Image Adaptive Watermarking Using Wavelet Domain Singular Value

96 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 15, NO. 1, JANUARY 2005

Transactions Letters________________________________________________________________

Image Adaptive Watermarking Using Wavelet Domain Singular ValueDecomposition

Paul Bao and Xiaohu Ma

Abstract—In this letter, we propose a novel, yet simple,image-adaptive watermarking scheme for image authenticationby applying a simple quantization-index-modulation processon wavelet domain singular value decomposition. Unlike thetraditional wavelet-based watermarking schemes where the wa-termark bits are embedded directly on the wavelet coefficients,the proposed scheme is based on bit embedding on the singularvalue (luminance) of the blocks within wavelet subband of theoriginal image. To improve the fidelity and the perceptual qualityof the watermarked image and to enhance the security of water-marking, we model the adaptive quantization parameters basedon the statistics of blocks within subbands. The scheme is robustagainst JPEG compression but extremely sensitive to maliciousmanipulation such as filtering and random noising. Watermarkdetection is efficient and blind in the sense only the quantizationparameters but not the original image are required. The quantiza-tion parameters adaptive to blocks are vector quantized to reducethe watermarking overhead.

Index Terms—Fragile watermarking, singular value decomposi-tion (SVD), statistic modeling, wavelet.

I. INTRODUCTION

THE ADVENT of the Internet and the advancement ofdigital technologies in the past decade have enabled

numerous applications in the areas of the multimedia com-munications and multimedia networking. While one of thegreat advantages of digital data is that it can be reproducedlosslessly, it is also vulnerable to imperceptive modificationand malicious tampering. Thus, the authentication and thecopyright protection from unauthorized manipulation of digitalaudio, image, and video data become an essential concern inthe digital multimedia era. Digital watermarking [1] has at-tracted considerable attention and seen numerous applicationsrecently. An effective authentication scheme should possessthe following characteristics: transparency, robustness to com-pressions, sensitivity (fragility) to malicious manipulation, andblind detection of watermarks. Among the several categoriesof watermarking schemes, the wavelet-based watermarkingschemes and image-adaptive watermarking schemes are ofgreat interest due to their impressive performance in trans-parency, robustness, sensitivity, and blind detection for thevarious applications.

Manuscript received April 22, 2003; revised July 27, 2003. This paper wasrecommended by Associte Editor E. Izquierdo.

P. Bao is with the School of Computer Engineering, Nanyang TechnologicalUniversity, 639798 Singapore (e-mail: [email protected]).

X. Ma is with the Department of Computer Science, Xuzhou Normal Univer-sity, Xuzhou 221004, China (e-mail: [email protected]).

Digital Object Identifier 10.1109/TCSVT.2004.836745

In 1997, Xia et al. [2] proposed a multiresolution water-marking method by inserting pseudorandom codes to thelarge coefficients at the high- and middle-frequency bandsof the dicrete wavelet transform (DWT) of an image. Theirwatermarking method is robust to some common image com-pressions and halftoning but the detection of the watermarkis dependent on the noise level in an image. Inoue et al.[3] proposed a watermarking scheme by classifying waveletcoefficients as insignificant or significant using zerotree andthen embedding a watermark in the location of insignificantcoefficients or in the location of the thresholded significantcoefficients at the coarser scales. Xie et al. [4] proposed ascheme combining watermarking with wavelet compression byengraving a watermark in the wavelet coefficients and encodingthe watermarked coefficients using SPIHT compression algo-rithm. Their method is nonadaptive and may alter the originalfrequency correlations of the images. Tsai et al. [5] proposeda watermarking scheme which utilizes the wavelet domainimage frequency components and the chaotic transformation toselect the location during the watermark embedding. Vehel etal. [6] presented a digital image watermarking by modifyingcertain subsets of the wavelet packet decomposition, deter-mined from a secret key and an image dependent procedure. Huet al. [7] proposed a watermarking scheme using pixel-basedscaling, where the scaling factors for the pixel-based methodare adaptively determined by the effect of luminance andlocal spatial characteristics. Taskovski et al. [8] presented alow-resolution content-based watermarking scheme, where thewatermark is embedded in the lowest resolution of three-levelwavelet decomposition incorporated with a visual modelingof the local image characteristics. Besides the aforementionedwatermarking schemes based on the structural distribution inwavelet domain for watermark embedding, schemes based onthe human perceptual modeling of the wavelet coefficients werealso proposed. Wei et al. [9] introduced a perceptually basedwatermarking technique where the watermark is inserted in thewavelet coefficients so that watermark noise does not exceedthe just-noticeable difference of each wavelet coefficient. Barniet al. [10] proposed a watermarking algorithm based on themasking of the watermark according to the characteristics ofthe human visual system (HVS).

