Print-and-Scan Resilient Watermarking Through Polarizing DCT Coefficients

Yuan-Liang Tang* and Sheng-Yu Tseng

Department of Information Management Chaoyang University of Technology

Taichung, Taiwan, R.O.C. *yltang@cyut.edu.tw

Abstract-Digital watermarking techniques have been used to assert the ownerships of digital images. That is, the

ownership information is embedded to an image as a watermark such that the owner of the image could be

identified. However, there are also many attacks trying to break or remove the embedded watermark. Therefore, the watermark should be very robust against various kinds of attacks. Among them, the print-and-scan (PS) attack is very

challenging because it not only alters the pixel values but also changes the positions of the original pixels. In this paper, we propose a watermarking system operating in the discrete cosine transform (DCT) domain. The polarities of the DCT coefficients are modified for watermark embedding. This is done by considering the properties of DCT coefficients under the PS attack. The proposed system is able to maintain the image quality after watermarking and the embedded

watermark is very robust against the PS attack as well.

Keywords-digital watermarking, print-and-scan attack, discrete cosine transform, geometric distortion

I. INTRODUCTION

As multimedia technologies advance, it is very easy to copy, modify, and distribute digital images. However, such convenience also brings about many problems; for example, unauthorized copying may lead to copyright infringement. Currently, watermarking techniques are used to solve the copyright problem by embedding the copyright information into the image for asserting its ownership. The embedded information thus should be very robust against any attempts to break or remove the watermark. Among the various attacks, the print-and-scan (PS) attack is very challenging because it not only alters the pixel values but also changes the positions of the original pixels. Most of the modem watermarking systems would fail under such an attack. In this paper, we propose a novel PS-attack resistant watermarking algorithm for color images. The algorithm operates in the discrete cosine transform (OCT) domain and takes advantages of the characteristics of the OCT coefficients under the PS attack. We first investigated the influence of the PS attack on the image pixels as well as the OCT coefficients. And then, the results of the investigation were used to design a robust watermarking algorithm which can resist the PS attack.

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II. PS ArrACK AND PS-RESISTANT WATERMARKING

After the PS attack, an image will experience two kinds of alterations: pixel value changes and geometric distortion.

A. Pixel Value Changes

The brightness, contrast, and colors of image pixels will be affected by the PS attack. Shi et al. [1] created an artificial image to test the impacts of PS on pixel values. The image was created by varying the pixel values from 0 to 255 and back to 0 again, and in the direction from lower­left comer to the upper-right comer. The gray levels of the image pixels is thus uniformly distributed. After the PS attack, the range of gray levels is reduced. That is, dark pixels become brighter and bright pixels become darker, as shown in Fig. 1.

gray'.ve'

(c)

Figure I. (a) The original image, (b) original histogram, (c) histogram after PS

B. Geometric Distortion

Another effect of the PS attack is that the image will experience geometric distortion such as scaling, rotation, and cropping. Most of these distortions result from improper human operations during the printing and scanning processes. Geometric distortion destroys the synchronization of the watermark, that is, the embedding positions of the watermark are changed so that detection of the watermark using the original positions would fail. These distortions need to be corrected before watermark detection.

C. PS-Resistant Watermarking Techniques

A number of researchers have made some efforts to tackle the PS attack program. Guo et al. [2] divided an image into blocks and performed the digital Fourier transform (OFT) on those blocks with complex texture. And then, the values of the coefficients in the mid-frequency areas are increased for watermark embedding. As complex textures are easily smoothed by PS, the embedded watermark is very vulnerable. Therefore, their method is more suitable for high-quality images.

Solanski et at. [3] used the differential quantization index modulation to embed information in the OFT phase spectrum of images. The embedding is done by quantizing the difference in phase of adjacent frequency locations. Their method well preserves the image quality; however, detection of the watermark requires the original image.

Jamming et al. [4] divided an image into blocks, performed OCT on each block, and then selected the coefficients whose absolute values are greater than some threshold for watermark embedding. The watermark is embedded by setting the relation between the numbers of positive and negative coefficients in each block. However, their method has higher error rate.

Shi et at. [4] also divided the image into blocks, followed by performing OCT on each of them. The mid­frequency coefficients are then selected for watermark embedding. A watermark bit is embedded by setting the all the OCT coefficients either to be positive (for embedding bit 1) or negative (for embedding bit 0). Such a method surely has huge impact on the image quality if a great number of coefficients change their signs. To overcome, Shi et al. recorded the relationship between positive and negative coefficients in each block: if the number of positive coefficients is more than that of negative ones, 1 is recorded; otherwise, ° is recorded. Therefore, the watermark bit is embedded by changing the signs of the coefficients with fewer numbers. As a result, the relationship information has to be stored for watermark detection later. This makes their system an informed watermarking system, rather than a more ideal blind watermarking system.

