watermark

P - p

q-LFD

Figure 4: Extraction based on q-SVD.

4 SIMULATION RESULTS

4.1 Test Images and Evaluational

Measures

To assess the performance of the proposed algorithm,

we conduct four colors images of the well known

SIDBA (Standard Image Data-BAse) database

. All

test images have size 512 × 512 pixels. The water-

mark image is a binary image with size 64×64 shown

in Figure 2(c).

In order to evaluate the quality of watermarked

images, we employ PSNR (Peak Signal to Noise

Ratio) criterion (Thanh et al., 2014). The PSNR of

N × N pixels of image I(i, j) and

I(i, j) is calculated

by:

www.vision.kuee.kyoto-u.ac.jp/IUE/IMAGE DATA

BASE/STD IMAGES/

VISAPP2015-InternationalConferenceonComputerVisionTheoryandApplications

Table 1: PSNR[dB], NC values using q and Q.

Q q 0.2 0.4 0.6 0.8 1.2 1.4 1.6 1.8 2.0

0.30 PSNR 38.4593 40.3052 41.9444 43.2561 45.5018 46.3084 47.0307 47.5226 48.1225

NC 0.971029 0.964782 0.956682 0.941818 0.918022 0.89495 0.885542 0.862428 0.85067

0.35 PSNR 36.8905 38.7757 40.4758 41.9163 44.2819 45.3985 46.1682 46.8607 47.2839

NC 0.977358 0.969377 0.963476 0.941196 0.938796 0.910206 0.883629 0.876834 0.860438

0.40 PSNR 35.4971 37.4385 39.1805 40.6326 43.2493 44.1945 45.214 46.0372 46.6467

NC 0.980723 0.974017 0.968718 0.94935 0.945882 0.92807 0.896696 0.880235 0.85553

0.45 PSNR 34.1959 36.205 37.9389 39.5019 42.0997 43.2704 44.178 45.13 45.8973

NC 0.984111 0.978375 0.969048 0.962175 0.943057 0.930975 0.903418 0.89034 0.871261

0.50

PSNR 33.0911 35.0678 36.8297 38.4515 41.1907 42.3449 43.3211 44.2749 45.1378

NC 0.984111 0.982753 0.975685 0.975763 0.94511 0.939008 0.917181 0.891637 0.877551

0.55 PSNR 32.0909 34.0549 35.8289 37.4512 40.2472 41.4019 42.568 43.3395 44.4058

NC 0.985472 0.985131 0.979374 0.970037 0.945847 0.943396 0.93117 0.900313 0.887457

0.60 PSNR 31.1681 33.1005 34.9007 36.5316 39.3755 40.5954 41.6975 42.716 43.5228

NC 0.98855 0.985131 0.981737 0.973684 0.945569 0.940174 0.928848 0.911775 0.887944

0.75 PSNR 30.2909 32.2614 34.0562 35.711 38.5476 39.9008 41.0083 42.0944 42.8494

NC 0.987179 0.985813 0.985131 0.97435 0.949017 0.945729 0.92867 0.913636 0.904137

PSNR = 20log

255

MSE

[dB]. (7)

MSE =

N × N

N−1

∑

i=0

N−1

∑

j=0

{I(i, j)−

I(i, j)}

(MSE : Mean Square Error).

To judge the robustness, we use the normalized

correlation (NC) value between the original water-

mark W and the extracted watermark W

(Thanh et

al., 2014). The value of NC is calculated by:

NC =

∑

i=0

∑

j=0

[W (i, j)×W

(i, j)]

∑

i=0

∑

j=0

[W (i, j)]

, (8)

where W (i, j) and W

(i, j) are the original watermark

bit and the extracted bit at the position (i, j).

In our experiments, we calculate the PSNR value

for each embedded image and the NC value for each

watermark extracted from the embedded images and

the attacked images. In general, if the PSNR value

is over 37dB, the quality of the embedded image is

considered to be close to the original image. When the

NC value is close to 1, it means that the watermarking

method is robust against the attacks.

4.2 Quality Evaluation and

Optimization of Parameters Q and q

In our method, by increasing the parameter Q of QIM,

we can achieve the robustness of the watermarking

method. However, the visible distortion of the em-

bedded image is more conspicuous. Fortunately, by

increasing the parameter q of the q-SVD, we can im-

prove the quality of the embedded image with keeping

the robustness of the watermark.

In order to optimize the values of the parame-

ters q and Q, we estimate the parameters q and Q

for obtaining the visual quality of the embedded im-

age and the robustness of the watermark information.

To compare the average PSNR and the average NC

values obtained from the embedded images based on

{Q,q}, the watermark strength Q and the parameter q

of the q-SVD are increased with uniform steps until

we can achieve the minimum acceptable PSNR and

NC value. Those are 37 dB for the PSNR and 0.9 for

the NC, respectively.

