Combined blur and RST invariant digital image ... - Semantic Scholar

2008 International Conference on Signals, Circuits and Systems

Combined blur and RST invariant digital image watermarking using complex moment invariants Hanjie Ji, Jie Zhu, Hongqing Zhu Department of Electronics & Communication Engineering, East China University of Science and Technology Shanghai, 200237 China Abstract-In this paper, we present a watermarking system

transform. However, this method is based on the DFT of the

including hiding, detecting and extracting a confidential

image which is highly sensitive to cropping attack. Image

two-dimension binary watermark, such as a school logo, into a

normalization, provides a convenient way for dealing with

still image, which is robust to geometric distortions and blurring.

geometric attacks; the key idea is to geometrically transform

Watermark embedding is performed in the DCT domain of the

the image into a standard form [3]. In [4], the author had

original image. The watermark detection is as simple as

proposed an image data hiding approach. By quantizing the

computing a set of complex moment invariants to illuminate the

magnitudes of Pseudo-Zernike moments of images, a multibit

robustness

image

watermark can be embedded imperceptibly at low error rates

manipulations. In the extraction scheme, we first estimate the

even without using error control codes, capable of combating

geometric distortion factors of the geometrically attacked

geometric distortions. In [5], a moment invariant-based

watermarked

the

watermark was designed to obtain robustness under image

geometrically attacked image can be transformed back to its

transformations, but the watermark insertion leads to an

original

lost

appreciable change of image contrast, making the image

synchronization for watermark extraction. The watermark is

unpleasantly brighter. We think this method is hard to

then extracted from the corrected image.

implement. All of these methods fail to image blurring

problem

image.

position,

size

under

With

and

general

these

geometric

estimated

shape

to

factors,

recover

the

manipulation. Keywords:

watermarking;

geometric

attack;

Some of common geometrical attacks on images are RST.

blurring;

In this paper, we propose a watermarking scheme in the

complex moment invariants; DCT;

invariant domain using complex moment invariant introduced by [6]. This class of invariants is robust to RST transform as

I. INTRODUCTION

well as blurring. Hence, they can be used to detect the watermark to address the robustness problem. In the

With the ever-growing expansion of digital multimedia and the Internet, the problem of ownership protection of digital

extraction

scheme,

the

watermark

synchronization

is

information has become increasingly important. Thus, digital

implemented by estimating the geometric distortion factors

watermarking was proposed as a viable solution to the need of

using geometric central moments. With these estimated

copyright protection and authentication of multimedia data in

factors, the geometrically transformed image can be

a networked environment. Geometric attacks are among the

transformed back to its original position; size and shape to

most challenging problems in present day watermarking [1].

recover the lost synchronize for watermark extraction. The

Such attacks are very simple to implement yet they can defeat

watermark is then extracted from the corrected image.

most of the existing watermarking algorithms without causing serious perceptual image distortion. Some attempts have been

II. METHODS

made to solve this problem. A method was presented in [2] in A. Complex Moment Invariant

which the watermark is inserted in rotation, scale and translation invariant parameters based on the Fourier-Mellin

978-1-4244-2628-7/08/$25.00 ©2008 IEEE

This study chooses a set of moment invariants proposed by

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2008 International Conference on Signals, Circuits and Systems

invariants which are functions of central moments up to 3rd

Liu et. al [6]. Here, we only consider six simplest moment order. And the relationships between complex moments and central moments are given.

I1 = C21C12 = c 2 (1) + s 2 (1)

Original Image

I 2 = Re ( C20 C122 ) = c ( 2 ) ª¬c 2 (1) − s 2 (1) º¼ + 2 s ( 2 ) c (1) s (1) I 3 = Im ( C20 C

2 12

) = −s ( 2 ) ª¬c (1) − s (1)º¼ + 2s ( 2 ) c (1) s (1) 2

Logo

2

I 4 = Re ( C30 C123 )

Zig-Zag Scan

DCT

Pseudo-Radom Generation

(1)

