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Image watermarking using tree-based spatial-frequency feature of wavelet transform
J. Vis. Commun. Image R. 14 (2003) 474–491 www.elsevier.com/locate/yjvci
Image watermarking using tree-based spatial-frequency feature of wavelet transform Xu-Dong Zhang,a Jian Feng,b and Kwok-Tung Loc,* a
Department of Electronic Engineering, Tsinghua University, Beijing 100084, PR China Department of Computer Engineering and Information Technology, City University of Hong Kong, Hong Kong c Centre for Multimedia Signal Processing, Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Hung Hom, Hong Kong
b
Received 22 January 2002; accepted 10 June 2003
Abstract In this paper, an image watermarking scheme is developed using the tree-based spatial-frequency feature of wavelet transform. With our approach, the watermark sequence is inserted in those high activity texture regions of an image having the maximum strength of just noticeable distortion (JND) tolerance of the human visual system (HVS). Simulation results show that the proposed method achieves a good compromise between the robustness and transparency. Ó 2003 Elsevier Inc. All rights reserved. Keywords: Watermarking; Wavelet transform; Multiresolution; Copyright protection
1. Introduction With the explosive growth of the Internet in recent years, a number of information servers are available for people to access various multimedia contents, such as digital images, video and audio. Through the servers, people can view the multimedia data on-line or download the data for viewing locally. As digital data can easily be copied and distributed, protection of the copyright of multimedia data becomes
*
Corresponding author. Fax: +852-23628439. E-mail address: [email protected] (K.-T. Lo).
1047-3203/$ - see front matter Ó 2003 Elsevier Inc. All rights reserved. doi:10.1016/S1047-3203(03)00047-6
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one of the most important topics in the Internet world. The digital watermarking technique (Cox et al., 1997; Dugad et al., 1998; Inoue et al., 1999; Kim and Moon, 1999; Kutter et al., 1999; Podilchuk and Zeng, 1998; Su and Girod, 1999; Swanson et al., 1998; Wu and Liu, 1999; Zeng and Liu, 1999) has been identified as one of the possible solutions for copyright protection in recent years. Watermarking is the process of embedding hidden copyright information into digital data by making small modifications on the data. In general, it is required that the embedded watermark should be not only transparent to human observers, but also robust enough so that it cannot be destroyed or removed after some processing or attacks. The watermark embedding process for digital images can be accomplished in either the spatial or frequency domain. It is shown that a better compromise between robustness and transparency can be obtained using the frequency domain scheme. Among various frequency domain methods, the wavelet transform approach (Dugad et al., 1998; Inoue et al., 1999; Kim and Moon, 1999; Podilchuk and Zeng, 1998) is one of the promising techniques for image watermarking. A number of wavelet-based image watermarking schemes (Dugad et al., 1998; Inoue et al., 1999; Kim and Moon, 1999; Podilchuk and Zeng, 1998; Wu and Liu, 1999) have been proposed in recent years. Podilchuk and Zeng (1998) have proposed a wavelet-based image-adaptive watermarking scheme, in which the visual models are used to determine the image-dependent upper bounds in watermark insertion. Dugad et al. (1998) have developed another wavelet-based watermarking method similar to the CoxÕs spread spectrum method (Cox et al., 1997). Recently, Kim and Moon (1999) have derived a wavelet-based scheme using a method called level-adaptive thresholding to select perceptually significant coefficients for watermark insertion. Both of the detection techniques with or without the original image were also discussed in their work. In this paper, a new wavelet-based image watermarking scheme is developed. In our proposed scheme, a full-tree matrix (FTM) (Lo et al., 2000) is first extracted from the wavelet coefficient array to represent the localizability and multiresolution feature of a region in an image. Based on the FTM, we can exploit the local spatial luminance sensitivity, frequency sensitivity, and texture activity to determine whether the watermark is inserted to this FTM. By exploiting the visual model of the FTM, our proposed scheme aims at embeding as much as information without degrading the visual quality of the watermarked image. Apart from copyright protection, integrality authentication is another application for digital watermarking. Most of the previous wavelet-based schemes cannot resolve the integrality authentication successfully because the regional detector is difficult to define. Based on the FTM, we also define a regional detector to evaluate the integrality of an image region in this paper. With our method, the same algorithmic framework can be used to resolve both the copyright protection and integrality authentication with different parameters. In the following of the paper, Section 2 describes the proposed image watermarking scheme using tree-based spatial-frequency feature of wavelet transform. The detailed steps of the proposed algorithm will be discussed in this section. Section 3 gives the detection theory of watermark for multifold applications. Experimental results are presented in Section 4 and the conclusion is given in Section 5.
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2. A wavelet-based image watermarking method The block diagram of our proposed image watermarking scheme using wavelet transform is shown in Fig. 1. In our proposed system, an input image first undergoes the discrete wavelet transform (DWT). For the resulting wavelet coefficient array, a completed tree from each coefficient in the LL subband is extracted to construct a FTM, which is used for representing both the spatial localizability and multiresolution decomposition of an overlapped local region in an image. Texture activity analysis is performed to determine whether the region is of high activity or low activity. Based on the visual model of FTM and the result of texture analysis, we insert the watermark into the high activity region. Finally, an inverse DWT is performed to obtain the watermarked image. We will describe the details of each building block in the following. 2.1. Full-tree matrix extraction Using the orthogonal wavelet base, a digital image can be decomposed into wavelet coefficients at different resolution levels and directions. The coefficient matrix of wavelet transform is written as C ¼ ½ci;j W H , where ci;j represents the (i,j)th wavelet coefficient in the matrix, W and H represents the width and height of an image, respectively. From a root coefficient cI;J in the LL subband (where the subscript I; J represents the ðI; J Þth coefficient in the LL band and is also the index of the full-tree), a full-tree (Lo et al., 2000) can be extracted as illustrated in Fig. 2. The coefficient set of a full-tree is arranged as a 2L 2L matrix according to the structure of wavelet decomposition, where L is the maximum level of wavelet transform. The FTM can be
Fig. 1. Proposed watermark inserting algorithm.
