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Chaotic scrambling can encrypt watermark information, and. Fresnel transform can provide different diffraction planes with different parameters, so attackers ...
2012 4th International Conference on Intelligent Human-Machine Systems and Cybernetics

A Digital Image Watermarking Algorithm Based on Chaos and Fresnel Transform

Zhaoshan Wang, Shanxiang Lv, Jiuchao Feng

Yan Sheng

School of Electronic and Information Engineering South China University of Technology Guangzhou, China [email protected]

Engineering Department Guangzhou Marine Geological Survey Bureau Guangzhou, China [email protected]

Abstract—In this paper, a digital image watermarking algorithm based on chaos and Fresnel transform is proposed. The original image is transformed into Fresnel diffraction plane by distance parameter, and watermark information is embedded in its amplitude spectrum after scrambled by chaotic sequence. The watermark information can be extracted without original image, and there is little influence on the original image after embedding. Chaotic scrambling can encrypt watermark information, and Fresnel transform can provide different diffraction planes with different parameters, so attackers couldn’t get right watermark information without knowing the parameters in these two processes. During the experiments, the algorithm is also robust against various common attacks, such as filtering, adding noise, JPEG compression and crop and so on. Experimental results show that this watermarking algorithm can provide enough invisibility, security and robustness. Keywords-digital image watermarking; transform; copyright protection;

I.

chaos;

Fresnel diffraction, whereas Fourier transform only describes the Fraunhofer diffraction in the far field. On the research of digital image watermarking using Fresnel transform, Weili Tang and Y. Aoki proposed transforming original image first, then embedding watermarking data [4]. This method is similar to other transform domain methods, but it’s not a blind watermarking algorithm because original image is needed in extracting process. Chao Cao et al. proposed another way, which transforms watermarking data by Fresnel transform, then embeds it in the third level sub-band of the DWT of original image [5]. This method can encrypt the watermarking data by Fresnel transform parameters, but the data becomes complex number after transformed, which adds much difficulty to embedding process. In this paper, we proposed a new image watermarking algorithm based on chaos and Fresnel transform, which uses chaotic mapping to scramble watermark information first, then embeds it into original image’s Fresnel transform domain amplitude spectrum. Chaotic scrambling can encrypt watermark information, protecting it against illegal recognition and stealing, and Fresnel transform can provide different spectrum planes with different parameters, while other transform means have only one spectrum plane. In addition, the embedding location is near the average of energy, so we also realise watermark’s blind extraction. The experiments show that our algorithm has little influence on original image, and has high security and robustness.

Fresnel

INTRODUCTION

Digital watermarking is a technique embedding some information in digital carriers, such as images, audio, radio, etc [1]. Watermarking will not affect the using of original carriers after embedded. As the development of network technology, the application of digital watermarking becomes more and more widely. It provides a good method to protect multimedia works by embedding copyright information in them [2]. Digital watermarking is also an important branch of information hiding, so it can also apply to military highstrength secure communication. According to the embedding location, watermarking techniques can be grouped into two classes: spatial domain methods and transform domain methods. The former is to embed watermark information by directly modifying the pixel values of the original carriers, while the latter is to transform original carriers first, then watermark information is embedded into particular regions of transform domain. DFT (Discrete Fourier Transform), DWT (Discrete Wavelet Transform) and DCT (Discrete Cosine Transform) are familiar transform methods. The advantage of transform domain methods is that the watermark information will spread through out the whole carrier, and this can provide higher invisibility and robustness [3]. In this paper, we use Fresnel transform, which describes the wave propagation in the 978-0-7695-4721-3/12 $26.00 © 2012 IEEE DOI 10.1109/IHMSC.2012.131

II.

FRESNEL TRANSFORM

Fresnel transform describes the wave propagation in the Fresnel diffraction region by simple functions. Supposed there are two planes x1-y1 and x2-y2, if a 2-D object pattern s(x1, y1) locates on the object plane x1-y1, its diffraction pattern F(x2, y2) on observed plane x2-y2 can be described by the following equation [6]. ∞ ∞ jπ F ( x2 , y2 ) = ³ ³ s ( x1 , y1 ) ⋅ exp{− ⋅ −∞ −∞ (1) D 2 2 [( x2 − x1 ) + ( y2 − y1 ) ]}dx1dy1 D = λz (2) where D is a distance parameter,  is wave length and z is the distance between two planes.