= − s ( 3) c (1) ª¬c 2 (1) − 3s 2 (1) º¼ + c ( 3) s (1) ª¬3c 2 (1) − s 2 (1) º¼

× ¢

+

+ +

Key

Inverse Zig-Zag Scan

I 5 = Im ( C30 C123 ) = c ( 3) c (1) ª¬c2 (1) − 3s 2 (1) º¼ + s ( 3) s (1) ª¬3c 2 (1) − s 2 (1) º¼

Inverse DCT

I 6 = C02 C20 = c ( 2 ) + s ( 2 ) 2

Watermarked Image

2

Fig.1. the scheme of watermarking embedding

Here 52 ­ c (1) = ( u30 + u12 ) u00 ° 52 ° s (1) = ( u03 + u21 ) u00 2 °° c(2) = ( u20 − u02 ) u00 ® 2 s ( 2 ) = 2u11 u00 ° 52 ° c(3) = ( u30 − 3u12 ) u00 ° 52 °¯ s ( 3) = ( 3u21 − u03 ) u00

First of all, the m×n binary logo that needs embedding is scanned and converted to a bit sequence of watermark L. L = {li ,1 ≤ i ≤ m × n}, li ∈ {0,1} (5)

(2)

The pseudo-random sequence P is generated using a secret key for the correct extraction of the watermark. The length of the pseudo-random sequence is equal to the length of bit sequence of watermark. P = { pi ,1 ≤ i ≤ m × n},

and the complex moment C (pqf ) of (p+q)-order of the image function f ( x, y ) is defined as 1

C (pqf ) =

1+

(f)º ªu00 ¬ ¼

p+q 2

ª º p q « ³³ ( x + jy ) ( x − jy ) f ( x, y ) dxdy » «¬ R2 »¼

u pq = ³

+∞

−∞

_

³

+∞

computed and scanned by the Zig-Zag scan. The 2-D DCT

(3)

coefficient is recorded into 1-D vector T after Zig-Zag scan which re-order the DCT coefficient from low frequency to

−∞

high frequency. On consideration of the balance between the robustness and visual transparency, the watermark is inserted

_

( x − x) p ( y − y ) q f ( x, y )dxdy

(6)

The 2-D DCT form of an M×N original image I is

where upq is central moments as follows: _

pi ∈ {−1,1}

(4)

into original image at mid-frequency X. T = {ti ,1 ≤ i ≤ M × N}

_

(7)

Where x , y is the centroid of the image. In the mid-frequency ranging from (X+1)th to (X+m™n)th of B. Watermark Embedding

the vector T, the DCT coefficient is reconstructed according to

The watermarking system proposed in this article includes

following rules.

the embedding of the watermarking, detection and extraction

ti' = ti + α ⋅ pi ⋅ li

of watermarking. Fig.1. depicts an overview of the watermark

i = 1, 2,.....m × n ,

(8)

where α is a scaling factor to determine the strength of the

embedding method.

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2008 International Conference on Signals, Circuits and Systems

watermark, which controls the trade-off between the transparency and robustness of the watermark. After being reconstructed, the DCT coefficient is re-ordered by the inverse Zig-Zag scan into 2-D vector and then transformed by the inverse DCT to obtain the watermarked image I ' .

C. Watermark Detection and Extraction Watermark detection and extraction is based on the comparison of invariants feature points of images in the feature space. How the watermark detector works, as shown in Fig.2, will be described in detail. The watermark feature space as the 6-D space spanned by the six complex moment invariants I1, I2,…,I6,. In this paper, we use the distance between two points in the space to measure the closeness of the two corresponding images. The distance between two points is defined as follows. °­ I i ( f ) − I i ( g ) °½ d ( f , g ) = max ® ¾ i ¯° max( I i ( f ) , I i ( g ) ) ¿°

(9)

Where I i ( f ) and I i ( g ) are the ith moment invariants of the image f and image g respectively. If the distance d < dth Fig.3. Block diagram of watermark extraction

(dth is threshold), the watermark is present, otherwise is not.