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Fig. 2. Three-level wavelet decomposition and a full-tree.
written as TI;J ¼ ½TI;J ði; jÞ2L 2L , where TI;J ði; jÞ represents the ði; jÞth coefficient in the ðI; J Þth FTM. FTM represents the local multiresolution decomposition of a spatial 2L 2L block although overlapping exists. The texture property of the related image block is also reflected by FTM. 2.2. Visual model for FTM The visual model of a FTM is divided into two parts: image independent frequency sensitivity and image-dependent luminance sensitivity. The luminance sensitivity is related to a block or a region, in other words, a FTM. The just noticeable distortion (JND) model is written as GI;J ¼ GsI;J GfI;J ¼ GsI;J ½gf ði; jÞ2L 2L ¼ ½gI;J ði; jÞ2L 2L ;
ð1Þ
where Gs is the luminance sensitivity relating to the average luminance TI;J ð0; 0Þ of a spatial local block and Gf is the frequency sensitivity including 3L þ 1 parameters. Gf can be represented in the following matrix format (Lo et al., 2000):
ð2Þ
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where En is an all-one matrix with size 2ðn1Þ 2ðn1Þ . In the block DCT domain, Gs ¼ ðTI;J ð0; 0Þ=Tð0; 0ÞÞa ; I;J
where a ¼ 0:649, TI;J ð0; 0Þ is the DC coefficient of the block, Tð0; 0Þ is the mean value of the DC coefficients for all blocks. This luminance sensitivity model can still be used in the wavelet domain, but the block DCT is replaced by the FTM. By empirical derivation, a simple visual model used in our watermarking scheme is as follows: gI;J ði; jÞ ¼ gf ði; jÞ maxf1; GsI;J g:
ð3Þ
Several parameter sets of GfI;J for image coding have been given by some researchers (Hontsch et al., 1997; Lo et al., 2000; Zhang et al., 1998) and they can be used in watermark insertion. Based on the visual model, the luminance and frequency tolerance of the human visual system (HVS) and texture activity for a local block can be analyzed using FTM. With the results of this analysis, we can determine whether a watermark is inserted into FTM or not so that we can insert as much as information without degrading the visual quality of the watermarked image.
2.3. Texture analysis In general, the coefficients of wavelet transform represent the frequency decomposition of spatial localizability. Significant wavelet coefficients are corresponding to edge, boundary, and high activity texture region. According to the characteristics of the human visual system, a larger visual tolerance is normally applied for large edges and high activity texture regions while the human eye is more sensitive to the changing of short edges and noise frequently appeared on peopleÕs face or other important regions of an image. Hence, for image watermarking, it is better to insert information in high activity regions rather than those smooth areas of an image. The following is an example to illustrate that watermarking the noise coefficients would increase the contrast of the noise point and background. In the example below, the original image block shown in Fig. 3(a) contains a noise point on a smooth background and its related Harr wavelet coefficients (only single level) are listed in Fig. 3(b). Assume JND ¼ 5 and the watermark bit is )1, )2, 1.4, respectively. The watermark bits are inserted into the high frequency coefficients, and the coefficients after watermark insertion are shown in Fig. 3(c). The watermarked image is obtained using the inverse wavelet transform and the result is shown in Fig. 3(d). It is noted from the figures that the contrast of the noise point and background is amplified by watermarking, and a non-perceptual noise has become perceptible. The similar distortion can be easily observed for a short edge. According to the above discussion, a better compromise between the robustness and transparency can be obtained when the watermark is only inserted into the high activity texture regions. Hence, we propose in this work to insert the watermark into the high activity texture region of an image. By doing so, we need to perform a texture analysis on the wavelet coefficients to see which spatial regions will have high activity texture.
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Fig. 3. Example of watermark insertion: (a) Original image block. (b) Wavelet coefficients (single level). (c) Coefficients after watermark insertion. (d) Watermarked image block.
Based on the content of FTM obtained before, there are two criteria in evaluating the texture activity of a spatial block. One is the number of significant wavelet coefficients in a FTM, and the other is the number of zero-tree in a FTM. Significant wavelet coefficients are corresponding to edge, boundary, and high activity texture region. Hence, if most of the coefficients have large magnitude, most likely the region is of high activity. Also, when the number of zero-tree in a FTM is large, it reflects that the region is of low activity, and vice versa. The zero-tree counting decision of the texture activity is easier to be compiled into the zero-tree image coder to construct a uniform watermarking and coding algorithm. Obviously, the two criteria can work independently but they also complement each other. Hence, we propose to check these two factors together when we perform the texture analysis. Given a FTM TI;J , we define a bit-map for it by checking the magnitude of the wavelet coefficients as follows: 1; TI;J ði; jÞ P VQ1 ; BI;J ði; jÞ ¼ ; ð4Þ 0; TI;J ði; jÞ < VQ1 ; where VQ1 is a threshold value determined by experiments. We first define an active factor A1I;J for the full-tree block based on the number of significant coefficients in a FTM as follows: X A1I;J ¼ BI;J ði; jÞ; 0 6 i; j 6 2L : ð5Þ i;j
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As the bit-map obtained in (4) has the same structure as FTM, the zerotree (Shapiro, 1993) can be used to represent the bit-map. A zerotree is a sub-tree from a root coefficient in a given level, in which all coefficients are zero. Twelve sub-trees in the bit-map are obtained from the 12 sign bits of high frequency subband coefficients in the L 1 level of the full-tree matrix. We represent the bit-map sub-tree as TL1;d , d ¼ 1; 2; . . . ; 12. We then define the zerotree sign as follows: 1; TL1;d is not a zerotree; SL1;d ¼ ð6Þ 0; TL1;d is a zerotree: We then define another active factor A2I;J of a full-tree block based on the number of zerotree in it as follows: X A2I;J ¼ SL1;d : ð7Þ d
The overall active factor of a FTM is then defined as AI;J ¼ a1 A1I;J þ a2 A2I;J ;
ð8Þ
where a1 and a2 are two weighting factors with a1 þ a2 ¼ 1. The decision threshold for determining the high activity texture is defined as Tr ¼ a1 Tr1 þ a2 Tr2 ; where Tr1 ¼ a
X
A1I;J
I;J
Tr2 ¼ a
X I;J
ð9Þ
X
1;
I;J
A2I;J
X
1:
I;J
If the overall active factor of a full-tree block is larger than the decision threshold, i.e., AI;J > Tr , the region is classified as a high activity region and the watermarking sequence will be inserted into this full-tree matrix. Otherwise, it is regarded as a low activity region and no watermark is inserted. 2.4. Watermark inserting algorithm Based on the above discussion, we formulate our proposed watermark inserting algorithm as follows: Step 1. Create a watermark array W ¼ ½wði; jÞ, where wði; jÞ is i.i.d. Gaussian random sequence with N ð0; 1Þ and seed by authorÕs signature. Step 2. The DWT coefficient matrix C of the image is obtained using the Mallat algorithm. Step 3. For a given root coefficient cI;J , a FTM TI;J is extracted from C, and an equal size submatrix WI;J is also extracted from W . The inserting position matrix PI;J ¼ ½pI;J ði; jÞ is created, where
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pI;J ði; jÞ ¼
1; 0;
TI;J ði; jÞ > gI;J ði; jÞ; otherwise:
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ð10Þ
Step 4. If AI;J < Tr , goto step 3 to extract the next FTM. Otherwise, insert the watermark into this FTM according to the following equation. W TI;J ði; jÞ ¼ TI;J ði; jÞ þ kgI;J ði; jÞpI;J ði; jÞwI;J ði; jÞ;
ð11Þ
where k is a control parameter according to the strength of the inserted watermark. The watermarked FTM is inserted back to matrix C and if this FTM is not the last one, goto step 3 to extract the next FTM. Step 5. The inverse DWT is applied to the watermarked coefficient matrix C W to obtain the watermarked image. 2.5. Watermark extraction The watermark sequence is extracted by using both the original image and watermarked image. Although a more reasonable extraction scheme is that the original image is not directly involved in the watermark detection process (Zeng and Liu, 1999), we are more concerned about the robustness of our FTM scheme when comparing with other methods (Cox et al., 1997; Podilchuk and Zeng, 1998). The inverse process of the inserting algorithm described in the last subsection is used to extract the watermark. For a given FTM, the watermark is extracted as 1 ^W ^ I;J ði; jÞ ¼ w TI;J ði; jÞ TI;J ði; jÞ pI;J ði; jÞ=gI;J ði; jÞ: ð12Þ k
