international journal of °c informaton and ......2008/04/07 · international journal of c 2008...

INTERNATIONAL JOURNAL OF c© 2008 Institute for ScientificINFORMATON AND SYSTEMS SCIENCES Computing and InformationVolume 4, Number 4, Pages 548–559

MULTI-BIT DIGITAL WATERMARKING BASED ON BITDECOMPOSITION

FANF LI, XUN LUO, FEIJUN DAI, AND FEI LIU

(Communicated by Ping Luo)

Abstract. Considering the property of multiple information bits of gray level

watermarks, we propose classifying gray level watermark bits via bit plane

decomposition and then embedding them according to the principle of pref-

erentially ensuring the security of the significant bits. As such, we introduce

the ideas and definitions of crucial and non-crucial bit planes. The crucial bit

planes, which have a noticeable effect on the watermark, are embedded in the

robust areas of the transform domain. For the non-crucial bit planes, a frac-

tal theory-based data compression method is proposed to divide the bit plane

into blocks and then search for the optimal similar blocks to reduce data. In

addition, in the adaptive embedding process an appropriate trade-off in in-

visibility, robustness and statistical invariance of the watermarked image is

achieved by adjusting the overall embedding strength parameter. This scheme

is very robust against common image processing such as compression, filtering

and cropping. The final presented experimental results demonstrate that our

proposed scheme is both accurate and efficient.

Key Words. Gray level watermark, non-crucial bit plane, bit plane decom-

position, self-similarity, wavelet transform.

1. Introduction

Digital watermarking is a technique of embedding secret information in a car-rier. The carriers can include various media such as images, audios and text.The secret information, that is the watermark, could be a meaningless randomsequence[1], meaningful binary images [2] or gray images [3],[4],[5],[6]. Previous stud-ies have mainly focused on the meaningless watermark or binary image watermark.For gray image watermarks, the main problems lie in how to embed such multipleinformation bits in the carrier without causing perceptual distortion and still allowthe perceptually acceptable watermark to be recovered in spite of the damage tothe data.

[3] and [4] applied a wavelet transform to the watermark image and then em-bedded the transform coefficients in various portions of the carrier to improve therobustness. [5] reduced the embedded data by performing the data compression onthe watermark image. [6] embedded the watermark data with a certain resolutionin carrier data with the same resolution to provide invisibility. Although these stud-ies solved the embedding problems of the gray level watermark in some respects,they have not completely exploited and made use of the characteristics of the gray

Received by the editors January 1, 2008 and, in revised form, March 22, 2008.This research was supported by the National ”973” Project (No. 2003CB314805) and the

National Natural Science Foundation of China (No. 90304014).

548

MULTI-BIT DIGITAL WATERMARKING BASED ON BIT DECOMPOSITION 549

level watermark. [3] and [4] did not make the best of the perceptual redundancyof the gray level watermark to reduce data. Although [6] considered adaptivelyembedding different resolutions of the watermark in the portions having differentstrengths, the amount of embedded information was still large. And although bitdecomposition was applied to the gray level watermark in [4] and [6], their goalswere only to convert the gray level watermark into binary images for convenientembedding. Therefore all bit planes were processed without difference. Studyingthe above methods, we find the contributions of the bit planes to the gray level wa-termark are not completely equal. And those bit planes having a noticeable effecton visibility should not be judged as equal to the other bit planes, but should beespecially protected so that with the better robustness of less data, we can retrievethe most perceptually acceptable watermark. In our proposed method, multi-bitsof the watermark are classified via bit plane decomposition and then embedded aswell as extracted according to the principle of the significant bits being preferen-tial. In addition, to resolve information redundancy of the watermark, we adoptthe method of searching for the optimal similar blocks to replace the bit planes.