The watermark extraction part is illustrated in Fig.3. Firstly, the extractor should estimate RST factors. Then, the corrupted watermarked image can be restored back to its original size and location. That is, we can recover synchronization of watermark embedding and extracting processing. Once the attacked image is synchronized with the original image, we can extract the watermark in its DCT domain. 1. Rotation angle estimation Using the major principal axis method [7], the principal axis moments are obtained by rotation the axis of the central moments until u’11 is zero. This rotation angle θ is 1 2

§

2u11 · ¸                           (10) © u20 − u02 ¹

θ = − tan −1 ¨

2. Scaling factor estimation If an image is transformed with unequal scale factors k1, k2 along x and y axes, respectively. The scaling transformed moments m00’ and m10’can be obtained as follows:

Fig. 2. The process of watermark detection

' m00 = k1k2 m00 ,  m10' = k12 k2 m10                      (11)

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2008 International Conference on Signals, Circuits and Systems

thus, the scale factors k1, k2 is

k1 =

' 10

(2) Attacks of Watermark Image

' 2 00 10 2 ' 00 10

We applied various attacks to the watermarked images such

m00 m m m ,    k2 =                       (12) ' m00 m10 m m

as rotation, scaling, translation and blurring. Fig.5 shows the

where mpq is moment of (p+q)th-order defined as follows:  m pq = ³³ x y f ( x, y )dxdy p

q

watermarked images after attacking.

(13)

R2

3. Translation factor estimation Due to the fact that image centroid ( x, y ) moves with the image under transform, the translation factor c and d along xand y-axis is: 

(a)

(b)

(c)

c = x − x '   d = y − y '                             (14) Here, ( x ' , y ' ) is coordinate of transformed image. 

(d)

III. EXPERIMENTAL RESULT

(e)

Fig.5 Watermarked images after RST distortion and blurring, (a) rotation of 45 degree,(b)scale(size193×193), (c) scale

In order to test the robustness of the proposed watermarking scheme, we applied various common attacks

(size320×320),(d) translation 40 pixels in x-axis and 60 pixels

such as rotation, scaling, translation and blurring to some

in y-axis, (e) blurring

images. In this paper, the experimental results are obtained (3) Watermark Detection

using the standard image ‘Lena’ shown in Fig.4 (a), a signature image, the logo of East China University of Science

The method of watermark detection was tested. We

and Technology, is shown in Fig.4 (b). The original image was

calculated the distance of feature space between watermarked

signed with factor α = 20 , X=35000, M×N=65535, m × n =

image and the various attacked watermarked image. The

9216, Key=96.

calculated distances d and dth are shown in Table 1. The results show that the proposed method can effectively detect the watermark under the various attacks, such as RST and

(1) Watermark Embedding

blurring.

First, the watermark embedding method was tested. Fig.4(c) shows the watermarked image. The Peak Signal to Noise Ratio (PSNR) of the watermarked image is 34.5 dB.

Table 1

Therefore, the watermarked image meets the need of

Experimental results of distance d for detection after RST

perceptual transparency.

attacking and blurring.

(a)

(b)

(c)

Fig.4 Original image and binary signature image, (a) original image Lena (size 256×256), (b)logo image(size 96×96 ), (c) watermarked image(size 256×256, PSNR=34.5 dB)

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Attacks

d

dth

Rotate 10degree

7.8331E-2

0.1

Rotate 45degree

3.4027E-2

0.1

Rotate 90degree

0

0.1

Scaling(98%)

8.4537E-2

0.1

Scaling(200%)

7.3256E-2

0.1

Scaling(400%)

0

0.1

Translate [20,0]

0

0.1

Translate[ 20,46]

0

0.1

2008 International Conference on Signals, Circuits and Systems

Translate [-60, -50]

0

0.1

impact on the quality of extracted watermark than scaling to

Blurring(radius 3)

1.87E-12

0.1

small size does. Finally, the extracted watermarks after

Blurring(radius 5)

4.16E-12

0.1

translation are shown in Fig. 9. From Fig. 9 and NC value of

Blurring(radius 10)

1.54E-11

0.1

extracted watermarks after translation distortion (shown in Talbe.1.), it is found that the effect on quality of extracted watermark

Here, we take scaling attack as an example to show the

after

translation

attacks

is

comparatively

detector response of 1000 watermarks generated by different

unobvious according to our extraction method. Therefore, the

keys. In Fig. 6, even the tested watermarked image is attacked

proposed watermarking extraction method performs well

by scaling distortion, the distance of correct key (#96) is the only one that is less than the threshold distance dth (dash line),

under translation attacking.

which means that the watermark is detected.