3. Watermark detection Watermark detection is based on the classical detection theory (Kay, 1998). Different to the Cox et al.Õs detector (1997), we define a normalized detector as PN ^ k wk w q ¼ k¼1 : ð13Þ N pffiffiffiffi The mean value of this detector is independent of N or N and can be used to evaluate different watermarking schemes with different length expediently. We model the detection problem (Kay, 1998) as choosing one between H0 , which is termed as the noise-only hypothesis, and H1 , which is the watermark present hypothesis, or symbolically ^ k ¼ nk ; H0 : w ^ k ¼ w k þ nk ; H1 : w
ð14Þ
where nk is i.i.d. Guassian noise sequence with zero mean and variance r2n (N ð0; r2n Þ) and is independent of wk . It is easy to derive:
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H0 : q N 0; r2n =N ; H1 : q N 1; r2n =N :
ð15Þ
There are two common detection methods. The first detector is to find a threshold to minimize the sum of the probability of error detection and the probability of false The alarm. The threshold is Tq ¼ 0:5. If qp> pffiffiffiffiffiffi exists. ffiffiffiffi Tq , we declare that the R 1watermark 2 average error probability is Pe ¼ Qð N =2rn Þ, where QðxÞ ¼ x ð1= 2pÞeðð1=2Þt Þ dt is referred as the right-tail probability. The second detector is to fix a false alarm probability Pf and to maximize the detection probability Pd . The threshold Tq is derived by Pf as follows: rn Tq ¼ pffiffiffiffi Q1 ðPf Þ; N
ð16Þ
where Q1 ðÞ is an inverse QðÞ function. The detection probability is also derived from Pf as pffiffiffiffi N 1 Pd ¼ Q Q ðPf Þ : ð17Þ rn Using the first detector, a large false alarm probability will be obtained when r2n is large, and the false judgement may happen. If the second detector is used and r2n is large, the detection probability is less than that of the first one and an existent watermark may be missed out. In different applications, we can select a reasonable detector for the specific purpose. In reality, an attacker cannot damage a watermarked image severely according to requested perceptual quality. Only part of the watermarking sequence inserted in the host image will be affected. For JPEG attacking with 10–100% quality factor, statistic results show that 0 6 r2n < 36. Let N ¼ 2000 as an example, we give the performance of the two detectors in Fig. 4. For a small r2n , a satisfactory result can be obtained by using either of the detectors. The detection theory can be extended to two types of detectors: multiresolution detector and regional detector. 3.1. Multiresolution detector Let qk denote a k-resolution detector that only employs the received watermark sequence from level k to level L in the wavelet domain. The multiresolution detector is defined as q ¼ maxfqk ; k ¼ 1; 2; . . . ; L 1g: k
ð18Þ
It is noted that our multiresolution detector is different from the PodilchukÕs maximum correlation detector (Podilchuk and Zeng, 1998) which chooses the maximum value from all the possible levels as well as the frequency direction. Our multiresolution detector is only according to the natural resolution, which we think is more reasonable. For example, for a 256 256 image, our detector will only obtain the detection results from resolutions starting from 256 256 to 128 128 and 64 64.
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Fig. 4. (a) False alarm probability with fixed threshold 0.5; (b) Detecting probability with fixed threshold 0.5; (c) Threshold to maintain Pf ¼ 10 106 ; (d) Detecting probability under Pf ¼ 10 106 (abscissa is rn ).
3.2. Regional detector When we carry out the integrality authentication of a digital image, we probably suspect a region whether it is replaced by another image, then a regional detection is desired. Let the interested region in an original image be fði; jÞjN1 6 i < N2 ; M1 6 j < M2 g, then the superscript set of the FTM is
C ¼ ðI; J Þ ceilðN1 =2L Þ 1 6 I < ceilðN2 =2L Þ; ceilðM1 =2L Þ 1 6 J < ceilðM2 =2L Þ ; ð19Þ where ceil(X ) rounds the X to the nearest integer toward the infinity. The received watermarking sequence from the FTM belonging to C is denoted as WC , then the regional detector is defined as P ^k wk 2WC wk w qr ¼ ; ð20Þ NC where NC is the number of elements in set WC . With the multiresolution detector and regional detector, we can perform both ownership identification and integrality authentication using the same algorithmic framework with different parameters.
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4. Simulation results In this section, we present the experimental results to illustrate the robustness and perceptual quality of our proposed watermarking scheme. Simulations are carried out for several standard monochrome images. Test image ÔBarbaraÕ is of size 128 128 while images ÔLena,Õ ÔBaboonÕ and ÔAirplaneÕ are of size 256 256. We first consider the applications on copyright protection and hence the multiresolution detector is used with the setting of k ¼ 1:5 and a ¼ 1. In our experiments, the threshold value VQ_1 is set equal to 10 for all test images. Fig. 5 shows the resultant watermarked image using our proposed scheme on image ÔBarbara.Õ Fig. 5(a) shows the original image and Fig. 5(b) illustrates the watermarked image. It is noted that there is almost no perceptual difference between the original image and watermarked image. Fig. 5(c) shows the resultant image by JPEG compression for the watermarked image using 40% quality factor and Fig. 5(d) shows the real watermark inserted in the image (using enlarged range to display). It is noted that the watermark is only inserted to high activity texture region. The response of the watermark detector to 400 randomly generated watermarks is shown in Fig. 5(e). We then test the robustness of the proposed watermarking scheme against several attacks. It is known that the most common signal attack for digital images is JPEG compression. For comparison purpose, the table also shows the results of the Cox et al.Õs (1997) and Podilchuk and ZengÕs (1998) methods. To be noted, the comparison is made on the ground that the visual quality of the watermarked images of the three schemes is roughly the same. Figs. 6 and 7 show the watermarked images using the three methods for test images Baboon and Lena. Table 1 shows the detection results under different JPEG quality factors for different test images. It is shown that our scheme is very robust to JPEG compression comparing with the other two methods. The length of each watermark sequence that was inserted in host image is shown in Table 2. It is noted that the most number of bits can be inserted in the host image by using the PodilchukÕs scheme, but its robustness and watermarked image quality are undesirable. Although the work in Podilchuk and Zeng (1998) gives a maximum correlation value detector that may receive a larger detection value, but larger false alarm is obtained based on the less N in the denominator of the detector for a fixed level and direction. The spread spectrum watermarking distribution is independent on the image content, and hence the length of watermark sequence is limited. With the increasing of watermark length, the image quality is decreasing rapidly. Our scheme that inserts watermark into high activity texture region overcomes these drawbacks with a robust detector. It is shown that a high quality watermarked image and an appropriate amount of watermarking can be obtained using our proposed method. Figs. 6 and 7 also show the inserted watermarking sequence using different schemes for images ÔLenaÕ and ÔBaboon.Õ It is seen that the positions for watermark insertion are quite different for these three methods and our scheme mainly inserts the watermark in the high activity region like the hair region in image ÔLena.Õ For other attacks like addition of white noise, cropping, re-scaling, and low-pass filtering, our scheme is also robust. Table 3 shows the simulation results of our scheme for several different attacks. For the white noise addition, the white noise
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Fig. 5. Simulation results for image ‘‘Barbara’’: (a) Original image. (b) Watermarked image. (c) JPEG compression for watermarked image using 40% quality factor. (d) Inserted watermarking sequence. (e) Detection results using 400 randomly generated watermarks.