In this paper, we propose a novel watermarking algorithm operating in the OCT domain. The signs of the OCT coefficients are manipulated for watermark embedding which leads to a very robust watermarking system against the PS attack. The image quality is preserved to a high standard as well.

III. THE PROPOSED METHOD

Our method is designed based on the properties of the OCT coefficients under the PS attack. The watermark is embedded by changing the polarity of a set of OCT coefficients. The polarity is defined as: if the number of the positive coefficients is greater than that of the negative ones, it is positive polarity. Otherwise, it is negative

polarity. The details of the watermarking system are described as follows.

A. Embedding Process

Fig. 2 briefly delineates the watermark embedding process: (1) The red channel of an RGB color image is first resized to a standard size of MxM, and is divided into blocks of size NxN, which produces (MIN)2 blocks in total. As the border blocks are more vulnerable to the PS attack, only the internal R = (MIN-2)2 blocks are used for embedding. (2) Perform OCT on each of the R blocks, followed by zig-zag scanning the coefficients to produce a 10 sequence of length }fl. (3) Supposing the watermark W consists of m bits: W = {Wi I Wi = 0, 1; i = l..m}, m mid­frequency coefficients are selected out of the }fl coefficients in each sequence for watermark embedding. This produces an mxR matrix. That is, one bit is embedded in R coefficients. (4) A secret key is used to generate a sequence of bits as the watermark, and each of the watermark bit is embed by changing the signs of the R coefficients such that they become positively (bit 1) or negatively (bit 0) polarized. (5) The final watermarked image is produced by inversely zig-zag scanning the watermarked coefficients, restoring to the original block positions, resizing to the original image size, and finally combining with the original G and B color channels,

Original Watermarked image image

Figure 2. The embedding process

In order to increase the robustness of the watermark, the embedding strength should be as high as possible. In other words, we should create a strong polarity by modifying more coefficients. However, modifying too many coefficients would also decrease the image quality. It is thus a trade-off between robustness and image quality, and some experiments were conducted to analyze how to balance between them. Supposing M= 512 (image size) and N= 32 (block size), the number of blocks are: R = 14x14 = 196. Also, let the length of the watermark be m = 1,024, thus 1,024 sets of mid-frequency coefficients are selected, with each set containing 196 coefficients. The values of coefficients before and after PS in each set are compared,

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and the results showed that less than one third of them changed their signs, as depicted in Fig. 3.

<Il 200

ii 150 U

}E 0)

100 0 () ....

� 0

50 .8 E 0 :::l

Z 0 200 400 600 800 1000

Block nwnber

Figure 3. Number of coefficients changing polarities

Furthermore, if we order the coefficients according to their absolute values and consider only the first 1/3 and 2/3 great-valued coefficients, the numbers of coefficients that change their polaries are in fact very few, as shown in Table 1. To conclude, OCT coefficients with a great value are relatively stable under the PS attack.

TABLE 1. RATIO OF GREAT-VALUE OCT COEFFICIENTS

CHANGfNG THEIR SIGNS AFTER PS

First 1/3 First 2/3 Lena 0.99% 6.13% Baboon 0.05% 2.20% Peppers 0.93% 3.08% Average 0.66% 381%

Base on the above analysis, supposing there are p and n positive and negative coefficients, respectively, the watermark embedding amounts to changing some of the coefficients' signs such that the resulting numbers of positive and negative coefficients maintain a predefined ratio, k (k > 1). That is:

p' = kn' or n' = kp',

where p' and n' are the numbers of positive and negative coefficients after modification, respectively. This is very different from Shi et al. 's method in that only a certain number of coefficients change their signs instead all of them. Furthermore, the signs of those coefficients whose absolute values are in the leading 10% remain intact in order to better preserve the image quality. After changing the polarity, all coefficients are multiplied by an embedding strength a. for further enhancing the robustness. The embedding process is described as follows:

(1) If Wi = 1: If p < kn, achieve a positive polarity by changing the signs of some coefficients such that p'

= kn'. else (Wi = 0):

If n < kp, achieve a negative polarity by changing the signs of some coefficients such that n' = /cp'.

(2) MUltiply the R coefficients by a. (a. > \) for further increasing the embedding strength.

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After the watermark embedding, perform inverse OCT on each block, rearrange the blocks, resizing the the original image size, and then combine the three color channels to produce the watermarked image.

B. Watermark Detection

Before actual detecting the watermark, we need to perform geometric correction on the image first.

/) Geometric Correction During the printing and scanning process, the image

may experience geometric distortions as a result of human operation errors. The most common are rotation and scaling. The former is due to improper alignment of the paper image during scanning, and the latter is due to different resolution settings between printing and scaling. In our method, the rotation distortion is recovered by first detecting the border lines of the scanned image using the Hough transform, and then rotating the image back accordingly. And the scaling distortion is corrected by setting the image to a standard size. In the scanned image, to detect the border lines of the original image, we first detect the edge pixels in the image. And then, the Hough transform is performed to detect the four border lines, whose slopes are used to rotate the image back to its proper orientation. The process is delineated in Fig. 4.