There are two watermark embedding methods: spatial domain and transform do-main method. The transform domain method is preferable due to its good invisibil-ity, in which the wavelet transform-based embedding method has been more studiedin the present literatures because of its flexibility and time-frequency localization.This embedding method can be implemented in low[7], median or high[8],[9],[10]

frequency sub-bands. The merit of embedding in specific sub-bands lies in notcausing the perceptual distortion of the carrier, but it is less robust than embed-ding in the low frequency sub-band. Therefore in [9] and [10], content-adaptiveembedding based on HVS was employed to increase the embedding strength of thelocal regions and the robustness of the watermark. As for the multi-bit watermark,adopting the adaptive embedding in the median and high frequency sub-bands cansatisfy the requirements of invisibility and robustness. But meanwhile due to itslarge amounts of embedded data, we should consider whether the statistical prop-erty of the carrier has been changed, in that detecting the variance of the statisticalhistogram of the carrier is a common attack method[11]. To resist this attack, thecurrent paper proposes adjusting the overall strength parameter in the adaptiveembedding to further satisfy the requirement of statistical invariance.

This paper is organized as follows. First, we discuss the pre-processing of thegray level watermark before it is embedded. In the third section we describe theembedding procedure. The extraction procedure is introduced in the fourth section.In the fifth section the experimental results are discussed to confirm the accuracyand efficiency of our method. Finally we draw some conclusions.

2. Watermark Preprocessing

In the beginning, we performed preprocessing of the watermark mainly in thefollowing two aspects. One is separating the crucial bit planes from the non-crucialbit planes of the multi-bit watermark so as to embed them from strongly to weakly.The other is partially reducing the bits of the non-crucial bit planes under thepremise of not affecting visibility to improve the invisibility of the watermarkedimage. To do so, we propose the following steps to perform watermark preprocessing(as depicted in Fig. 1).

2.1. Crucial Bit Planes and Non-crucial Bit Planes. We consider embeddingthe watermark in the wavelet transform domain of the original image. Due tomultiple information bits of the gray level watermark, if we embed all the bits

550 F. LI, X. LUO, F. DIA, AND F. LIU

Secret key k

Bit From high

decomposition to low

Select by Secret key k

From high similarity

to low Divide

Gray

level

water-m

ark

Ordered crucial

bit planes

Pseudo crucial

bit planes

Crucial bit

planes

Pseudo

optimal

similar

blocks

Optimal

similar

blocks

Ordered

non-crucial

bit planes

Sub

blocks

Non-crucial

bit planes

Figure 1. Watermark preprocessing procedure

without difference, the error ratio of the extracted bits will be equal after destructiveattacks, and thereby the quality of the extracted watermark image is hard to ensure.However, if by means of the knowledge that the wavelet transform coefficients withdifferent significance have different robustness[12], we separate the watermark bitsand embed the crucial bit planes that have a noticeable effect on the watermarkinto the significant coefficients and the bit planes with less effect on the watermarkinto the non-significant coefficients, then even if the watermarked image is attackedand some bits are lost, we can still retrieve a satisfactory watermark image withthe remaining crucial bit planes.

To illustrate the above concept, we employed an 8-bit gray image watermark with64×64 pixels in this study. In the practical implementation of this concept, the graylevel watermark is decomposed into eight binary images via bit plane decomposition,which is, from high to low, the bit planes b7, b6, b5, b4, b3, b2, b1 and b0. The employedgray level watermark and the results for its bit plane decomposition are shown inFig. 2.

a gray level watermark b sequential bit planes b7, b6, b5, b4, b3, b2, b1 and b0

Figure 2. Gray level watermark and its of bit plane decomposi-tion result

In order to evaluate the property of the above bit planes, we adopted imagecomplexity c[13], which is defined as the sum of change times of adjacent pixels inthe bit plane, from 0 to 1 and from 1 to 0 horizontally and vertically. The greater


the complexity c, the more random the bit plane’s content is, which means thebit plane has less contribution to the watermark image. By contrast, the less thecomplexity c is, the more continual form the bit plane has, which means the bitplane contributes more to the watermark image. Hence, according to the definitionof c, we can compute the complexity of the above bit planes to get their values asshown in Table 1.

Table 1 Complexity of the bit planes

Bit

plane b7 b6 b5 b4 b3 b2 b1 b0

c 2217 2271 3001 3689 4004 4045 4105 4021

In order to distinguish the crucial bit planes from the non-crucial bit planes, wepresent their definitions as follows.