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Fig. 6. Simulation results for image ‘‘Baboon’’: (a) Inserted watermark using our scheme. (b) Inserted watermark using Cox et al.Õs scheme (1997). (c) Inserted watermark using Podilchuk and ZengÕs scheme (1998). (d) Watermarked image using our scheme. (e) Watermarked Image using Cox et al.Õs scheme (1997). (f) Watermarked Image using Podilchuk and ZengÕs scheme (1998).
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Fig. 7. Simulation results for image ÔLenaÕ: (a) Inserted watermark using our scheme. (b) Inserted watermark using Cox et al.Õs scheme (1997). (c) Inserted watermark using Podilchuk and ZengÕs scheme (1998). (d) Watermarked image using our scheme. (e) Watermarked image using Cox et al.Õs scheme (1997). (f) Watermarked image using Podilchuk and ZengÕs scheme (1998).
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Table 1 Detection results for JPEG compression attack Image
JPEG quality (%)
Cox et al.Õs scheme (1997)
Podilchuk and ZengÕs scheme (1998)
Our scheme
Barbara (128 128)
60 40 10
0.75 0.67 0.32
1.01 0.89 0.51
1.18 1.02 0.58
Lena (256 256)
60 40 10
0.9552 0.9129 0.7045
0.8145 0.7385 0.5719
1.1479 0.9719 0.9013
Baboon (256 256)
60 40 10
0.9768 0.9810 0.83
0.9897 0.9229 0.5558
1.1074 1.0633 0.7304
Airplane (256 256)
60 40 10
0.9432 0.9012 0.6896
0.9003 0.8345 0.4224
1.1338 1.0354 0.8821
Table 2 Length of watermarking sequence for 256 256 images Image
CoxÕs scheme
PodilchukÕs scheme
Our Scheme
Lena Baboon Airplane
1000 1000 1000
5583 11862 6230
3050 7168 3913
Table 3 Detection results for different attacks Attack
Lena
Baboon
Airplane
Addition of white noise in spatial domain Addition of white noise in frequency domain Cropping Low-pass filtering Re-scaling
1.1864 1.2092 0.7873 0.6931 1.2236
1.1188 1.1099 0.5738 0.7909 1.1134
1.1763 1.1290 0.6203 0.5403 1.1987
with variance r2 ¼ 100 is added in the spatial domain and frequency domain of the watermarked image. For image cropping, the right half of the watermarked image is cropped and replaced by the original image. In the low-pass processing, a low-pass filter only preserves one fourth of the low-frequency bank. Lastly, a half resolution watermarked image is first made by averaging four neighbouring pixels and then the re-scaled image is obtained by linear interpolation. By examining the results in Table 3, we can find that the detector output is always larger than 0.5. Therefore, we could conclude that our watermarking scheme is robust enough to those attacks mentioned before and has a better perceptual quality.
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We then evaluate the performance of our watermarking scheme in integrality authentication, which is another important application of digital watermarking. For instance, when a photo of news release is transmitted through the Internet, some sorts of protection are required for different attacks. If we suspect that a part of the photo has been modified by others, the regional detector is used to resolve the integrality authentication. Given an image, we will first use the multiresolution detector to check whether a particular watermark exists or not for ownership identification. If a watermark is detected and we suspect that a part of the image has been modified by others, the regional detector is then used to resolve the integrality authentication. In our experiments for integrality authentication, we set k ¼ 0:5 and a ¼ 0:5. For image ÔLena,Õ the face is extracted and only the four lowest frequency DCT coefficients are maintained and other coefficients are set to zero, then the inverse transformed face region is inserted to the original image and JPEG compression is carried out with 60% quality factor for the completed image. The resultant image is shown in Fig. 8(a). Similar procedures are applied to image ÔBaboonÕ and the resultant image
Fig. 8. Test images with local content modification: (a) Lena and (b) Baboon.
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Table 4 Detection results for regional and global detector Detector
Regional detector
Global detector
Lena Baboon
0.0172 0.2019
0.8242 0.7476
is shown in Fig. 8(b). Table 4 shows the detection results of using both the regional and global detector on the modified test images. It is shown that the regional detector can detect the changes of local content of the image while the global detector is difficult to observe these changes. Such result implies that the image is belonging to a particular owner but the content was modified.
5. Conclusion In this paper, an image watermarking scheme using wavelet transform is developed. The proposed scheme is based on the full-tree matrix (FTM), which is extracted from the coefficient matrix of the DWT to represent both the localizability and multiresolution features of an image. Simulation results show that, given the same visual quality of the watermarked image, our proposed method achieves a better compromise between the robustness and transparency than some other wavelet image-adaptive schemes. Besides the global detector, a regional detector is also derived so that the same algorithmic framework can be used not only for ownership identification but also for integrality authentication.
References Cox, I.J., Kilian, J., Leighton, F.T., Shamoon, T., 1997. Secure spread spectrum watermarking for multimedia. IEEE Trans. Image Process. 6 (12), 1673–1687. Dugad, R., Ratakonda, K., Ahuja, N., 1998. A new wavelet-based scheme for watermarking image. In: Proceedings ICIPÕ98, pp. 419–423. Hontsch, I., Karam, L.J., Safranek, R.J., 1997. A perceptually tuned embedded zerotree image coder. In: Proceedings ICIPÕ97, pp. 41–44. Inoue, H., Miyazak, A., Katsura, T., 1999. An Image watermarking method based on the wavelet transform. In: Proceedings ICIPÕ99, Kobe, Japan, October, vol. 1, pp. 296–300. Kay, S.M., 1998. Fundamentals on Statistical Signal Processing: Detection Theory. Prentice-Hall, PTR. Kim, J.R., Moon, Y.S., 1999. A robust wavelet-based digital watermarking using level-adaptive thresholding. In: Proceedings ICIPÕ99, Kobe, Japan, October, vol. 2, pp. 226–230. Kutter, M., Bhattacharjee, S.K., Ebrahimi, T., 1999. Towards second generation watermarking schemes. In: Proceedings ICIPÕ99, Kobe, Japan, vol. 1, October, pp. 320–323. Lo, K.T., Zhang, X.D., Feng, J., Wang, D.S., 2000. Universal perceptual weighted zerotree coding for image and video compression. IEE Proc. Vis. Image Signal Process. 147 (3), 261–265. Podilchuk, C.I., Zeng, W., 1998. Image-adaptive watermarking using visual models. IEEE J. Sel. Areas Commun. 16 (4), 525–539. Shapiro, J.M., 1993. Embeded image coding using zerotrees of wavelet coefficients. IEEE Trans. Signal Process. 41, 3445–3462.