The experimental results of the color image, Lena,

are given in Table 1. According to the results shown

in Table 1, it can be observed that we can control the

visual quality of the watermarked image and the ro-

bustness of the watermark information based on the

parameter q of q-SVD domain and the embedding

strength parameter Q. When q is larger, the PSNR

value is larger. It means that the visual quality of the

embedded image is better if q increases. When Q is

larger, the NC value is close to 1. It means that the ro-

bustness of watermark is better if Q increases. There-

fore, to achieve high quality of the embedded image

and the robustness of watermark, we can choose the

appropriate the parameters q and Q for the watermark-

ing method.

In order to ﬁnd the appropriate values for the pa-

rameters Q and q, we set the upper bound and the

lower bound values of these parameters Q and q. In

our experiments, we cannot arbitrarily increase the

value of Q and decrease the value of q because the

quality of the embedded image may become worse in

the case of PSNR< 37 dB. On the other hand, we also

BlindWatermarkingusingQIMandtheQuantizedSVDDomainbasedontheq-LogarithmFunction

(a) (b) (c) (d)

Figure 5: The watermarked color images (q = 1.2,Q = 0.40). (a) Baboon, PSNR=33.39, (b) F16, PSNR=35.90, (c) Lena,

PSNR=43.67, and (d) Scene, PSNR=39.25.

(a) F16, JPEG compression with quality 60,

PSNR=30.42, NC=0.9426

(b) F16, JPEG compression with quality 50,

PSNR=29.99, NC=0.9187

(d) F16, JPEG compression with quality 30,

PSNR=29.05, NC=0.8420

PSNR=29.52, NC=0.8869

(e) F16, JPEG compression with quality 20,

PSNR=28.16, NC=0.7542

(f) F16, JPEG compression with quality 10,

PSNR=26.44, NC=0.5552

Figure 6: Watermarks extracted from embedded image F16 after JPEG compression with quality factors 60, 50, 40, 30, 20,

and 10, respectively, when q = 1.2,Q = 0.40.

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90$

Jia's$method$

Ours(q=1.4,Q=0.6)$

Ours(q=1.2,Q=0.4)$

Quality factor

Figure 7: JPEG compression attack.

cannot decrease the value of Q and increase the value

of q to obtain the better quality of the embedded im-

ages because this may decrease the robustness of the

watermark in the case of NC< 0.9. By considering

the upper bound and lower bound values, the appro-

priate values for the parameters Q and q are in the

gray region shown in Table 1.

4.3 Simulation Results and Comparison

Without loss of generality, we choose {q = 1.2,Q =

0.40} and {q = 1.4, Q = 0.60} to simulate the exper-

imental images. We embed the watermark into the

original image and try to extract the watermark from

the suspected image under intentional and uninten-

tional attacks.

In order to evaluate the robustness of our pro-

posed method, we compare our results with that of the

method of Jia (Jia, 2014). In the case of Jia’s method,

to be fair, we implement his method employing the

grayscale watermark instead of the color watermark.

4.3.1 Robustness Against JPEG Compression

Robust against JPEG compression is a basic require-

ment for the image watermarking. Therefore, we

test our proposed method against JPEG compression

with various quality factors. The simulation results

VISAPP2015-InternationalConferenceonComputerVisionTheoryandApplications

Table 2: PSNR[dB], NC values under JPEG compression with QF (q = 1.2,Q = 0.40)/(q = 1.4,Q = 0.60).

Image Quality factor No attack 90 80 70 60 50

Lena PSNR 43.67/41.08 37.04/36.35 32.75/32.47 31.92/31.70 31.37/31.17 30.96/30.78

NC 0.952/0.951 0.877/0.881 0.808/0.830 0.752/0.786 0.706/0.744 0.667/0.696

F16 PSNR 35.90/32.38 33.85/31.30 31.44/29.80 30.92/29.44 30.41/29.08 29.99/28.81

NC 0.996/0.994 0.989/0.986 0.982/0.978 0.963/0.974 0.943/0.961 0.919/0.946

Baboon PSNR 33.39/32.83 29.22/29.00 25.76/25.66 25.12/25.03 24.62/24.54 24.24/24.17

NC 0.961/0.966 0.906/0.911 0.814/0.823 0.761/0.795 0.725/0.766 0.686/0.725

Scene PSNR 39.25/35.73 31.82/30.86 28.52/28.00 28.09/27.55 27.77/27.34 27.44/27.17

