Adaptive Watermarking Using Relationships between ... - CiteSeerX

Adaptive Watermarking Using Relationships between Wavelet Coefficients Yueh-Hong Chen, Jun-Min Su and H.-C. Fu

Hsiang-Cheh Huang

Dept of Computer Science and Information Engineering National Chiao-Tung University HsinChu, Taiwan, 300 ROC Email: {yuehhong, sujunmin, hcfu}@csie.nctu.edu.tw

Department of Electronics Engineering

Abstract— In this paper, we propose an approach that hides watermarks in relationships between wavelet coefficients. This approach would minimize the perceptual distortion of watermarked images, measured with PSNR or just noticeable distortion (JND). Therefore, the strength of watermarks can be enlarged to increase the robustness of the watermarks, while keeping the quality of watermarked images visually accepted. Experimental results show that the watermark is still detectable after common image processing operations such as JPEG compression, Gaussian filtering and sharpening.

I. I NTRODUCTION Digital watermarking is one of the active research topics in the multimedia area. Among all kings of digital content, image data has attracted much attention because of its popularity on the Internet. Moreover, an image watermarking scheme could possibly deal with video data with minor modifications. Several different watermarking methods have been developed in recent years to deal with image data [1]. Hiding watermarks in the relationship between values is one kind of the watermarking approaches whose detection process can be performed blindly. These values with watermarks embedded may be pixels in spatial domain or coefficients in frequently domain. The detector can extract the watermark by comparing these values, and then correlate the result with the original watermark to determine if the watermark exists or not. Several watermarking methods based on this idea have been proposed. In [3], the pixels of an image are divided into two groups. The sum of the pixels in one group is subtracted from the sum of the pixels in the other group to obtain a detect statistic, which is then compared against a threshold to determine whether the watermark is present. In [4], selected coefficients in 8×8 DCT blocks of the image are grouped as ordered pair. Each bit of watermark information is encoded in each pair, according to whether or not the first coefficient is larger than the second. [5] uses middle frequency coefficients selected from the same or neighboring 8×8 DCT blocks to embed watermarks. A similar method using coefficients selected from the same DCT block was proposed in [6]. However, these approaches would not take the quality of images into account when embedding watermarks. Thus, in this paper, an adaptive watermarking approach using relationship between wavelet coefficients is proposed. While

Hsiao-Tien Pao Department of Management Science National Chiao-Tung University HsinChu, Taiwan, 300 ROC Email: {huangh, htpao}@cc.nctu.edu.tw embedding watermarks, the proposed approach can adaptively optimize the image quality in the sense of PSNR or just noticeable distortion (JND). By minimizing the images distortion, the strength of watermarks can be enlarged to increase the robustness of the watermarks, while keeping the quality of watermarked images visually accepted. The experimental results shown in section III illustrate the performance of the proposed approach. II.

WATERMARKING USING RELATIONSHIPS BETWEEN WAVELET COEFFICIENTS

Two watermarking algorithms using relationships between wavelet coefficients are proposed in this section. The manner to represent a binary string using relationships of coefficients is first described. A PSNR-maximized algorithm is then proposed in subsection II-B for comparing with most existing approach. Finally, an extension is made on the algorithm such that JND [2] can be used as a measurement of image quality. A. Hiding binary string into relationships of wavelet coefficients It is assumed in this paper that a watermark consists of 0’s and 1’s. All bits of the watermark are embedded into a image with the same manner, separately. To embed one bit of the watermark, the image is firstly transformed into Haar wavelet domain, and then a number of coefficients in LH2, HL2 or HH2 subband are randomly chosen and modified. Finally, inverse wavelet transform is applied to obtain the watermarked image. When one bit of the watermark is embedded, an userspecified number of coefficients are chosen randomly. These coefficients are then modified such that the first one, in the order of being chosen, is the largest if an ’1’ is embedded. If a ’0’ is embedded, the coefficients should be modified such that the first one is the smallest. Suppose ci , i = 1, · · · , n are the chosen coefficients, and n is the number of coefficients. The modified coefficients will satisfy equation (1)  ′ ′ ′ ′ c1 ≥ max(c2 , c3 , · · · , cn ) if W = 1 (1) ′ ′ ′ ′ c1 ≤ min(c2 , c3 , · · · , cn ) if W = 0