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Su, J.K., Girod, B., 1999. Power-spectrum condition for energy-efficient watermarking. In: Proceedings ICIPÕ99, Kobe, Japan, vol. 1, October, pp. 301–305. Swanson, M.D., Kobayashi, M., Tewfik, A.H., 1998. Multimedia data embedding and watermarking technologies. Proc. IEEE 86 (6), 1064–1087. Wu, M., Liu, B., 1999. Digital watermarking using shuffling. In: Proceedings ICIPÕ99, Kobe, Japan , vol. 1, October, pp. 291–295. Zeng, W., Liu, B., 1999. A statiscal watermark detection technique without using original images for resolving rightful ownerships of digital image. IEEE Trans. Image Process. 8 (11), 1534–1548. Zhang, X.D., Wang, D.S., Peng, Y.N. 1999. A low bit-rate video coding algorithm based on blocking regional wavelet transform with border processing. In: Proceedings ICSPÕ98, Beijing, China, October, pp. 823–826.
Image watermarking using tree-based spatial-frequency feature of wavelet transform Xu-Dong Zhang,a Jian Feng,b and Kwok-Tung Loc,* a
Department of Electronic Engineering, Tsinghua University, Beijing 100084, PR China Department of Computer Engineering and Information Technology, City University of Hong Kong, Hong Kong c Centre for Multimedia Signal Processing, Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Hung Hom, Hong Kong
b
Received 22 January 2002; accepted 10 June 2003
Abstract In this paper, an image watermarking scheme is developed using the tree-based spatial-frequency feature of wavelet transform. With our approach, the watermark sequence is inserted in those high activity texture regions of an image having the maximum strength of just noticeable distortion (JND) tolerance of the human visual system (HVS). Simulation results show that the proposed method achieves a good compromise between the robustness and transparency. Ó 2003 Elsevier Inc. All rights reserved. Keywords: Watermarking; Wavelet transform; Multiresolution; Copyright protection
1. Introduction With the explosive growth of the Internet in recent years, a number of information servers are available for people to access various multimedia contents, such as digital images, video and audio. Through the servers, people can view the multimedia data on-line or download the data for viewing locally. As digital data can easily be copied and distributed, protection of the copyright of multimedia data becomes
*
Corresponding author. Fax: +852-23628439. E-mail address: [email protected] (K.-T. Lo).
1047-3203/$ - see front matter Ó 2003 Elsevier Inc. All rights reserved. doi:10.1016/S1047-3203(03)00047-6
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one of the most important topics in the Internet world. The digital watermarking technique (Cox et al., 1997; Dugad et al., 1998; Inoue et al., 1999; Kim and Moon, 1999; Kutter et al., 1999; Podilchuk and Zeng, 1998; Su and Girod, 1999; Swanson et al., 1998; Wu and Liu, 1999; Zeng and Liu, 1999) has been identified as one of the possible solutions for copyright protection in recent years. Watermarking is the process of embedding hidden copyright information into digital data by making small modifications on the data. In general, it is required that the embedded watermark should be not only transparent to human observers, but also robust enough so that it cannot be destroyed or removed after some processing or attacks. The watermark embedding process for digital images can be accomplished in either the spatial or frequency domain. It is shown that a better compromise between robustness and transparency can be obtained using the frequency domain scheme. Among various frequency domain methods, the wavelet transform approach (Dugad et al., 1998; Inoue et al., 1999; Kim and Moon, 1999; Podilchuk and Zeng, 1998) is one of the promising techniques for image watermarking. A number of wavelet-based image watermarking schemes (Dugad et al., 1998; Inoue et al., 1999; Kim and Moon, 1999; Podilchuk and Zeng, 1998; Wu and Liu, 1999) have been proposed in recent years. Podilchuk and Zeng (1998) have proposed a wavelet-based image-adaptive watermarking scheme, in which the visual models are used to determine the image-dependent upper bounds in watermark insertion. Dugad et al. (1998) have developed another wavelet-based watermarking method similar to the CoxÕs spread spectrum method (Cox et al., 1997). Recently, Kim and Moon (1999) have derived a wavelet-based scheme using a method called level-adaptive thresholding to select perceptually significant coefficients for watermark insertion. Both of the detection techniques with or without the original image were also discussed in their work. In this paper, a new wavelet-based image watermarking scheme is developed. In our proposed scheme, a full-tree matrix (FTM) (Lo et al., 2000) is first extracted from the wavelet coefficient array to represent the localizability and multiresolution feature of a region in an image. Based on the FTM, we can exploit the local spatial luminance sensitivity, frequency sensitivity, and texture activity to determine whether the watermark is inserted to this FTM. By exploiting the visual model of the FTM, our proposed scheme aims at embeding as much as information without degrading the visual quality of the watermarked image. Apart from copyright protection, integrality authentication is another application for digital watermarking. Most of the previous wavelet-based schemes cannot resolve the integrality authentication successfully because the regional detector is difficult to define. Based on the FTM, we also define a regional detector to evaluate the integrality of an image region in this paper. With our method, the same algorithmic framework can be used to resolve both the copyright protection and integrality authentication with different parameters. In the following of the paper, Section 2 describes the proposed image watermarking scheme using tree-based spatial-frequency feature of wavelet transform. The detailed steps of the proposed algorithm will be discussed in this section. Section 3 gives the detection theory of watermark for multifold applications. Experimental results are presented in Section 4 and the conclusion is given in Section 5.
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2. A wavelet-based image watermarking method The block diagram of our proposed image watermarking scheme using wavelet transform is shown in Fig. 1. In our proposed system, an input image first undergoes the discrete wavelet transform (DWT). For the resulting wavelet coefficient array, a completed tree from each coefficient in the LL subband is extracted to construct a FTM, which is used for representing both the spatial localizability and multiresolution decomposition of an overlapped local region in an image. Texture activity analysis is performed to determine whether the region is of high activity or low activity. Based on the visual model of FTM and the result of texture analysis, we insert the watermark into the high activity region. Finally, an inverse DWT is performed to obtain the watermarked image. We will describe the details of each building block in the following. 2.1. Full-tree matrix extraction Using the orthogonal wavelet base, a digital image can be decomposed into wavelet coefficients at different resolution levels and directions. The coefficient matrix of wavelet transform is written as C ¼ ½ci;j W H , where ci;j represents the (i,j)th wavelet coefficient in the matrix, W and H represents the width and height of an image, respectively. From a root coefficient cI;J in the LL subband (where the subscript I; J represents the ðI; J Þth coefficient in the LL band and is also the index of the full-tree), a full-tree (Lo et al., 2000) can be extracted as illustrated in Fig. 2. The coefficient set of a full-tree is arranged as a 2L 2L matrix according to the structure of wavelet decomposition, where L is the maximum level of wavelet transform. The FTM can be
Fig. 1. Proposed watermark inserting algorithm.