In all the previous wavelet-based watermarking schemes, thewatermark bits would be directly embedded in the locations ofthe wavelet coefficients determined by the various modeling.While the watermarks embedded in the wavelet coefficients

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 15, NO. 1, JANUARY 2005 97

may be able to preserve the visual perceptions of the originalimages, it is vulnerable to compressions since the watermarkedcoefficients may be subject to thresholding and quantization inthe compression process, thus damaging the watermark bits.Aiming at the indirect watermarking embedding, Gorodetski etal. [11] proposed a simple singular value decomposition (SVD)domain watermarking scheme by embedding the watermarkto the singular values (SVs) of the images, to achieve a bettertransparency and robustness. But the method is not image adap-tive and unable to offer a consistent perceptual transparency ofwatermarking for different images. Liu et al. [12] presented arobust SVD domain watermarking scheme where a watermark(in the form of a matrix) is added to the singular value matrix ofthe watermarking image in spatial domain. Liu’s scheme offersgood security against tampering and common manipulations forprotecting rightful ownership. But since the scheme is designedfor the rightful ownership protection, where the robustnessagainst manipulations is desired, it is suitable for authentication.The scheme is also nonadaptive thus unable to offer a consistentperceptual transparency of watermarking for different images.

Chen et al. [13], [14] introduced a framework for characteringthe inherent tradeoffs between the robustness of the embedding,the degradation to the host image, and the amount of data em-bedded and designed a framework of information embeddingsystems,namelyquantizationindexmodulation(QIM),aimingatoptimizing the rate-distortion-robustness tradeoffs. They devel-oped a method, the dither modulation, to realize and demonstratethe QIM framework, where the embedded information wouldmodulate the dither signal of a dithered quantizer. The QIMschemes can achieve an optimal tradeoff between the embeddingrate, the distortion and the robustness by freely adjusting thenumber of quantizers, the quantization steps and the minimumdistance, respectively, for different requirements such as robust-ness to a known manipulation. But the QIM schemes manipulatethe quantization-index modulation directly in the original signaldomain and fail to take the advantages offered by wavelet-basedor other indirect watermarking schemes in achieving a betterperformance in all the characteristics.

Synthetically, it seems that none of the schemes could si-multaneously offer the characteristics of adaptive transparency,robustness to compressions, sensitivity to malicious manipula-tion and blind detection of watermarks. To address this issue, wedesign a novel image-adaptive watermarking scheme for imageauthentication by applying a quantization-index-modulationprocess on the SVs of the images in wavelet-domain in thisletter. In this scheme, the watermark bits are embedded on theSVs in the SVD layers for each of the wavelet domain blocks,with the quantization steps adaptive to the statistical modelof the block, which ensures that the overall luminance changebe minimized and perceptually unnoticeable. The block size,together with the weighting parameters and the minimum andmaximum quantization steps, would determine how well a blockcould be modeled statistically leading to a unified framework forcontrolling the transparency, robustness against compressions,fragility to malicious manipulations, and embedding rate. Sincethe watermark is distributed at the luminance (the SVs) in all thesubbands where the relative luminance (thus,the watermark) inwavelet domain would be well preserved during the coefficient

quantization, it is extremely robust to the JPEGcompressions.Onthe other hand, the watermarks so embedded are very fragile toany malicious manipulations such as filtering or random noisingsince any manipulation attempt would most probably damagewatermark bits in all the subbands, thus destroy the authenticityof the watermark. The watermark detection in our scheme isblind, i.e., only the quantization parameters but not the originalwatermark image are needed. Furthermore, since the watermarkembedding is based on the quantization of the SV of blocks wherethe quantization parameters are modeled by the block statistics inthe wavelet domain, it is, thus, impossible to maliciously detectthe watermark without the quantization parameters.

