Research of a Digital Image Watermarking Algorithm Resisting Geometrical Attacks in Fourier Domain

Xiu-mei Wen, Wei Zhao, Fan-xing Meng Hebei Institute of Architecture Civil Engineering

Zhang Jia Kou, China xiumeiwen@163.com, zhaowei_1977@163.com, sir363@163.com

Abstract—A digital image watermarking algorithm based on Fourier domain is proposed. This algorithm calculates an Invariant Centroid of the image and uses it as the origin of logarithm polar mapping (LPM). Then two-dimensional Discrete Fourier Transform (DFT) is performed on the LPM image. And then the amplitude of intermediate frequency is used as the watermarking embedding domain. In order to enhance the safety of the algorithm, it is necessary to encrypt the watermarking signal with the key K, then carry out BCH code on the encrypted signal in order to enhance robustness of resisting various attacks of this algorithm. Therefore the algorithm has a promising prospect of wide use in the fields of the copyright protection of the digital image etc.

Keywords-Image watermarking; Robustness; copyright protection; Fourier Domain

I. INTRODUCTION

Digital watermarking is a new technology of digital media protection, which is the process of embedding hidden messages within digital media such as text, images, video and audio to protect copyright. The hidden messages could be copyright information or secret messages. At the same time these messages have a very little influence on host media and have specific restore methods. These messages should be invisible to illegal receivers. With the global information and ecommerce boosting, the requirement of the copyright protection becomes more and more urgent. Under this condition, the watermark technique is put forward and becomes one of the research hotspots in recent years.

The basic characteristics of digital watermarking are perceptibility, robustness, detectability and safety.

II. DISCRETE FOURIER TRANSFORM

In the development process of signal processing and analysis technology, the Discrete Fourier Transform (DFT) has played an important role and this technology is still very important now. In the digital watermarking embedding process of transform domain, the Fourier transform has been widely used too. The sampling values of Image and audio signal are real numbers, Fourier transform is a complex

transform. It can embed watermark not only in the amplitude of transform domain but also in the phase degree of transform domain if it is satisfied with the real numbers inverse transform. In this paper, the algorithm embedds the watermark in the amplitude of transform domain.

From the definition of two-dimensional discrete Fourier transform, we can draw the conclution that when the origin point of image f(x,y) that is in the space region is shifted to the point (a,b), the corresponding spectrum transform relations is:

)](exp[),(),( bvaujvuFbyaxf +−↔++ (1)

It means that if the spectrum is multiplied by the negative exponent, the phase will be shiftted, but the amplitude does not change. The reason is:

),(]/)(2exp[),( vuFNvyuxjvuF =+− π (2)

The algorithm mainly uses the shiftting characteristic of the spatial domain, it uses the amplitude coefficient after the image uses the Fourier transform as embedding domain of watermark information.

III. LOGARITHM POLAR MAPPING (LPM)

A. Invariant centroid

In order to eliminate the impact of geometric attacks on the images, we intercept a small invariant image L from the original image I and find an invariant centroid IC of L. So, IC is used as the origin of LPM transform.

We calculate IC through an iterative method. Its flow chart is shown in Figure 1.The specific process is: firstly, we carry through low-pass filter on original image I to reduce the impact of signal processing attacks; and then use the following formula to calculate the centroid of C0(Cx,Cy).

∑ ∑=

x yx xyxC ),(ρ

(3)

2009 International Conference on Computational Intelligence and Security

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DOI 10.1109/CIS.2009.30

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∑ ∑=

x yy yyxC ),(ρ

(4)

Thereinto, ∑ ∑=ρx y

)y,x(I)y,x(I)y,x( , it is the image density function. The the centre of a new circle region is C0, the radius is R, then calculate the centroid C1 of the new circle region. C1 is used as the centroid of another circle region whose radius is still R, continue to calculate centroid C2 for the circle region. Repeat the above process until the centroid is convergent to one point, that is Ci = Ci-1 in the flow chart. So, the Ci has become IC, and we can write it Cf. It is very effective to use this method to calculate IC. It can find accurately IC of the images that is attacked by a variety of geometric attack.

Figure 1. flow chart of calculating IC

B. Logarithm polar coordinate transform

Logarithm polar coordinate transforma has a very important character: it can convert the rotation operation of the image to its cyclic shift in the polar coordinates. The image I is processed with LPM using the following formula and Cf is the origin:

θθ sin,cos rr eyex == (5)

Thereinto, both x and y are Cartesian coordinate coefficients, r and θ are coordinate coefficients of LPM. Thus, the rotation operation of the image I is converted to cycle shift of the LM(r, θ) in the logarithm polar coordinate system, it is shown in Figure 2 and Figure 3.

Figure 2. the image L Figure 3. LPM of the image L

Spatial domain displacement of the images leads to its linear displacement of the phase in Fourier transform’s domain, the amplitude remains unchanged. We carry out the Fourier transform on LM (r, θ), and embed the watermarking information into the amplitude, thus it can resist the rotation attacks.