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Fig. 2. Three-level wavelet decomposition and a full-tree.
written as TI;J ¼ ½TI;J ði; jÞ2L 2L , where TI;J ði; jÞ represents the ði; jÞth coefficient in the ðI; J Þth FTM. FTM represents the local multiresolution decomposition of a spatial 2L 2L block although overlapping exists. The texture property of the related image block is also reflected by FTM. 2.2. Visual model for FTM The visual model of a FTM is divided into two parts: image independent frequency sensitivity and image-dependent luminance sensitivity. The luminance sensitivity is related to a block or a region, in other words, a FTM. The just noticeable distortion (JND) model is written as GI;J ¼ GsI;J GfI;J ¼ GsI;J ½gf ði; jÞ2L 2L ¼ ½gI;J ði; jÞ2L 2L ;
ð1Þ
where Gs is the luminance sensitivity relating to the average luminance TI;J ð0; 0Þ of a spatial local block and Gf is the frequency sensitivity including 3L þ 1 parameters. Gf can be represented in the following matrix format (Lo et al., 2000):
ð2Þ
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where En is an all-one matrix with size 2ðn1Þ 2ðn1Þ . In the block DCT domain, Gs ¼ ðTI;J ð0; 0Þ=Tð0; 0ÞÞa ; I;J
where a ¼ 0:649, TI;J ð0; 0Þ is the DC coefficient of the block, Tð0; 0Þ is the mean value of the DC coefficients for all blocks. This luminance sensitivity model can still be used in the wavelet domain, but the block DCT is replaced by the FTM. By empirical derivation, a simple visual model used in our watermarking scheme is as follows: gI;J ði; jÞ ¼ gf ði; jÞ maxf1; GsI;J g:
ð3Þ
Several parameter sets of GfI;J for image coding have been given by some researchers (Hontsch et al., 1997; Lo et al., 2000; Zhang et al., 1998) and they can be used in watermark insertion. Based on the visual model, the luminance and frequency tolerance of the human visual system (HVS) and texture activity for a local block can be analyzed using FTM. With the results of this analysis, we can determine whether a watermark is inserted into FTM or not so that we can insert as much as information without degrading the visual quality of the watermarked image.
2.3. Texture analysis In general, the coefficients of wavelet transform represent the frequency decomposition of spatial localizability. Significant wavelet coefficients are corresponding to edge, boundary, and high activity texture region. According to the characteristics of the human visual system, a larger visual tolerance is normally applied for large edges and high activity texture regions while the human eye is more sensitive to the changing of short edges and noise frequently appeared on peopleÕs face or other important regions of an image. Hence, for image watermarking, it is better to insert information in high activity regions rather than those smooth areas of an image. The following is an example to illustrate that watermarking the noise coefficients would increase the contrast of the noise point and background. In the example below, the original image block shown in Fig. 3(a) contains a noise point on a smooth background and its related Harr wavelet coefficients (only single level) are listed in Fig. 3(b). Assume JND ¼ 5 and the watermark bit is )1, )2, 1.4, respectively. The watermark bits are inserted into the high frequency coefficients, and the coefficients after watermark insertion are shown in Fig. 3(c). The watermarked image is obtained using the inverse wavelet transform and the result is shown in Fig. 3(d). It is noted from the figures that the contrast of the noise point and background is amplified by watermarking, and a non-perceptual noise has become perceptible. The similar distortion can be easily observed for a short edge. According to the above discussion, a better compromise between the robustness and transparency can be obtained when the watermark is only inserted into the high activity texture regions. Hence, we propose in this work to insert the watermark into the high activity texture region of an image. By doing so, we need to perform a texture analysis on the wavelet coefficients to see which spatial regions will have high activity texture.
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Fig. 3. Example of watermark insertion: (a) Original image block. (b) Wavelet coefficients (single level). (c) Coefficients after watermark insertion. (d) Watermarked image block.
Based on the content of FTM obtained before, there are two criteria in evaluating the texture activity of a spatial block. One is the number of significant wavelet coefficients in a FTM, and the other is the number of zero-tree in a FTM. Significant wavelet coefficients are corresponding to edge, boundary, and high activity texture region. Hence, if most of the coefficients have large magnitude, most likely the region is of high activity. Also, when the number of zero-tree in a FTM is large, it reflects that the region is of low activity, and vice versa. The zero-tree counting decision of the texture activity is easier to be compiled into the zero-tree image coder to construct a uniform watermarking and coding algorithm. Obviously, the two criteria can work independently but they also complement each other. Hence, we propose to check these two factors together when we perform the texture analysis. Given a FTM TI;J , we define a bit-map for it by checking the magnitude of the wavelet coefficients as follows: 1; TI;J ði; jÞ P VQ1 ; BI;J ði; jÞ ¼ ; ð4Þ 0; TI;J ði; jÞ < VQ1 ; where VQ1 is a threshold value determined by experiments. We first define an active factor A1I;J for the full-tree block based on the number of significant coefficients in a FTM as follows: X A1I;J ¼ BI;J ði; jÞ; 0 6 i; j 6 2L : ð5Þ i;j
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As the bit-map obtained in (4) has the same structure as FTM, the zerotree (Shapiro, 1993) can be used to represent the bit-map. A zerotree is a sub-tree from a root coefficient in a given level, in which all coefficients are zero. Twelve sub-trees in the bit-map are obtained from the 12 sign bits of high frequency subband coefficients in the L 1 level of the full-tree matrix. We represent the bit-map sub-tree as TL1;d , d ¼ 1; 2; . . . ; 12. We then define the zerotree sign as follows: 1; TL1;d is not a zerotree; SL1;d ¼ ð6Þ 0; TL1;d is a zerotree: We then define another active factor A2I;J of a full-tree block based on the number of zerotree in it as follows: X A2I;J ¼ SL1;d : ð7Þ d
The overall active factor of a FTM is then defined as AI;J ¼ a1 A1I;J þ a2 A2I;J ;
ð8Þ
where a1 and a2 are two weighting factors with a1 þ a2 ¼ 1. The decision threshold for determining the high activity texture is defined as Tr ¼ a1 Tr1 þ a2 Tr2 ; where Tr1 ¼ a
X