′

where ci , i = 1, · · · , n are the modified coefficients, W is one bit of watermark information. For example, if an ’1’ is to be embedded and five coefficients, -5, 112, -1, 107 as well as 13, are chosen, then a straightforward manner is to increase the value of the first coefficient, -5, to a value equal to or larger than 112. Among modified coefficients, suppose the difference between the first and second largest (smallest) coefficients was specified by a parameter δ, δ ≥ 0. The first coefficient, -5, should be increase to 112 + δ to embed an ’1’. The simplest extracting algorithm is to pick up the same coefficients and determine if the first coefficient is the largest or smallest. However, the watermarked image may be distorted such that the first coefficient is no longer the largest (smallest). Hence, the purposed extracting algorithm is to compare the first coefficient to the largest and smallest ones among remaining coefficients. If the value of the first coefficient is closer to the largest one among remaining coefficients, an ’1’ will be extracted; otherwise, a ’0 will be extracted. The extracting process is described in equation (2): ( c”max +c”min ” ′ 1 if c ≥ 1 2 W = (2) 0 otherwise c”max = max(c”2 , c”3 , · · · , c”n ) c”min = min(c”2 , c”3 , · · · , c”n )

(3)

where c”i , i = 1, · · · , n are the coefficients obtained from a ′ image, and W is the extracted watermark bit. Then, a normalized correlation (NC) value between the extracted binary string and the watermark is calculated and compared with a threshold to determine if the watermark exists or not. B. PSNR-maximized embedding The main idea of the PSNR-maximized embedding algorithm is to modify more than one coefficient at the same time. On embedding an ’1’, if the first coefficient c1 is increased to x+δ, then all coefficients larger than x should be decreased to x to fit the rule shown in equation (1). Therefore, it is possible to find the optimal value of x such that the watermarked image have the highest PSNR value. If the mean square error (MSE) of the modified coefficients is minimized, the PSNR value is maximized simultaneously. Suppose a bit of ’1’ is to be embedded into n coefficients. If c1 is increased to x + δ and all coefficients larger than x are decreased to x, the square error (SE) value can be calculated as equation (4): X (ci − x)2 (4) SE(x) = ((x + δ) − c1 )2 + ci >x

Then the minimum of SE(x) can be obtained by finding out the value of x where the first derivative of SE(x) is equal to 0. The first derivative of SE(x) is shown in equation (5), and the optimal value of x is shown in equaion (6). X d (x − ci ) (5) SE(x) = 2 × (x + δ − c1 ) + 2 × dx c >x i

x=



P

ci >x

ci



+ c1 − δ

k+1

,

i = 1, · · · , n

(6)

where k is the number of coefficients larger than c1 . In equation (6), it is assumed that only k largest coefficient and c1 be modified. Therefore, the value of x should be larger than the (k + 1)-th largest coefficient but smaller than k-th largest coefficient. The algorithm to find the optimal value x is as follow:

Obtain d1 , d2 , · · · , dn by sorting c1 , c2 , · · · , cn such that d1 ≥ d2 ≥ · · · ≥ dn Suppose c1 is the (k + 1)-th largest value If (k + 1) = 1 xopt = d2 , Stop End If For i = 1 to P k i
dj +dk+1 −δ j=1 x= i+1 If di+1 < x ≤ di xopt = x, Stop End If End For xopt = c1 , Stop After the algorithm finishes, the optimal value of x can be found. c1 can then be modified to x + δ, and all coefficients larger than x be modified to x to embed a bit of ’1’. A similar algorithm to find the optimal value to embed a ’0’ is as follow:

Obtain d1 , d2 , · · · , dn by sorting c1 , c2 , · · · , cn such that d1 ≤ d2 ≤ · · · ≤ dn Suppose c1 is the (k + 1)-th smallest value If (k + 1) = 1 xopt = d2 , Stop k i For i = 1 to P
dj +dk+1 +δ j=1 x= i+1 If di+1 > x ≥ di xopt = x, Stop End If End For xopt = c1 , Stop Finally, c1 is decreased to x − δ, and all coefficients smaller than x be increased to x to embed a bit of ’0’. Continuing the example in previous subsection, if δ = 0, the SE(x) value is:  (x − 112)2 + (x + 5)2     if 107 ≤ x < 112    (x − 112)2 + (x − 107)2 + (x + 5)2 SE(x) = if −1 ≤ x < 107     (x − 112)2 + (x − 107)2 + (x + 1)2 + (x + 5)2    if −5 ≤ x < −1 By applying the proposed algorithm, the optimal value of x, about 71.3, can be obtained. The curve of SE(x) is shown in figure 1. It is clear that SE(x) is the minimum when x = 71.3.