Definition: The crucial bit plane is the high bit plane with a lower c value andthe non-crucial bit plane is the low bit plane with a higher c value.

According to the above definition, the crucial bit planes of the employed water-mark image are b7, b6, b5, b4 and b3 and the non-crucial bit planes are b2, b1 and b0.Thus, if we order the crucial bit planes and the non-crucial bit planes according totheir significance to the watermark, the order of the crucial bit planes is b7, b6, b5, b4

and b3, and the order of the non-crucial bit planes is b2, b1 and b0. To ensure thesecurity of the watermarking system, we use the secret key k as the input of thepseudo-random generation to obtain the pseudo-random sequence of each crucialbit plane. We can apply the same key or different keys to each bit plane accordingto the actual need, so that an attacker would not be able to retrieve the real bitplane even if he obtained the bit plane with a pseudo-random sequence.

2.2. Data Compression of the Non-crucial Bit Plane. It is well known thatwith the increase of watermark data, the invisibility of the watermarked image,as well as the robustness, will be decreased. However, according to the perceptualredundancy of the gray level watermark, it is preferable to maintain the perceptuallysignificant crucial bit planes and reduce the data of the less significant bit planes.To reduce the data of the non-crucial bit planes, our method is implemented byadapting ideas from fractal image encoding[14].

Obviously, the bit planes b0 and b1 have the least effect on the watermark imageand their complexity values c are greater. The higher complexity illustrates thatthe bit plane is closer to white noise and also has more noticeable self-similarity.Therefore, according to the concept of fractal image encoding, the sub blocks of thebit plane with self-similarity can be obtained by searching for the correspondingdomain blocks and performing all kinds of affine transforms. But the encounteredproblems are that searching for the appropriate domain block is not easy and thecomputation of the affine transforms is complex. As such, by studying the resultsof the bit plane decomposition, we discover that since the bit planes b0 and b1 havegood self-similarity and their modification cannot affect visibility, we can develop asimple method to reduce data by searching for the optimal similar sub blocks. Thealgorithm’s steps are outlined as follows.

Step 1. Divide the bit plane into 8× 8 sub blocks.Step 2. In order to evaluate the similarity between sub blocks, compute the

mean square error (MSE) values of each 8× 8 sub block with respect to the othersub blocks. The definition of the mean square error is:


MSE =∑m,n

(Im,n − I′m,n)2/(M ×N)

where Im,n, I′m,n represents the intensity value of two sub blocks at position (m,

n) respectively and M, N represents the size of the sub block. The MSE valueillustrates the deviation of similarity between two sub blocks.

Step 3. For a definite 8 × 8 sub block, there is a corresponding MSE valuewith respect to each of the other sub blocks. All the MSE values of this block aresummed up to get its total deviation of similarity. The sub block with the minimumtotal deviation of similarity in the bit plane is identified. The selected sub block iscertain to be the block with the best similarity in the whole bit plane. Thereforereconstructing the bit plane with it will result in the minimum total deviation.

Now we consider the bit plane b2. Since the bit plane b2 is more significantthan bit planes b0 and b1, adopting a similar sub block method should satisfythe requirement of less deviation. As such, our adopted method is to divide b2

into four sections, and then further divide each of them into 16 × 16 sub blocks.Because adjacent blocks have good similarity between each other, by searching forthe optimal similar block in each section and then reconstructing the local bit planewith it, the total deviation will be controlled in a limited range.

Using the compression method described above, the bit planes b1 and b0 adopt an8×8 optimal similar sub block instead of the bit plane, and the bit plane b2 adoptsfour 16 × 16 optimal similar blocks instead of the bit plane. Consequently, thetotal watermark data is decreased by 1/3, which is rather beneficial to watermarkembedding.

Finally, we employ the secret key k to obtain the pseudo-random sequence of theoptimal similar block of b2, b1 and b0, which is regarded as the embedded data.