Figure 4.

Edge detection; clearing center region points

Geometric correction

Geometric correction

As the Hough transform is very time consuming, it is necessary to develop some means to reduce the computation complexity. Since the Hough transform is computed based on edge pixels, the more edge pixels found in the image, the more time it will spend on computing. Because we are interested in finding only the four border lines, pixels less possible of belonging to the borders should not be taken into account. Thus, if the rotation angle, e, is supposed to be within some range, say -\ 0° < e < 10°, which is a reasonable assumption for a human trying to align a paper image properly during scanning, we may consider only those pixels which are in the possible regions for the borders to appear, as shown in gray in Fig. 5. That is, the edge pixels in the center region (shown in white) can be ignored. Such a consideration greatly reduces the computational cost.

Figure 5.

M

Possible region (shown in gray) in which borders may appear

2) Watermark Detection The watermark detection is proceeded as follows. First

extract the red channel of the scanned color image, and then perform geometric correction, followed by scaling the image to the predefined MxM standard size. The rest of the steps are similar to those in the embedding process: divide the image into blocks of size NxN, select internal R blocks, performance OCT on each block, select m mid-frequency coefficients to form an mxR array, and finally detect each watermark bit in each set of R coefficients using the following decision formula to obtain the detected watermark W':

w;=I, ifp'?n'

1 '

w; =0, otherwise

The detected watermark, W', is then compared with the watermark, W, generated by the secret key, which produces the error rate E as follows. If E is less than some threshold, the watermark is declared to exist.

1 I

m I ' 1 E=- w-w. m i::::l I I

IV. EXPERIMENTAL RESULTS

Three color images were tested in our experiments: Lena, Baboon, and Peppers. The standard image size MxM and block size NxN are set to be 512x512 and 32x32, respectively. There are thus (512/32) x (512/32) = 16x16 =

256 blocks in total, in which the internal R = 14x 14 = 196 block are chosen for watermark embedding. The length, m, of the watermark is 195, which means m mid-frequency coefficients are selected in each block, and a watermark bit is embedded in a set of R coefficients by changing its polarity.

The HP Color Laser Jet 380_dn laser printer and the EPSON 1640_Su scanner were used to print and scan the test images, respectively, both with resolution of 600 dpi. We set two embedding strengths, (J. = 1.5 and 2, to test the system, and the results of the error rates and the qualities of the images (PSNR) are shown in Table 2.

TABLE 2. ERROR RATES AND PSNRs

Embedding Error rate PSNR strength

Lena 1.5 0.5% 39.9 2 0% 38.2

Baboon 1.5 0.5% 39.5 2 0% 37.1

Pepper 1.5 3.5% 44.1

2 0% 41.6

The above experimental results clearly show that if the embedding strength is set to 2, the watermark are correctly detected (i.e., error rate = 0%), and the watermarked image has high PSNR as well. In comparison with the 5.5% average error rate of Shi et al. 's method, the performance of our method is much better. In addition, the PSNRs of the watermarked images produced by our method are also better than theirs, as shown in Table 3. Thus, our method produces more robust watermarks, and the quality of the watermarked images are better as well.

Lena Baboon Peppers

TABLE 3. Shi et (l1.'s

method 33.6 32.5 33.6

COMPARISON OF PSNRs

The proposed method a=1.5 a=2

39.9 38.2 39.5 37.1

44.1 41.6

V. CONCLUSIONS

In this paper, we proposed a watermarking system which operates in the OCT domain and is very robust against the PS attack. The watermark is embedded by setting the polarity of OCT coefficients. By analyzing the PS characteristics, carefully choosing the OCT coefficients for modification, and well setting the embedding strength, the system is able to achieve a high rate of watermark detection. The qualities of the watermarked images are also well preserved.

REFERENCES

[I) Dongcheng Shi, Qi Wang, and Chao Liang, "Digital Watermarking Algorithm for Print-and-Scan Process used for Printed Matter Anti­Counterfeit," Congress on Image and Signal Processing, Vol. 5, 2008, pp. 697-70 I.

[2] Chengqing Guo, Guoai Xu, Xinxin Niu, Yixian Yang, and Yang Li, "A Color Image Watermarking Algorithm Resistant to Print-Scan," Wireless Communications, Networking and Information Security, 2010, pp. 518-521.

[3] K. Solanki, U. Madhow, B.S. Manjunath, S. Chandrasekaran, and I. EI-Khalil, "Print and Scan Resilient Data Hiding in Images," Information Forensics and Security, Vol. 4, 2006, pp. 464-478.

[4] J. Jamming, X. Yuhong, and H. Huiman, "A Practical DCT Based Blind Image Watermarking Scheme for Print-and-Scan Process," HP Laboratories Technical Reports, Vol. 7538, 20 10.

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