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A. Chaotic Scrambling of Watermark Image Watermark image usually has some special significance with strong correlation between adjacent pixels. If the attacker is familiar with embedding algorithm, the watermark information will face the danger of leakage. In order to improve security of the algorithm, we use the classic Logistic mapping to scramble the watermark image. Its kinetic equation is as follows: xn +1 = μ ⋅ xn (1 − xn ) (6)

Eq.(1) can be indicated as the integral of the convolution of function s ( x1 , y1 ) and the following phase function p ( x, y ) ,which also called as propagator .

jπ ⋅ ( x 2 + y 2 )] (3) D According to convolution theorem, Fresnel transform function Eq.(1) can be calculated by two-times of Fourier transforms as follows: (4) F = FT −1[ FT [ s ] ⋅ FT [ p ]] -1 Where FT and FT denote Fourier and inverse Fourier transform respectively. The Fourier transform of phase function p ( x, y ) is: p( x, y ) = exp[−

P( μ ,ν ) = FT [ p] = ³

jπ 2 ( x + y 2 )] ⋅ D exp[− j 2π ( μ x + ν y )]dxdy ∞

³



−∞ −∞

μ ∈ (0, 4] called branch parameter; x0 ∈ (0,1) called initial value. When 3.5699456 ≤ μ ≤ 4 , Logistic where

mapping will be chaotic [8]. This chaotic sequence is easy to implement and extremely sensitive to initial value. If an attacker doesn’t know branch parameter or initial value, he couldn’t get recognizable watermarking data even if embedding algorithm has been leaked [9]. The following is scrambling algorithm: reshape watermark image into one-D sequence W = {w(k ) | k = 1, 2,3,..., L} , then use Logistic mapping to generate a chaotic sequence X = {x(k ) | k = 1, 2,3,..., L} . By sorting X, we get an index sequence I = {i (k ) | k = 1, 2,3,..., L} , which records the original position of each element. Now we can use this index sequence to scramble W as follows: (7) w' (i ( k )) = w( k )

exp[−

(5)

= − jD ⋅ exp[ jπ D ( μ + ν )] where  and  are spatial frequencies. The inverse Fresnel transform is a Fresnel transform of Fresnel diffraction pattern, so we just need to set the distance parameter –D in Eq.(1) to calculate it [7]. Fig. 1 shows the flow of Fresnel transform using a 64×64 binary image where the distance parameter D=0.2. When conducting inverse Fresnel transform, we need to choose D= – 0.2 to get original image, so Fresnel transform provides a secure mechanism for digital watermarking itself. 2

2

where w' is watermark information after scrambled, then reshape it back into two-D. B. Watermark Embedding Fig. 2 diagrams the flow of watermark embedding process of our algorithm. As other transforms, in Fresnel transform domain the low frequency part has great influence on image because of centralizing most energy, while high frequency part is very sensitive to low-pass filtering, so people often choose IF(intermediate frequency) part as data embedding location [10]. This paper also adopted this idea, and watermarking data is embedded in the amplitude spectrum of the point closest to the mean energy.

FT

×P (, ) FT-1

Figure 1. The flow of Fresnel transform.

III.

WATERMARKING ALGORITHM

This paper proposes a new image watermarking algorithm which combines chaos and Fresnel transform in order to increase the security and robustness of system. First, we scramble the watermark image using a chaotic sequence and divide the original image into sub-blocks sized 8×8, then transform each of them into Fresnel transform domain and embed watermarking data into the amplitude spectrum with certain intensity. After that, we need to transform the sub-block inversely into spatial domain. Lastly, combine all sub-blocks together and the embedding process will be completed.

Figure 2. The flowchart of watermark embedding.

The algorithm of watermark embedding can be described as follows:

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A. The Quality of Watermarked Image Watermark’s invisibility indicates the quality of image after data embedded. It can be measured by PSNR (peak signal to noise ratio). A higher PSNR indicates smaller distortion of original image and better invisibility of watermarking data [11]. PSNR for 8 bits gray image is defined as: 2552 PSNR = 10 log10 dB (15) M N 1 [ S ( x, y ) − S ' ( x, y )]2 ¦¦ MN x =1 y =1

Step 1: Divide original image S into sub-blocks sized 8×8. The following is sub-block row i column j: si , j =

x = 8i , y = 8 j

*

S ( x, y )

(8)

x = 8i − 7, y = 8 j − 7

Step 2: Select distance parameter D and carry out Fresnel transform on sub-block s as follows: F ( m, n) = FT −1[ FT [ s ] ⋅ FT [ p ]] 0 ≤ m ≤ 7, 0 ≤ n ≤ 7 (9) Then calculate the mean energy E: 1 7 7 E= (10) ¦¦ | F (m, n) |2 64 m = 0 n = 0 Step 3: Find the point (m0 , n0 ) closest to the mean energy as follows: (11) | E − | F ( m0 , n0 ) |2 |= min(| E − | F ( m, n) |2 |) This coordinate information will be recorded and used in extraction process. Step 4: Embed watermark information in point (m0 , n0 ) as follows: ­° E + σ , w' (i, j ) = 1 | F (m0 , n0 ) |= ® (12) ' °¯ E − σ , w (i, j ) = 0

where S is original image, S ' is watermarked image, M and N are their length and width. In embedding experiment, we set Distance parameter D=0.1; Embedding intensity σ = 5 ; Chaos branch parameter μ = 3.9 ; Initial value x0 = 0.35 . After embedding, we get PSNR=34.91dB, which is high enough to ensure better invisibility. We can also see that the watermarked image looks almost unchanged from Fig. 3(b). B. The Quality of Extracted Watermark Image The quality of extracted watermark image can be measured by NC (normalized correlation), which indicates the similarity between two images.