NC 0.981/0.980 0.889/0.887 0.811/0.830 0.662/0.762 0.595/0.673 0.576/0.600

0.8$

0.82$

0.84$

0.86$

0.88$

0.9$

0.92$

0.94$

0.96$

0.98$

10$

20$

30$

40$

50$

60$

70$

80$

90$

100$

Jia's$method$

Ours(q=1.4,Q=0.6)$

Ours(q=1.2,Q=0.4)$

Angle

0.7$

0.75$

0.8$

0.85$

0.9$

0.95$

0.3$

0.5$

0.7$

0.9$

1.1$

1.3$

1.5$

1.7$

1.9$

Jia's$method$

Ours(q=1.4,Q=0.6)$

Ours(q=1.2,Q=0.4)$

Scaling

Figure 8: Geometric attack.

of the color images, Baboon, F16, Lena, and Scene,

are given in Figure 5 and Table 2. Table 2 shows

the NC values of the extracted watermarks and the

PSNR values of the watermarked images after attack-

ing by JPEG compression with different quality fac-

tors (QF). In the JPEG compression, the QF for the

compression process is ranged from 1 to 100, which

denotes the predetermined image quality of the JPEG

compression. When QF is larger, lower compression

ratio of the JPEG image is obtained and better visual

quality of the JPEG image is retained.

According to Table 2, we ﬁnd that even if un-

der high compression ratios, high NC values can be

obtained. It means that our proposed method is ro-

bust against the JPEG compression attack. The im-

age watermarking needs to be robust against, at least,

JPEG compression to ensure for image transmission

via network. Note that, image is always compressed

to JPEG image with quality factor equals to 75∼80

before transmission. Figure 6 illustrates the water-

mark extracted from the embedded image F16 after

the JPEG compression with low quality factors 60, 50,

40, 30, 20, and 10. It is clear that the extracted water-

marks can be easily recognized by human eyes. Addi-

tionally, Figure 7 shows that our methods achieve bet-

ter performance compared to Jia’s method (Jia, 2014).

Therefore, according to the results of Table 2 and Fig-

ure 7, our proposed method is useful under the JPEG

compression and image transmission via network.

Comparing the results of Table 2, we ﬁnd that

when we use {q = 1.4,Q = 0.60} instead of {q =

1.2,Q = 0.40}, the visual quality of watermarked im-

ages are remained, and the robustness of watermark

is improved. Normally, when the parameter Q is in-

creased, the quality of the embedded image is de-

graded. However, by using the larger q of the q-

SVD domain, the quality of the embedded image is

improved.

4.3.2 Robustness Against Geometric and

Processing Attacks

In our experiments, the embedded images are subject

to the following attacks.

Firstly, the geometric attacks are considered as the

ﬁrst challenge because they destroy the synchroniza-

tion in the embedded image. The embedded images

are scaled with different scaling factors (scaling at-

tack). They are also rotated by several angles (rota-

tion attack). The scaling factors with ranging from

0.3 to 1.9 and the rotation angles with ranging from

to 100

are employed in our tests. In order to

obtain good extraction, the attacked image should be

rescaled or re-rotated by an estimated scaling factor

or an estimated rotation angle in the opposite direc-

tion. To be fair, the estimation algorithm in (Thanh et

al., 2014) is performed. The results in Figure 8 shows

that our methods are better than the method of Jia (Jia,

2014) in the rotation attacks. However, our methods

in the scaling attacks are worse than the method in

(Jia, 2014).

Secondly, noise addition attack is common distor-

BlindWatermarkingusingQIMandtheQuantizedSVDDomainbasedontheq-LogarithmFunction

0.8$

0.82$

0.84$

0.86$

0.88$

0.9$

0.92$

0.94$

0.96$

0.98$

0.1$

0.2$

0.3$

0.4$

0.5$

0.6$

0.7$

0.8$

Jia's$method$

Ours(q=1.4,Q=0.6)$

Ours(q=1.2,Q=0.4)$

0.7$

0.75$

0.8$

0.85$

0.9$

0.95$

2%$

3%$

4%$

5%$

6%$

7%$

8%$

9%$

Jia's$method$

Ours(q=1.4,Q=0.6)$

Ours(q=1.2,Q=0.4)$

 p

(a) Gaussian noise addition

(b) Pepper and salt noise addition

Figure 9: Noise addition attack.

0.65%

0.66%

0.67%

0.68%

0.69%

0.7%

0.71%

0.72%

0.73%

0.74%

0.75%

3x3%

5x5%

7x7%

9x9%

11x11%

13x13%

15x15%

Jia's%method%

Ours(q=1.4,Q=0.6)%

Ours(q=1.2,Q=0.4)%

0.58%

0.6%

0.62%

0.64%

0.66%

0.68%

0.7%

0.72%

0.74%

3x3%

5x5%

7x7%

9x9%

11x11%

13x13%

15x15%

Jia's%method%

Ours(q=1.4,Q=0.6)%

Ours(q=1.2,Q=0.4)%

Window size Window size

(a) Median filter

(b) Gaussian blur filter

Figure 10: Filtering attack.