A1I;J
I;J
Tr2 ¼ a
X I;J
ð9Þ
X
1;
I;J
A2I;J
X
1:
I;J
If the overall active factor of a full-tree block is larger than the decision threshold, i.e., AI;J > Tr , the region is classified as a high activity region and the watermarking sequence will be inserted into this full-tree matrix. Otherwise, it is regarded as a low activity region and no watermark is inserted. 2.4. Watermark inserting algorithm Based on the above discussion, we formulate our proposed watermark inserting algorithm as follows: Step 1. Create a watermark array W ¼ ½wði; jÞ, where wði; jÞ is i.i.d. Gaussian random sequence with N ð0; 1Þ and seed by authorÕs signature. Step 2. The DWT coefficient matrix C of the image is obtained using the Mallat algorithm. Step 3. For a given root coefficient cI;J , a FTM TI;J is extracted from C, and an equal size submatrix WI;J is also extracted from W . The inserting position matrix PI;J ¼ ½pI;J ði; jÞ is created, where
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pI;J ði; jÞ ¼
1; 0;
TI;J ði; jÞ > gI;J ði; jÞ; otherwise:
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ð10Þ
Step 4. If AI;J < Tr , goto step 3 to extract the next FTM. Otherwise, insert the watermark into this FTM according to the following equation. W TI;J ði; jÞ ¼ TI;J ði; jÞ þ kgI;J ði; jÞpI;J ði; jÞwI;J ði; jÞ;
ð11Þ
where k is a control parameter according to the strength of the inserted watermark. The watermarked FTM is inserted back to matrix C and if this FTM is not the last one, goto step 3 to extract the next FTM. Step 5. The inverse DWT is applied to the watermarked coefficient matrix C W to obtain the watermarked image. 2.5. Watermark extraction The watermark sequence is extracted by using both the original image and watermarked image. Although a more reasonable extraction scheme is that the original image is not directly involved in the watermark detection process (Zeng and Liu, 1999), we are more concerned about the robustness of our FTM scheme when comparing with other methods (Cox et al., 1997; Podilchuk and Zeng, 1998). The inverse process of the inserting algorithm described in the last subsection is used to extract the watermark. For a given FTM, the watermark is extracted as 1 ^W ^ I;J ði; jÞ ¼ w TI;J ði; jÞ TI;J ði; jÞ pI;J ði; jÞ=gI;J ði; jÞ: ð12Þ k
3. Watermark detection Watermark detection is based on the classical detection theory (Kay, 1998). Different to the Cox et al.Õs detector (1997), we define a normalized detector as PN ^ k wk w q ¼ k¼1 : ð13Þ N pffiffiffiffi The mean value of this detector is independent of N or N and can be used to evaluate different watermarking schemes with different length expediently. We model the detection problem (Kay, 1998) as choosing one between H0 , which is termed as the noise-only hypothesis, and H1 , which is the watermark present hypothesis, or symbolically ^ k ¼ nk ; H0 : w ^ k ¼ w k þ nk ; H1 : w
ð14Þ
where nk is i.i.d. Guassian noise sequence with zero mean and variance r2n (N ð0; r2n Þ) and is independent of wk . It is easy to derive:
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H0 : q N 0; r2n =N ; H1 : q N 1; r2n =N :
ð15Þ
There are two common detection methods. The first detector is to find a threshold to minimize the sum of the probability of error detection and the probability of false The alarm. The threshold is Tq ¼ 0:5. If qp> pffiffiffiffiffiffi exists. ffiffiffiffi Tq , we declare that the R 1watermark 2 average error probability is Pe ¼ Qð N =2rn Þ, where QðxÞ ¼ x ð1= 2pÞeðð1=2Þt Þ dt is referred as the right-tail probability. The second detector is to fix a false alarm probability Pf and to maximize the detection probability Pd . The threshold Tq is derived by Pf as follows: rn Tq ¼ pffiffiffiffi Q1 ðPf Þ; N
ð16Þ
where Q1 ðÞ is an inverse QðÞ function. The detection probability is also derived from Pf as pffiffiffiffi N 1 Pd ¼ Q Q ðPf Þ : ð17Þ rn Using the first detector, a large false alarm probability will be obtained when r2n is large, and the false judgement may happen. If the second detector is used and r2n is large, the detection probability is less than that of the first one and an existent watermark may be missed out. In different applications, we can select a reasonable detector for the specific purpose. In reality, an attacker cannot damage a watermarked image severely according to requested perceptual quality. Only part of the watermarking sequence inserted in the host image will be affected. For JPEG attacking with 10–100% quality factor, statistic results show that 0 6 r2n < 36. Let N ¼ 2000 as an example, we give the performance of the two detectors in Fig. 4. For a small r2n , a satisfactory result can be obtained by using either of the detectors. The detection theory can be extended to two types of detectors: multiresolution detector and regional detector. 3.1. Multiresolution detector Let qk denote a k-resolution detector that only employs the received watermark sequence from level k to level L in the wavelet domain. The multiresolution detector is defined as q ¼ maxfqk ; k ¼ 1; 2; . . . ; L 1g: k
ð18Þ
It is noted that our multiresolution detector is different from the PodilchukÕs maximum correlation detector (Podilchuk and Zeng, 1998) which chooses the maximum value from all the possible levels as well as the frequency direction. Our multiresolution detector is only according to the natural resolution, which we think is more reasonable. For example, for a 256 256 image, our detector will only obtain the detection results from resolutions starting from 256 256 to 128 128 and 64 64.
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Fig. 4. (a) False alarm probability with fixed threshold 0.5; (b) Detecting probability with fixed threshold 0.5; (c) Threshold to maintain Pf ¼ 10 106 ; (d) Detecting probability under Pf ¼ 10 106 (abscissa is rn ).
3.2. Regional detector When we carry out the integrality authentication of a digital image, we probably suspect a region whether it is replaced by another image, then a regional detection is desired. Let the interested region in an original image be fði; jÞjN1 6 i < N2 ; M1 6 j < M2 g, then the superscript set of the FTM is
C ¼ ðI; J Þ ceilðN1 =2L Þ 1 6 I < ceilðN2 =2L Þ; ceilðM1 =2L Þ 1 6 J < ceilðM2 =2L Þ ; ð19Þ where ceil(X ) rounds the X to the nearest integer toward the infinity. The received watermarking sequence from the FTM belonging to C is denoted as WC , then the regional detector is defined as P ^k wk 2WC wk w qr ¼ ; ð20Þ NC where NC is the number of elements in set WC . With the multiresolution detector and regional detector, we can perform both ownership identification and integrality authentication using the same algorithmic framework with different parameters.