II. WATERMARKING BASED ON SVD

A grayscale digital image is specified by an matrix. If a color image is represented in RGB then it

can be converted to the corresponding luminance matrix. An arbitrary matrix can be repre-

sented by its SVD in the following form:

(1)

where and are orthogonal and matrices,respectively, and is a diagonal matrix with nonnegative ele-ments. Diagonal terms of matrix are SVs ofmatrix and is the rank of matrix . SVD possesses sev-eral attractive mathematical properties, one of which is that eachSV specifies the luminance of the SVD image layer, whereasthe respective pair of singular vectors specifies intrinsic geom-etry properties of images. It was discovered that slight varia-tions of SVs do not affect the visual perception of the coverimage, which motivates the watermarking embedding throughslight modifications of SVs in the segmented images.

The proposed scheme is briefly described as follows. Animage represented in matrix format is segmented into blocksof size (in our experiment, is generally set to 4) andthe SVD for each of the blocks is performed. Then, one bit ofdata is embedded through a slight modification of the SV ofthe block. Let be the current bit of the watermark image tobe embedded into this block . The embedding algorithm isdescribed as follows.

1) Segment the image into blocks of size ,, where is the number of the blocks.

2) Compute , where ,is a vector formed by the SVs of each block .

3) Compute integer number , where is thequantization step for corresponding to the block .

4) Embed one bit of watermark image as follows.If , then

If is odd number, thenELSE remains unchanged

If , thenIf is even number, thenElse remains unchanged.

5) Compute the value and the modifiedSV


TABLE ICONSTANT QUANTIZATION STEP d: THE QUALITY OF WATERMARKED IMAGE (PSNR) AND BER OF THE EXTRACTED WATERMARKS CORRESPONDING TO

SEVERAL JPEG COMPRESSIONS, RESPECTIVELY

6) Compute the matrix of the block using the modified SV

7) Reconstruct the watermarked image from all the blocks.

It should be noticed that quantization step would be servedas a secret key to ensure the authorized access to the watermark.The extraction of the watermark is straightforward. Let be ablock with an embedded watermark bit.

1) Segment watermarked image into blocks of size, , where is the number of the blocks.

2) Compute the value , ,where is a vector formed by the SV ofeach block .

3) Compute .4) If is even number, then the embedded bit is 1. Other-

wise, it is 0.

III. MODELING OF THE QUANTIZATION PARAMETERS

A. Quantization Parameters Based on Spatial DomainModeling

For a watermarking scheme, it is desired that the water-marked images achieve a high PSNR while the watermark canbe detected and extracted robustly against any compressionschemes, i.e., possessing a lower bit-error ratio (BER) againstcompressions. In the aforementioned SVD-based watermarkingscheme, it is obvious that the increase of the value leadsto more robust watermark embedding (lower BER) but poorertransparency of the watermarked image (lower PSNR) and viceversa. Table I gives the PSNRs of the watermarked images usingseveral constant quantization steps and their correspondingBERs against JPEG compressions. Fig. 1 shows the visualperceptions of the watermarked images for various quantizationsteps, respectively.

From Table I, it can be observed that the perceptual quality ofwatermarked image is reversely proportional to the robustnessagainst JPEG compression. In order to preserve the high percep-tual quality of the watermarked image while retaining a goodrobustness to JPEG compression, we propose an image-adap-tive quantization for image watermarking. With this adaptive

quantization scheme, a watermarking scheme with high trans-parency and robustness to JPEG compressions can be obtained.The method can be described as follows.

1) Calculate the standard deviation for each block .2) Calculate the maximum value and minimum value

for all the .3) Compute the quantization step for the block as

(2)

where is the number of all blocks, and areminimum and maximum quantization step values, respec-tively, specifiable by user.

Table II gives some comparison results with the basic algorithmin Section III and Fig. 2 gives the visual examples of the water-marked images, where 9 and 36 or 45.

Note from Table II that the BERs increase rapidly as the JPEGcompression ratios. This is because that the watermarking distri-bution is only adaptive to the standard deviation of each block inthe spatial domain. Thus, the SVs of a more spatially structuredblock (larger deviation) would be significantly modified whichmay be insignificant in wavelet domain and thus be thresholded.On the other hand, the SVs of a less spatially structural block(small deviation) would be slightly modified, which, however,could be significant in wavelet domain allowing the embeddingof more watermark information. Thus, the aforementioned wa-termarking distribution scheme would result in a less satisfyingtransparency and a poor robustness to compressions.