tion in which the noise is added to the embedded im-

age. There are two types of noise, Gaussian white

noise and ‘pepper and salt’ noise, which are normally

added into the embedded images. For the purpose of

our experiments, Gaussian white noise of zero mean

and variance ranging from 0.1 to 0.9, and ‘pepper and

salt’ noise with percentage ranging from 2% to 9%

are added into the embedded image. As shown in Fig-

ure 9, our methods are not as robust against the Gaus-

sian noise and ‘pepper and salt’ noise as the method of

Jia (Jia, 2014). However, as we can see the watermark

image in Figure 6 with NC>0.8, the watermark image

has still good quality. Hence, our methods can be ac-

ceptable under the noise addition attacks since the NC

values of the extracted watermark are over 0.8.

Thirdly, the ﬁltering attack is also tested in

our experiments. There are two kinds of the ﬁlter-

ing attacks, median ﬁltering and Gaussian blur ﬁl-

tering, are used and adopted with window sizes are

3 × 3, 5 × 5, 7 × 7,9 × 9,11 × 11,13 × 13,15 × 15. As

in Figure 10, we can assert our proposed methods are

better than the method in (Jia, 2014) under strong ﬁl-

tering attacks.

Fourthly, we present the shearing attack on the

embedded images. In our experiment, the shearing

percentages in x axes with ranging from 10% to 90%

0.7$

0.75$

0.8$

0.85$

0.9$

0.95$

0.1$

0.2$

0.3$

0.4$

0.5$

0.6$

0.7$

0.8$

0.9$

Jia's$method$

Ours(q=1.4,Q=0.6)$

Ours(q=1.2,Q=0.4)$

Shearing percentages

Figure 11: Shearing attack.

are applied. For re-shearing the attacked images, to be

fair, we also use the method in (Thanh et al., 2014).

After re-shearing, the watermark images are extracted

from the the re-sheared images. As shown in Fig-

ure 11, our methods achieve better performance com-

pared to (Jia, 2014) when the shearing percentages

become higher.

For showing the robustness of our proposed

method, we pick up several extracted watermark im-

age of Lena image compared to Jia’s method. It can

be seen from Figure 12, the robustness of watermark

in the proposed method is better than (Jia, 2014).

In order to show the robustness of our proposed

VISAPP2015-InternationalConferenceonComputerVisionTheoryandApplications

Attack type Jia’s method Ours (q=1.4, Q=0.6) Ours (q=1.2, Q=0.4)

NC=0.86

NC=0.92 NC=0.91

Rotation 40°

NC=0.88 NC=0.86

NC=0.94

Scaling 1.5

NC=0.86 NC=0.85

NC=0.88





NC=0.89 NC=0.86

NC=0.77



NC=0.73 NC=0.71

NC=0.69



NC=0.80 NC=0.87

NC=0.84



NC=0.93 NC=0.94

NC=0.95





Figure 12: Comparison of extracted watermarks in terms of visual perception, NC values for Lena image.

method against common image processing attacks,

we apply several attacks to the embedded Lena image

such as tampered attacks by text “TA MINH”, quar-

ter of cropping, center cropping with radius of cycle

equals to 100, 2/3 of cropping, grayscale and swirl

attack. Here, we extract the watermark image from

those attacked images and calculate the NC values.

The results are illustrated in Figure 13. We can also

easily recognize the watermark by human eyes.

5 CONCLUSION

A robust image watermarking based on the q-SVD

domain using QIM technique have been proposed in

this paper. As far as we know, it is the ﬁrst scheme for

watermarking. The watermark is embedded into the

low-frequency of q-SVD domain in order to achieve

the robustness of watermark and to keep the quality of

embedded image. According to our experimental re-

sults, the embedded watermark can successfully sur-

vive after attacked by image processing attacks, es-

pecially for the JPEG compression. Moreover, since

we have employed QIM method for the watermark

embedding and extracting processes, our methods are

simple and the watermark can be extracted without

the original image. Beside, the tradeoff of robustness

and quality can be controlled by the parameter Q of

QIM and the parameter q of logarithm transform.

Our method requests neither the extra data nor

the original image during the extracting procedure.

Furthermore, since only the authenticator knows the

private key for extraction process, our method can

achieve more security.

BlindWatermarkingusingQIMandtheQuantizedSVDDomainbasedontheq-LogarithmFunction

Figure 13: Some examples of simulation results against common image processing attacks on Lena image with parameters

{q = 1.2,Q = 0.40}.

ACKNOWLEDGEMENTS

This work is supported by the Ministry of Edu-

cation, Science, Sports and Culture, Grant-in-Aid

for Scientiﬁc Research (A) No.24240001 and (C)

No.23500010, a grant of I-System Co. Ltd., NTT Se-

cure Platform Laboratories.

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