'

where w (i, j ) is the chaotic scrambled watermark information corresponding to the location of sub-block s, and σ is the intensity of embedding, which is very important to the invisibility and robustness of system. If the intensity is bigger, the watermark will be stronger, but its invisibility will be lower. Step 5: Carry out inverse Fresnel transform on F (m, n) , then we get the sub-block with watermark information. Step 6: Conduct step (1) to step (5) on all sub-blocks, and combine them together to form the watermarked image.

i = a j =b

¦¦ [ w(i, j) ⋅ v(i, j )] NC=

i =1 j =1

i = a j =b

¦¦ w(i, j )

2

i =1 j =1

(16) where w is embedded watermark information, w' is extracted watermark information, a and b are their length and width. In extracting experiment, distance parameter D should be set as –0.1, other parameters should be the same as those in embedding experiment. In the condition of non attack on the watermarked image, we measured that NC=1, which indicates that the watermark image extracted is the same as that embedded. Fig. 3 (d) shows the extracted image.

C. Watermark Extraction Extraction is an inverse process or embedding. First, the watermarked image is divided into sub-blocks sized 8×8, and transformed into Fresnel transform domain. Then we calculate the mean energy, and extract the watermark information according to the following equation: ­°1, F ' (m , n ) ≥ E ' 0 0 v ' (i, j ) = ® (13) ' °¯0, F (m0 , n0 ) < E ' where F ' : Fresnel transform of a watermarked sub-block; E ' : the mean energy of F ' ; v ' (i, j ) : extracted watermark information. Lastly, sort the extracted watermark information by inverse chaotic scrambling as follows. Then we can get the ordinal extracted watermark image. (14) v ( k ) = v ' (i ( k )) IV.

EXPERIMENT AND DISCUSSION

In our experiments, the gray image boat 512×512 is used as original image and a 64×64 binary image is used as watermark image.

(a)

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Original image

(b)

D. Robustness of Algorithm Robustness is another important feature of digital watermarking. When large numbers of digital images transmitted on the network, they often face a variety of attacks. Attackers usually try to tamper or remove the watermark information in images [12], so high robustness is necessary for a watermarking algorithm. In this paper, we conduct experiments by carrying out some common attacks such as filtering, adding noise, JPEG compression and crop on the watermarked image and then extracting the watermark. The simulation results are shown in Table I in details. Fig. 5 shows some of them where mask size of median filtering is 3×3, sigma of Gaussian low-pass filtering is 0.5, density of salt and pepper noising is 0.020 , variance of Gaussian noising is 0.010, quality of JPEG compression is 70 and the crop size is 1/9.

Watermarked image

TABLE I

NC OF WATERMARK IMAGES UNDER DIFFERENT ATTACKS Parameters and NC

Attacks median filtering

mask

3×3







NC

0.876









Figure 3. Watermark embedding and extraction.

Gaussian lowpass filtering

sigma

0.1

0.3

0.5

0.7

0.9

NC

1

1

1

0.982

0.943

C. Security of Algorithm A secure watermarking algorithm should ensure that the embedded watermark would not be acquired illegally. This feature becomes particularly important when watermarking technique is used on secure communication. Compared to other image watermarking algorithm using DCT or DWT, our algorithm has an obvious advantage at the secure respect. Because in DCT or DWT, the transform plane is single, but in Fresnel transform adopted by this paper, there are a variety of transform planes, because every distance parameter can provide one. So attackers couldn’t get the watermark embedding plane without knowing this parameter, let alone the watermark information. In order to enhance the security, watermark image is scrambled by chaotic sequence before embedded. During this process, there are another two parameters: branch parameter and initial value of Logistic mapping, which increase the key space vastly and add more difficulty in cracking the watermark information. Fig. 4 shows how the extracted watermark will be on condition that the above three parameters have a small difference of 0.01. From this experiment, we can see that if there is a little deviation on any parameter, the extracted watermark will be unrecognizable. So the security of our algorithm could be confirmed well.

salt and pepper noise

density

0.010

0.015

0.020

0.025

0.030

NC

0.976

0.969

0.954

0.941

0.921

Gaussian noise

variance

0.006

0.008

0.010

0.012

0.014

NC

0.960

0.931

0.906

0.884

0.870

JPEG compression

quality

90

80

70

60

50

NC

1

1

0.997

0.990

0.967

(c)