In the following discussion, we will analyze whether there is perceptual vari-ance between the original watermark and the watermark composed of the crucialbit planes and the reconstructed non-crucial bit planes with the optimal similarblocks. Since the gray level watermark is composed of the bit planes in the se-quence of b7, b6, b5, b4, b3, b2, b1 and b0, we can compute the PSNR values of thepartly composed images with respect to the original image to evaluate their per-ceptual quality. Thus, for the gray level watermark employed in this study, weshould first compose the crucial bit planes in sequence from b7 to b3, then add inthe non-crucial bit planes b2, b1 and b0 in turn. In Table 2 the PSNR values ofthe gray level watermark composed of the original bit planes and composed of thereconstructed bit planes are compared.

Table 2 Quality of watermarks composed of the original bit planes

and composed of the reconstructed bit planes

Composed

bit planes From b7 to b3 From b7 to b2 From b7 to b1 From b7 to b0

Original bit

planes 35.6 42.6 50.7 80.5

Reconstructed bit

planes 35.6 39.5 41.3 43.2

From Table 2 we can see that the quality of the watermark composed of thereconstructed bit planes is worse than that composed of the original bit planes,which results from the similarity deviation of the optimal similar blocks. However,according to HVS, images with a PSNR above 42 dB have no effect on visibility,


which means the human eye cannot distinguish the original watermark image fromthe watermark image composed of the reconstructed bit planes. Hence, this illus-trates that the proposed method of replacing the non-crucial bit planes with theoptimal similar blocks is practical.

3. Watermark Embedding

We adopted embedding in the wavelet transform domain of the original image.The original image is decomposed into three levels and content-adaptive embed-ding is applied in the median frequency sub-bands of it. The basic principle ofembedding that we propose is that the ordered bit planes’ data should be adap-tively embedded in the sub blocks ordered by the significance of the original image.The embedding strength should be considered in respect to both the locality andthe whole, by adjusting the adaptive embedding strength coefficient and the overallstrength parameter respectively.

3.1. Adaptive Embedding Strength Coefficient. According to the propertyof HVS, the human eye cannot detect the variation of regions with complex texturesand but can detect the variance of flat regions, so we can increase the embeddingstrength of regions with complex textures. We applied standard deviation to eval-uate the texture complexity of the region of the original image in this study. Thelarger the standard deviation, the more complex the texture of the region is. Thesmaller the standard deviation, the flatter the region is. We can compute thetexture complexity of the region in the low frequency sub-band, that is, the ap-proximation image, to save computation. We divide the approximation image into8 × 8 sub blocks and compute the standard deviation σi of each block. Similarly,the sub-bands LH3 and HL3 of the original image are divided into 8×8 sub blocks,and LH2 and HL2 are divided into 16× 16 sub blocks. Each of these sub blocks ismapped to the block of the approximation image at the same spatial location on aone-to-one correspondence.

Since the watermark embedding is implemented in several median frequencysub-bands, the human eye also has different degrees of sensitivity to different sub-bands and orientations. Thus, we can correspondingly employ different embeddingstrengths. To do so, we consider the sensitivity function corresponding to differentorientations of the sub-bands and different decomposition levels as follows[15]:

f(l, θ) ={ √

2 θ = 31 θ = 1, 2

}∗

1.00 l = 10.32 l = 20.16 l = 3

where θ = 1, 2 and 3 represents the horizon, vertical and diagonal orientation,respectively. l represents the number of the decomposition level. Thus we definethe embedding strength coefficient of the median frequency sub block as ei = σi ∗f, where σi is the standard deviation of the corresponding low frequency sub blockat the same spatial location.

3.2. Embedding Procedure. In order to adaptively embed the ordered bit planes’data of the watermark in the original image, we must order the sub blocks of theoriginal image according to their significance. The adopted method computes theaverage absolute value of each block’s coefficients in LH3, HL3, LH2 and HL2 sub-bands and orders them from large to small. The sub block with a greater averagevalue is more significant to visibility. Since the more significant sub blocks havebetter robustness, they should be embedded with the high bit planes’ data, while


the less significant sub blocks should be embedded with the low bit planes’ data.The embedding formula[16] is:

C ′(i) = sign(C(i))× {|round(C(i)/(2ei · p)) · 2ei · p|+ ei · p · b(i)},where C(i) and C ′(i) are the wavelet transform coefficients of the original image andthe watermarked image respectively, b(i) is the watermark bit, ei is the above de-fined adaptive embedding strength coefficient of the watermark and p is the overallstrength parameter. The bit planes b7, b6, b5, b4, b3, b2, b1 and b0 of the watermarkare embedded in the ordered sub blocks from strong to weak in turn.