(a)

(b)

(c)

Fig. 7. The extracted signature image after rotation distortion, (a) rotate 10 degree, (b) rotate 45 degree, (c) rotate 90 degree

(a)

(b)

(c)

Fig.8. The extracted signature image after scaling distortion,

Fig.6. Detector response of the watermarked image to 1000

(a) scale(230×256), (b) scale(230×280), (c) scale(512×512)

randomly generated watermarks. (4) Watermark Extraction Once the correct key and the original image are possessed, the signature image can be obtained by the proposed watermark extraction method even if the watermarked image has been attacked by rotation, scaling and translation. In the

(a)

following experiments, we tested the effectiveness of

(b)

(c)

Fig.9. The extracted signature image after translation

proposed extraction method. Fig. 7 illustrates the extracted

distortion, (a) translate 20 pixels in x-axis, (b) translate 20

watermark after several rotation attacks. From the extracted

pixels in x-axis and 46 pixels in y-axis, (c) translate -60 pixels

signature images and their NC value after rotation distortion

in x-axis and -50 pixels in y-axis

(shown in Table.1), one can see that the rotation of 90 degree has the least effect on the quality of extracted watermark. In

Table.1. The NC value of extracted signature after

Fig. 8, the extracted watermarks of scaling attacks are shown.

watermarked image is attacked by rotation, scaling and

From the extracted watermark and NC value of extracted

translation

signature image after scale distortion ( shown in Table 1), one can see that scaling the image to large size has much less

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2008 International Conference on Signals, Circuits and Systems

[4] Y. Xin and S. Liao and M. Pawlak, “Circularly Orthogonal

Attacks

NC

Rotate 10degree

0.91042

Moments

Rotate 45degree

0.85483

Watermarking,” Pattern Recognition, Vol. 40, Issue 12, PP

Rotate 90degree

0.98999

3740-3752, 2007

scale(230×256)

0.95126

scale(256×280)

1.00000

scale(256×512)

1.00000

Translate [20,0]

1.00000

Translate[ 20,46]

1.00000

Translate [-60, -50]

1.00000

for

Geometrically

Robust

Image

[5] M. Alghoniemy and A. H. Tewfik, “Image Watermarking by Moment Inviarants,” IEEE Conference on Image Processing, pp. 73-76, 2000 [6] J. Liu and T. Zhang, “Recognition of the blurred image by complex moment invariants,” Pattern Recognition Letters, 26, pp.1128-1138, 2005 [7] Reeers, A. P., Prokop, R. P. Andrews, S.E., Kuhl, F. P.: Three-dimensional shape analysis using moments and

The results described above show that our watermarking

Fourier descriptors. IEEE Trans. Pattern Anal. Mach. Intell.

method is robust to various kinds of geometrical distortions

10, pp. 937-943, 1988

such as rotation, scaling, translation and blurring. The method can successfully detect the existence of the watermark. With the correct key and the original image, it is also able to extract the watermark after RST distortion, protecting the copyright of the owner. IV. CONCLUSION This study had proposed a watermarking scheme based on the 2-D DCT and use complex moment invariants to detect and extract the watermark. The proposed scheme, which is robust to geometric transform and blurring, can be used for hiding 2-D binary watermark into digital image to identify the copyright. The experimental results show that this method is promising for protection of owner’s copyright of the image. Future work will focus on the watermark extraction of blurring image. REFERENCES [1] D. Zheng, Y. Liu and J. Zhao, “A Survey of RST Invariant Image Watermarking Algorithms,” The IEEE Canadian Conference on Electrical and Computer Engineering, pp. 2086-2089, 2006. [2] J. O’Ruanaidn and T. Pun, “Rotation, Scale and Translation invariant digital image watermarking,” Proc. IEEE International Conference on Image Processing, vol.1, pp.536-539, 1997. [3] M. Alghoniemy and A. H. Tewfik, “Geometric Invariance in Image Watermarking,” IEEE Transactions on Image Processing, vol.13, pp.145-153, 2004 -6-