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4. Simulation results In this section, we present the experimental results to illustrate the robustness and perceptual quality of our proposed watermarking scheme. Simulations are carried out for several standard monochrome images. Test image ÔBarbaraÕ is of size 128 128 while images ÔLena,Õ ÔBaboonÕ and ÔAirplaneÕ are of size 256 256. We first consider the applications on copyright protection and hence the multiresolution detector is used with the setting of k ¼ 1:5 and a ¼ 1. In our experiments, the threshold value VQ_1 is set equal to 10 for all test images. Fig. 5 shows the resultant watermarked image using our proposed scheme on image ÔBarbara.Õ Fig. 5(a) shows the original image and Fig. 5(b) illustrates the watermarked image. It is noted that there is almost no perceptual difference between the original image and watermarked image. Fig. 5(c) shows the resultant image by JPEG compression for the watermarked image using 40% quality factor and Fig. 5(d) shows the real watermark inserted in the image (using enlarged range to display). It is noted that the watermark is only inserted to high activity texture region. The response of the watermark detector to 400 randomly generated watermarks is shown in Fig. 5(e). We then test the robustness of the proposed watermarking scheme against several attacks. It is known that the most common signal attack for digital images is JPEG compression. For comparison purpose, the table also shows the results of the Cox et al.Õs (1997) and Podilchuk and ZengÕs (1998) methods. To be noted, the comparison is made on the ground that the visual quality of the watermarked images of the three schemes is roughly the same. Figs. 6 and 7 show the watermarked images using the three methods for test images Baboon and Lena. Table 1 shows the detection results under different JPEG quality factors for different test images. It is shown that our scheme is very robust to JPEG compression comparing with the other two methods. The length of each watermark sequence that was inserted in host image is shown in Table 2. It is noted that the most number of bits can be inserted in the host image by using the PodilchukÕs scheme, but its robustness and watermarked image quality are undesirable. Although the work in Podilchuk and Zeng (1998) gives a maximum correlation value detector that may receive a larger detection value, but larger false alarm is obtained based on the less N in the denominator of the detector for a fixed level and direction. The spread spectrum watermarking distribution is independent on the image content, and hence the length of watermark sequence is limited. With the increasing of watermark length, the image quality is decreasing rapidly. Our scheme that inserts watermark into high activity texture region overcomes these drawbacks with a robust detector. It is shown that a high quality watermarked image and an appropriate amount of watermarking can be obtained using our proposed method. Figs. 6 and 7 also show the inserted watermarking sequence using different schemes for images ÔLenaÕ and ÔBaboon.Õ It is seen that the positions for watermark insertion are quite different for these three methods and our scheme mainly inserts the watermark in the high activity region like the hair region in image ÔLena.Õ For other attacks like addition of white noise, cropping, re-scaling, and low-pass filtering, our scheme is also robust. Table 3 shows the simulation results of our scheme for several different attacks. For the white noise addition, the white noise
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Fig. 5. Simulation results for image ‘‘Barbara’’: (a) Original image. (b) Watermarked image. (c) JPEG compression for watermarked image using 40% quality factor. (d) Inserted watermarking sequence. (e) Detection results using 400 randomly generated watermarks.
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Fig. 6. Simulation results for image ‘‘Baboon’’: (a) Inserted watermark using our scheme. (b) Inserted watermark using Cox et al.Õs scheme (1997). (c) Inserted watermark using Podilchuk and ZengÕs scheme (1998). (d) Watermarked image using our scheme. (e) Watermarked Image using Cox et al.Õs scheme (1997). (f) Watermarked Image using Podilchuk and ZengÕs scheme (1998).
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Fig. 7. Simulation results for image ÔLenaÕ: (a) Inserted watermark using our scheme. (b) Inserted watermark using Cox et al.Õs scheme (1997). (c) Inserted watermark using Podilchuk and ZengÕs scheme (1998). (d) Watermarked image using our scheme. (e) Watermarked image using Cox et al.Õs scheme (1997). (f) Watermarked image using Podilchuk and ZengÕs scheme (1998).
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Table 1 Detection results for JPEG compression attack Image
JPEG quality (%)
Cox et al.Õs scheme (1997)
Podilchuk and ZengÕs scheme (1998)
Our scheme
Barbara (128 128)
60 40 10
0.75 0.67 0.32
1.01 0.89 0.51
1.18 1.02 0.58
Lena (256 256)
60 40 10
0.9552 0.9129 0.7045
0.8145 0.7385 0.5719
1.1479 0.9719 0.9013
Baboon (256 256)
60 40 10
0.9768 0.9810 0.83
0.9897 0.9229 0.5558
1.1074 1.0633 0.7304
Airplane (256 256)
60 40 10
0.9432 0.9012 0.6896
0.9003 0.8345 0.4224
1.1338 1.0354 0.8821
Table 2 Length of watermarking sequence for 256 256 images Image
CoxÕs scheme
PodilchukÕs scheme
Our Scheme
Lena Baboon Airplane
1000 1000 1000
5583 11862 6230
3050 7168 3913
Table 3 Detection results for different attacks Attack
Lena
Baboon
Airplane
Addition of white noise in spatial domain Addition of white noise in frequency domain Cropping Low-pass filtering Re-scaling
1.1864 1.2092 0.7873 0.6931 1.2236
1.1188 1.1099 0.5738 0.7909 1.1134
1.1763 1.1290 0.6203 0.5403 1.1987
with variance r2 ¼ 100 is added in the spatial domain and frequency domain of the watermarked image. For image cropping, the right half of the watermarked image is cropped and replaced by the original image. In the low-pass processing, a low-pass filter only preserves one fourth of the low-frequency bank. Lastly, a half resolution watermarked image is first made by averaging four neighbouring pixels and then the re-scaled image is obtained by linear interpolation. By examining the results in Table 3, we can find that the detector output is always larger than 0.5. Therefore, we could conclude that our watermarking scheme is robust enough to those attacks mentioned before and has a better perceptual quality.
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We then evaluate the performance of our watermarking scheme in integrality authentication, which is another important application of digital watermarking. For instance, when a photo of news release is transmitted through the Internet, some sorts of protection are required for different attacks. If we suspect that a part of the photo has been modified by others, the regional detector is used to resolve the integrality authentication. Given an image, we will first use the multiresolution detector to check whether a particular watermark exists or not for ownership identification. If a watermark is detected and we suspect that a part of the image has been modified by others, the regional detector is then used to resolve the integrality authentication. In our experiments for integrality authentication, we set k ¼ 0:5 and a ¼ 0:5. For image ÔLena,Õ the face is extracted and only the four lowest frequency DCT coefficients are maintained and other coefficients are set to zero, then the inverse transformed face region is inserted to the original image and JPEG compression is carried out with 60% quality factor for the completed image. The resultant image is shown in Fig. 8(a). Similar procedures are applied to image ÔBaboonÕ and the resultant image
Fig. 8. Test images with local content modification: (a) Lena and (b) Baboon.
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Table 4 Detection results for regional and global detector Detector
Regional detector
Global detector
Lena Baboon
0.0172 0.2019
0.8242 0.7476
is shown in Fig. 8(b). Table 4 shows the detection results of using both the regional and global detector on the modified test images. It is shown that the regional detector can detect the changes of local content of the image while the global detector is difficult to observe these changes. Such result implies that the image is belonging to a particular owner but the content was modified.
5. Conclusion In this paper, an image watermarking scheme using wavelet transform is developed. The proposed scheme is based on the full-tree matrix (FTM), which is extracted from the coefficient matrix of the DWT to represent both the localizability and multiresolution features of an image. Simulation results show that, given the same visual quality of the watermarked image, our proposed method achieves a better compromise between the robustness and transparency than some other wavelet image-adaptive schemes. Besides the global detector, a regional detector is also derived so that the same algorithmic framework can be used not only for ownership identification but also for integrality authentication.
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