At last, we apply the inverse wavelet transform to the decomposed images toobtain the watermarked image.

3.3. Overall Strength Parameter. When embedding all the bit planes’ datausing the method proposed above, we need to adjust the overall strength param-eter p to achieve invisibility, robustness and statistical invariance. Ordinarily awatermarking system is only considered to satisfy the former two requirements,but image attacks by means of statistical detection is rather common. Therefore,the watermarked image should also retain statistical properties in accordance withthe original image, which is realized by adjusting the overall strength parameter.As such, we propose using the overall strength parameter to further satisfy therequirement of statistical invariance.

We employ PSNR and BER, which are obtained from a common JPEG com-pressed watermarked image, to evaluate invisibility and robustness[17] respectively.In general, as the parameter p increases, the BER will increase and the PSNR willdecrease; as the parameter p decreases, the converse occurs. Under the trade-off,we chose the maximum value of p with the PSNR above the perceptual acceptancevalue 38dB and the BER less than 0.2. The selected value p is regarded as the initialvalue of the overall strength parameter. Next we should determine whether the sta-tistical property of the original image has been changed and adjust the initial valuep by using the following method. The statistical histogram of the original image iscompared with the watermarked image. If the latter has sharply changed from theformer, we should adjust the p value to keep the statistical property unchanged.After progressive adjustment, the resulting value p is 0.2, and in the meantime thePSNR is 38.3 and the BER is 0.14.

4. Watermark Extraction

First, the watermarked image is decomposed into three levels in the waveletdomain. Second, we employ the same method as embedding to divide the medianfrequency sub-bands into blocks. Then the blocks are ordered by their significanceand the bit planes are extracted from them in turn. The extraction procedure isdepicted in Fig.3.

The method for extracting the bit planes data is as follows[16]. First, compute

h(i) = mod(|C ′(i)|, 2ei · p),

if h(i) < (3ei · p)/2 and h(i) > (ei · p)/2, then b(i) = 1; else b(i) = 0, where C ′(i) isthe wavelet transform coefficient of the watermarked image and b(i) is the extractedwatermark bit.


Secret key

Pseudo crucial

bit planes

Non-crucial

bit planes

Crucial bit

planes Gray

level

water-m

arkOptimal

similar

blocks

Pseudo

optimal

similar

blocks

Watermarked

image

Secret key

Figure 3. Procedure for gray level watermark extraction

5. Experimental Results

In order to illustrate the accuracy and efficiency of our proposed method, someexperimental results are presented as follows. In this study, the original image wasthe gray image ”Lena” (512×512×8), which was decomposed into three levels by theHaar wavelet transform. The original image and the watermarked image are shownin Fig.4. The statistical histograms of the original image and the watermarkedimage are shown in Fig. 5. As Fig. 5 shows, there is a minute difference betweenthe original image and the watermarked image, which means that the requirementof retaining the statistical properties of the original image has been satisfied andconsequently the choice of the overall strength parameter value p is appropriateand efficient.

(a) original image (b) watermarked image

Figure 4. Original image and watermarked image

To confirm the efficiency of the proposed watermark preprocessing, two experi-ments were conducted as follows.

In the first experiment, we demonstrated the role of reduction of the embeddeddata. Two embedding methods were compared: in one, all bit plane data of thewatermark were embedded in the original image after bit plane decomposition, andin the other, some of the data of the non-crucial bit planes were reduced by usingthe watermark preprocessing presented in this paper and then the watermark imagewas embedded in the original image. Both methods use the same overall strengthparameter value in the embedding process. The results are shown in Table 3.