Embedded watermark

(d) Extracted watermark

crop (top-left)

size

1/16

1/9

1/4

1/2



NC

0.939

0.892

0.750

0.720



It can be seen from the results that the median filtering impacts much on the watermark image, but we can still recognize it clearly. While according to Gaussian low-pass filtering, salt and pepper noise, Gaussian noise and JPEG compression, the algorithm shows large resistance. It’s worth noting that the robustness against crop is better than some watermarking techniques which embed watermark image directly. This is another advantage of chaotic scrambling, because it scatters the cropped area over the whole watermark image. The influence of crop depends mostly on the crop size, and the watermark image is still recognizable when the size is 1/4 or even 1/2.

(a) median filtering (a)D=–0.11

(b) μ = 3.91

(c) x0 = 0.36



(d) Right extraction

D = −0.1, μ = 3.9, x0 = 0.35 Figure 4. Extracted watermark images with small deviation on parameters.

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(b) Gaussian low-pass filtering

(c) salt and pepper noise

(d) Gaussian noise

Technology, China and By the fund for Higher-level Talent in Guangdong Province, China (No. N9101070). REFERENCES [1]

(e) JPEG compression

S. H. Sun, Z. M. Lu and X. M. Niu, “Digital Watermarking Technology and Its Application”, Beijing, China, Science Press, 2005. [2] J. Z. Li, X. S. Zhang, S. Liu and et.al, “An Adaptive Secure Watermarking Scheme for Images in Spatial Domain Using Fresnel Transform,” in 1th International Conference on Information Science and Engineering, 2009, pp. 1630-1633. [3] N. K. Nishchal, T. Pitkäaho and T. J. Naughton, “Digital Fresnel Hologram Watermarking,” in 9th Euro-America Workshop on Information Optics, 2010, pp. 1-3. [4] W. L. Tang and Y. Aoki, “A Watermarking Method Based on Fresnel Diffraction,” in Fourth International Conference on Signal Processing Proceeding, 1998, vol. 2, pp: 951–953. [5] C. Cao, R. Y. Wang, M. H. Huang and et.al, “A New Watermarking Method Based on DWT and Fresnel Diffraction Transforms, ” in IEEE International Conference on Information Theory and Information Security, 2010, pp. 430-433. [6] S. Kang and Y. Aoki, “Image Data Embedding System for Watermarking Using Fresnel Transform,” in IEEE International Conference on Multimedia Computing and Systems, 1999, vol.1, pp. 885~889. [7] S. Kang and Y. Aoki, “Data Hiding System by Fresnel Transform,” in TENCON 99. Proceedings of the IEEE Region 10 Conference, 1999, vol.1, pp. 625-628. [8] J. C. Feng, “Chaos Signal and Information Processing”, Beijing, China, Tsinghua University Press, 2012. [9] L. J. Zhou, B. Wang and J. C. Feng, “A Digital Watermarking Algorithm Based on Chaos and Fractional Fourier Transformation,” Acta Physica Sinica, vol.57, pp: 2750-2753, May 2008. [10] M. Zhao, M. Jiang and X. D. Gan, “A Digital Watermarking Algorithm Based on Chaos and Fourier Transform,” Computer Technology and Development, vol.21, pp: 189-193, Feb. 2011. [11] L. M Cai, J. C. Feng and Y. H. Xiao, “A Blind Detection Method of Digital Watermark Based on Coordinates Calibration,” Computer Science, vol.34, pp: 234-236, May 2007. [12] Q. L. Huang, J. L. Liu, H. D. Mao and et.al, “Blind Digital Watermarking Technique Using Fresnel Hologram and Phase Encryption Mask,” in IET International Conference on Wireless, Mobile and Multimedia Networks, 2006, pp. 1-4.

(f) crop

Figure 5. Extracted watermark images under different attacks.

V.

CONCLUSION

Invisibility, security and robustness are very important to watermarking technique. In this paper, a new image watermarking approach based on chaos and Fresnel transform has been presented. During experiments, the embedded watermark shows little influence on original image and can be blindly extracted without original image. And there are several parameters in chaotic scrambling and Fresnel transform, which provide high security to the watermark information. The algorithm can also resist filtering, adding noise, JPEG compression and crop well, showing strong robustness against these common attacks. But this algorithm is not perfect, such as the watermark image can only be binary image. Further research should be done to increase its performance. ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Grant No. 60872123), the Joint Fund of the National Natural Science Foundation and the Guangdong Provincial Natural Science Foundation (Grant No. U0835001), the Fundamental Research Funds for the Central Universities (Grant No. 2011ZM0033), South China University of

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