Fig. 1. Curves of (x − 112)2 + (x + 5)2 (curve 1), (x − 112)2 + (x − 107)2 +(x+5)2 (curve 2) and (x−112)2 +(x−107)2 +(x+1)2 +(x+5)2 (curve 3)

C. perceptually adaptive embedding Several researchers have been indicated that PSNR may not be a ideal measurement of image quality [2]. Thus, the algorithm proposed in previous subsection is extended so that the watermark can be embedded based on JND. A level of distortion that can be perceived in 50% experimental trials is often referred to as just noticeable difference, or JND [2]. Suppose all the JND values are larger than zero. The perceptual distortion could be measure by weighting with the JND value the difference between original and modified coefficients, as shown in equation (7)  2 X  2 (x + δ) − c1 ci − x SW E(x) = + (7) w1 wi c >x i

where wi , i = 1, · · · , n is the JND value of ci . Then, similar result can be obtained: X  x − ci  2 × (x + δ − c1 ) d (8) + 2 × SW E(x) = dx w12 wi2 c >x i

The optimal value of x can then be obtain as shown in equation (9)   P ci + wc12 − wδ2 w2 1 1 ci >x i   x= (9) P 1 1 + 2 2 w w 1

ci >x

i

According to equation (9), an algorithm similar to that described in previous subsection can be used to find the optimal value of x for embedding watermarks. Intuitively, the extracting algorithm described in Section IIA can be used to extract watermarks embedded with PSNRmaximized or perceptually adaptive embedding algorithm. In the next section, several experimental results are presented to show the robustness and fidelity of the proposed algorithms. III.

EXPERIMENTAL RESULTS

In this section, results of experiments using Strmark [7] are proposed to show the robustness of the proposed algorithms. An 1000-bit watermark was generated randomly and

used throughout the experiments. To embed one bit of the watermark, twelve coefficients were chosen from LH2, HL2 or HH2 subband. In other words, n was equal to 12 in our experiments. The strength parameter δ was assigned to 0. The method proposed in [8] was used to evaluate JND values in perceptually adaptive embedding algorithm. To determine the threshold of NC value, 58600 images chosen from Corel Gallery 1000000 were watermarked using PSNR-maximized embedding and perceptually adaptive embedding algorithm. Then, the threshold was chosen such that watermarked and unwatermarked images could be well separated. According to the experimental result, the value of threshold was assigned to 0.6 in all following experiments. To evaluate the robustness of the proposed approach, six popular testing images: Lena, Babbon, F16, Fishing Boat, Pentagon and Peppers were watermarked with the proposed watermarking approaches. Then, four image processing operations, JPEG compression, Gaussian filtering, sharpening and line removing were applied on the watermarked images. The result are shown in figure 2-4. As shown in figure 2, it is obvious that the watermark was still detectable until JPEG quality was lower than 15%. Similar results can be obtained after line removing, Gaussian filtering or sharpening. These experimental results show that the proposed watermarking approaches are robust on minimizing the perceptual distortion. IV.

CONCLUSIONS

In this paper, we propose a strategy that hide watermarks in the relationship between wavelet coefficients. The proposed strategy would minimize the perceptual distortion of embedded images, measured by PSNR or JND. Experimental results illustrate the robustness of the proposed algorithm after common image processing operations such as JPEG compression, Gaussian filtering and sharpening. Since the appropriate image quality is different from application to application, it should be able to be pre-specified by the user. The proposed method can also be used to embed watermarks under the constraint of pre-specified image quality after slightly modification. R EFERENCES [1] I. Cox and M. Miller, “The first 50 years of electronic watermarking,” JASP, vol. 2002, no. 2, pp. 126–132, 2002. [2] I. J. Cox, M. L. Miller, and J. A. Bloom, Digital Watermarking. New York: Morgan Kaufmann Publishers, 2002. [3] W. Bender, D. Gruhl, N. Morimoto, and A. Lu, “Techniques for data hiding,” IBM Systems Journal, vol. 35, no. 3,4, pp. 313–336, 1996. [4] E. Koch and J. Zhao, “Towards robust and hidden image copyright labeling,” in Proc. of 1995 IEEE Workshop on Nonlinear Signal and Image Processing, Halkidiki, Greece, June 1995, pp. 452–455. [5] C.-T. Hsu and J.-L. Wu, “Hidden digital watermarks in image,” IEEE Trans. Image Processing, vol. 8, no. 1, pp. 58–68, January 1999. [6] F. Y. Duan, I. King, L.-W. W. Chan, and L. Xu, “Intra-block maxmin algorithm for embedding robust digital watermark into images,” Multimedia Information Analysis and Retrieval, pp. 255–264, 1998. [7] M. Kutter and F. A. P. Petitcolas, “A fair benchmark for image watermarking systems,” in Proc. SPIE Security and Watermarking of Multimedia Contents, vol. 3657, San Jose, CA, USA, 25–27 Jan. 1999, pp. 226–239. [8] W. Zhu, Z. Xiong, and Y. Q. Zhang, “Multiresolution watermarking for images and video,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 9, no. 4, pp. 545–550, 1999.

(a) PSNR-maximized embedding Fig. 2.

Results of watermark detection after JPEG compression

(a) PSNR-maximized embedding Fig. 3.

(b) perceptively adaptive embedding

Results of watermark detection after line removing attack

(a) PSNR-maximized embedding Fig. 4.

(b) perceptively adaptive embedding

(b) perceptively adaptive embedding

Results of watermark detection after Gaussian filtering and sharpening