0 50 100 150 200 250

0

2000

4000

6000

8000

10000

12000

14000

0 50 100 150 200 250

0

2000

4000

6000

8000

10000

12000

14000

(a) histogram of the original image (b) histogram of the watermarked image

Figure 5. Comparison between the statistical histogram of theoriginal image and the watermarked image

Table 3 Comparison between embedding with all data of the watermark

and embedding with compressed watermark

Embedding amount PSNR BER

Overall embedding 35.2 0.17

Partial embedding 38.3 0.14

From Table 3 we can see that the reduction of the embedded data results infewer modifications of the original image. Thereby, the watermarked image hasgood perceptual quality. Also, fewer watermark bits can be embedded into therelatively significant coefficients of the original image, and therefore the robustnessof the watermark is improved.

In the second experiment, we demonstrated the role of adaptively embeddingvarious bit planes of the watermark in the various portions of the original image.Table 4 shows the bit error ratio values of the extracted bit planes after commonimage compression using the scheme proposed in this paper.

Table 4 Comparison of the stability of the extracted bit planes

Bit

plane b7 b6 b5 b4 b3 b2 b1 b0

BER 0.08 0.09 0.09 0.11 0.14 0.15 0.17 0.18

We can see from Table 4 that the bit planes with different significance are adap-tively embedded into the sub blocks with different significance of the original image,making the BER of the high bit planes less than the low bit planes, and thereforethe robustness of the crucial data of the watermark is superior to the other dataand even if the image is attacked, a perceptually acceptable gray level watermarkcan still be retrieved.

We compared the stability of our proposed scheme with [6]. After JPEG compres-sion we computed the normalized cross-correlation coefficients (NC) of the extractedwatermark in two algorithms to demonstrate the stability of the watermarking.


Table 5 Comparison of stability between [6] and our proposed scheme (NC)

JPEG(QF) [6] Proposed scheme

50 0.78 0.79

60 0.82 0.82

70 0.85 0.86

80 0.89 0.92

90 0.95 0.97

100 1.00 1.00

Obviously, compared with [6], our proposed scheme has some improvements inthe accuracy of the extracted watermark. This illustrates that a watermarking sys-tem can achieve good robustness against attacks by partly reducing the embeddeddata, selectively embedding the watermark in the perceptually significant portionsof the original image and adopting adaptive embedding to increase local strengthas well. Seen from the retrieved gray level watermark, after image compression,the retrieved watermark of [6] is blurred because the high frequency signals of theimage’s margin are lost, while in our proposed scheme the retrieved watermark hassome variances in luminance due to the loss of the lower bit planes’ data.

The following table shows the test results of the accuracy of the extracted wa-termark after the watermarked image has been corrupted by some common attacksusing Stirmark.

Table 6 Experimental results for resistance against attacks

Attack type BER

Sharpen 0.08

Median_3 0.14

Median_5 0.28

Crop_75 0.07

Crop_50 0.15

As Table 6 shows, our proposed scheme has good performance in common imagefiltering operations, as well as a lower detection error ratio in cropping operationsto some degree.

6. Conclusion

According to the properties of the gray level watermark including multiple in-formation bits and perceptual redundancy, we proposed a method separating thewatermark data via bit plane decomposition and processing them in different ways.The crucial bit planes noticeably affecting the quality of the watermark are sepa-rated and embedded in the robust areas of the original image. However, for thenon-crucial bit planes, the embedded data can be partially reduced by searchingfor the optimal similar blocks, so as to increase the invisibility of the watermarkedimage. Also due to the reduction of the embedded data, the overall strength pa-rameter can be increased, so that the robustness of the watermark is better. As animportant parameter adjusting the invisibility, robustness and statistical invarianceof the watermarked image, the overall strength parameter plays a significant role inthe trade-off between invisibility, robustness and statistical invariance. The exper-imental results show that in the gray level watermark extracted with the proposedmethod, the more significant data have better stability; therefore a perceptually


acceptable gray level watermark can be retrieved. This scheme has good perfor-mance in common attacks except for geometric attacks. Future research work couldapply the fractal technique to the higher bit planes of the watermark. With theprogress of the fractal technique, if the computation of the affine transforms couldbe simplified, the embedded watermark data could be further reduced by means ofthis technique, so as to improve the performance of the watermarking system.