IV. WATERMARKING EMBEDDING ALGORITHM

In this paper, the flow chart of watermarking embedding algorithm is shown in Fig. 4. We intercept a circular image L from original image in which invariant centroid Cf is the origin and R is the radius. Then carry out the LPM transform to the image L whose origin is Cf, thus we can obtain LM(r,θ). Then carry out two-dimensional DFT. From the algorithm principle, we can see that the amplitude

),R(A Θ has the translation and rotation invariance after it is processed with 2-D DFT. It can resist translation with shear and rotation attack. In this paper we use a binary image as the embedding watermark image. It is decreased one-dimensional binary watermarking signal before it is embedded. In order to enhance the safety of the algorithm, we encrypt it with the key K. Then we carry out (63,24) BCH code on the encrypted signal in order to enhance robustness of resisting various attacks of this algorithm. Embed the watermarking signal Wi (1<=i<=M, M is the length of watermark signal that has been encoded) into the middle-frequency amplitude of Fourier transform, use the following formula to embed:

)1)(,(),(' iiiii wRARA α+Θ=Θ (6)

Thereinto, α is the embedding amplitude. The watermarking signal Wi also embeds

into ),R(A ii Θ−− , because Foutier transform coefficient has conjugate symmetry characteristic, otherwise the Foutier inverse transform will be error.

In fact, the image L doesn’t be carried out the LPM transform. From the Figure 4 we can see that the

),R(A ii Θ′ does the IDFT, then subtract ),( iiRA Θ and obtain LMW(r,θ), it can embed into image L directly after doing ILPM conversion. It may lead to decrease the image quality because part of the information will be lost in the ILPM process. Its advantage is that only the embedding watermarking signal suffers damage because it does the ILPM conversion, but the image L does not suffer damage. Finally, the image L is put into the original image I.

low-pass filter

calculate centroid Ci that origin is Ci-1 and R is radius

i=1

Ci= Ci-1

i=i+1

original image I

Y

N

calculate centroid C0 of the original image

Invariant center Cf

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Figure 4. flow-chart of embedded watermarking

V. WATERMARKING DETECTION ALGORITHM

Calculate the IC(Cf') of the image I' which has been

embedded watermarking information; Extract a circle image L' whose IC is Cf

' and radius is R; finally, carry out LPM and 2-D DFT on the image L', fetch the middle-frequency amplitude ),R(A ii Θ′ of embedding watermarking information. Calculate the watermarking signal Wi

' using the following formula:

α/)),(),(( iiiii RARAW Θ−Θ′=′ (7)

Thereinto, α is watermarking embedding intensity and ),( iiRA Θ is the corresponding middle-frequency amplitude value of the original image. Process the Wi

' with BCH decoding and using key K to decrypt, thus we can obtain the embedded watermarking image.

VI. EXPERIMENT RESULT

In the experiment, we use MATLAB software to simulate, the original image is the Lena image of 256×256. When we calculate the centroid, the radius R is 64; When we extract the circle image L, the radius R is also 64. The watermarking is a binary image in the experiment, shown in Figure 5(48×48), watermarking embedded intensity factor

α=0.2, the peak signal-to-noise ratio of embedded watermarking image is 43.7dB. The human eyes cann’t feel the difference between the embedded watermark image and the original image, shown in Figure 6.

Figure 5. watermark Figure 6. image I' of embedded watermark

To do the cutting shift(shown in Figure 7) and rotation(shown in Figure 9) respectively for the image with embedded watermarking, watermark extraction results are shown in Figure 8 and Figure 10, the image is clearly discernible. We can also extract watermarking image after the zoom image is corrected to the original image, the effect is poor, but it can be identified. To do JPEG compression (shown in Figure 11) and mean filter (shown in Figure 13) respectively for the image with embedded watermarking, watermark extraction results are shown in Figure 12 and Figure 14, the watermarking image can still be identified. Therefore, this algorithm has better robustness, detectability, it can resist geometric attacks and signal processing attacks in the mean time.

Figure 7. I' after shifting

Figure 8. extracted watermarking image from Fig. 7

LM(r,θ)

P(r,θ)

encrypt

BHC code

Modify middle-frequency amplitude

2-D DFT

LPM

2-D IDFT

+

-

ILPM

Binary watermark signal Key K

Wi

A'(R,Ө)

LM ' (r,ө)

A(R,Ө)

circular image embedded watermark image Lw

LM W(r,ө)

IL M W(r,ө)

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Figure 9. I' after rotating 15 degrees

Figure 10. extracted watermarking image from Fig. 8

Figure 11. I' after JPEG compression

Figure 12. extracted watermarking image from Fig. 11

Figure 13. I' after 3×3 mean filter

Figure 14. extracted watermarking image from Fig. 13

VII. CONCLUSION The new watermarking algorithm is proposed in this

paper, it can resist geometric attacks including shift with cutting and rotation, it can resist zoom attack by correction. This watermarking algorithm can also resist signal processing attacks including JPEG compression, mean filter and so on. This algorithm enhances robustness because it does pretreatment of encryption and BCH coding before the watermarking signal embeds into the image. Experimental results show that this method has good invisibility and it can resist all kinds of image processing attacks, it is an effective method of image identification.

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