References

[1] Cox .I, et al, Secure spread spectrum watermarking for multimedia, IEEE Transactions onImage Processing, 1997, 1673-1687.

[2] Tsai, M. et al, Joint wavelet and spatial transformation for digital watermarking, IEEETransactions on Consumer Electronics, 2000, 241-245.

[3] Mohsen Ashourian and Yo-Sung Ho., Multiple description coding for image data hiding jointlyin the spatial and DCT domains, ICICS 2003, 179-190.

[4] Pik-Wah Chan and Michael R. Lyu., A DWT-based digital video watermarking scheme witherror correcting code, ICICS 2003, 202-213.

[5] Huang, J. and Shi, Y. Q., Embedding gray level images, Proc. of IEEE Int. Sym. on circuitsand systems, 2001, 239-242.

[6] Niu Xiamu et al., Digital watermarking technique based on multi-resolution decomposition,Journal of Electronics, 2000, 1-4.

[7] Wang H. J. and Kuo C. C. J., Image protection via watermarking on perceptually significantwavelet coefficients, Proc. of IEEE Multimedia Signal Processing Workshop, 1998, 278-284.

[8] Xia Xiang-Gen et al., Wavelet transform based watermark for digital images, Optics Express,1998, 497-511.

[9] Ki-Ryong Kwon et al., Content adaptive watermark embedding in the multi-wavelet transformusing a stochastic image model, IWDW2002, 249-263.

[10] Dan Yu and Farook Sattar., A new blind watermarking technique based on independentcomponent analysis, IWDW2002, 51-63.

[11] Elke Franz., Steganography preserving statistical properties, Information Hiding, 2002, 278-293.

[12] Dugad R. etal., A new wavelet-based scheme for watermarking images, Proc. of IEEE ICIP,1998.

[13] Hideki Noda et al., Bit-plane decomposition steganography combined with JPEG2000 com-pression, Information Hiding, 2002, 295-309.

[14] Jacquin, A. E., Image coding based on a fractal theory of iterated contractive image trans-formations, IEEE Transactions on Image Processing, 1992, 18-30.

[15] Barni M. etal, An improved wavelet-based watermarking through pixel-wise masking, IEEETransactions on Image Processing, 2001,783-791.

[16] Luo Yong et al, Translucent digital watermark based on wavelet and error-correct code,Journal of Computers, 2004, 1533-1539.

[17] Yong C. Kim and Byeong C. Choi, Two-step detection algorithm in a HVS-based blindwatermarking of still image, IWDW2002, 235-248.

[18] Glowinski, R., Lions, J. L. and Tremolieres, R., Numerical Analysis of Variational Inequalities,Norh-Holland Publishing Company, 1981.

[19] Ladyzenskaya, O.A., Solonnikov, V.A. and Uralceva, N.N., Linear and Quasi-linear Equationsof Parabolic Type, AMS, 1988.

[20] Lions, J.L. and Magenes, E., Non-Homogeneous Boundary Value Problems and ApplicationsI-II, Springer-Verlag, New York, 1972.


Fang Li, is from Lanzhou Institute of Electrical Technol-ogy, China. She received M.S. in Computer Science from theTsinghua University, Beijing, China in 2006. Her current re-search interests include Digital watermarking, Compressionand Partial encryption for image set. She has published sev-eral papers in these areas.

Xun Luo, a student from School of Electronic and Engi-neering, University of Electronic Science and Technology ofChina. His current research interests include Digital water-marking, algorithm and speciality is electronic and informa-tion Engineering.

Lanzhou Institute of Electrical Technology, Lanzhou, P.R. ChinaE-mail : [email protected]

School of Electronic and Engineering, University of Electronic Science and Technology of China,Chengdu, P.R. China

E-mail : [email protected]

Jiangnan Institute of Computing Technology, Wuxi, P.R. China, 214083

Jiangnan Institute of Computing Technology, Wuxi, P.R. China, 214083

international journal of °c informaton and ......2008/04/07 · international journal of c 2008...

Documents