B. Adaptive Quantization Parameters Based on WaveletDomain Modeling

In view of this potential drawback, we propose a set of quanti-zation parameters modeled adaptively to both the deviation andthe expectation of each block within the wavelet domain wherethe SVs for the real structures will be largely modified with wa-termarking whereas that of the nonstructural background will beslightly modified to ensure a high perceptual quality of water-marked image and a low BER of the detected watermark. Thescheme is detailed as follows.

1) An image is transformed into wavelet subbands. In each ofthe subbands, the coefficients are segmented into blocksof size and SVDs for each of the blocks are com-puted.


Fig. 1. Visual appearances of the watermarked images obtained by constant quantization steps. (a) Watermark image. (b)–(c) Two original images. (b1)–(b3)Watermarked images corresponding to the original image (b) when quantization steps d are set to 9,27, and 54, respectively. (c1)–(c3) Watermarked imagescorresponding to (c) when d = 9, 27, and 54, respectively.

TABLE IIIMAGE ADAPTIVE QUANTIZATION STEP d : THE QUALITY OF WATERMARKED IMAGE (PSNR) AND BER OF THE EXTRACTED WATERMARK CORRESPONDING TO

SEVERAL JPEG COMPRESSION RATIOS, RESPECTIVELY

2) Calculate the standard deviation and average valuefor DWT coefficients of each block .

3) Calculate the value for each block

(3)

where and are the weight parameters for and.

4) Calculate the maximum value and minimum valuefrom all the .

5) Compute the quantization step for block as follows:

(4)

where is the number of the blocks, and and are theminimum and maximum quantization step values, respectively,specifiable by user.

We model the quantization parameters based on both the ex-pectation and deviation of the block to capture both the struc-tural and background statistics in quantizing the modificationof the SV. In our experiment, we set andor , and let , . The value is formu-lated so that both the baseband and the high-pass bands can bewatermarked and the modifications of the SVs can be adjustedusing parameters and . Parameter controls the quanti-zation weighting for the background while for the structures.


TABLE IIITHE QUALITY OF WATERMARKED IMAGE (PSNR) AND BER OF THE EXTRACTED WATERMARK CORRESPONDING TO 40% JPEG COMPRESSION FOR DIFFERENT

VALUES OF PARAMETER c AND c , RESPECTIVELY

Fig. 2. Experimental results of the wavelet domain image-adaptiveSVD watermarking scheme. (a) Watermark image. (b) Original images.(c)Watermarked images with PSNRs 38.6755, 38.3048, 39.3839, 38.9264, and37.4773, respectively. (d) Detected watermark image from LL band, whered 2 [9; 45] or d 2 [9; 36].

Table II presents the quality of the watermarked image (PSNR)and the BER of the extracted watermark corresponding to sev-eral JPEG compression ratios, respectively. Table III gives thequality of the watermarked image (PSNR) and the BER of theextracted watermark corresponding to the different values of theparameter and .

C. Vector Quantization of the Quantization Parameters

In the proposed watermarking scheme, the image-adaptivequantization parameters are adopted as the secrete keys for the

watermark extraction. The experiment shows that while thetransparency of watermarked images can be well preserved, thenumber of the error bits detected in the detected watermark isvery small, an obvious advantage in watermarking applications.However, these image-adaptive quantization parameters mustbe transmitted as the secrete key for the correct extraction ofthe embedded watermark from the watermarked image and thusthe size of the quantization parameters would be an overheadconcern if they were not efficiently encoded. In this section, wepropose using the vector quantization to compress the secretekeys without affecting the effectiveness of the watermarkingscheme.

The vector quantization for the image-adaptive quantizationparameters is described as follows.

1) Create the new range [0,14] from the original range [9,36],which can be describe as follows:

2) Divide the new quantization parameter matrix into 5 5subblocks, and arrange each of the subblocks as 5 5 4vectors.

3) A codebook with size is established using the Gen-eralized Lloyd algorithm. In our experiment, can begenerally set to 64 or 32.

4) Encode the index of each 5 5 quantization parameter inthe codebook.

The compression ratio and the perceptual quality of the wa-termarked image are illustrated in Fig. 3 using 200 200 Lena,Peppers, and Baboon with different codebook sizes. The file sizeof the original image Lena (200 200) is 118 KB in bitmap un-compressed format or 37 KB in JPEG compressed format. Fromthe Fig. 3, it can be observed that the high quality of the water-marked image can been preserved when and the wa-termark key is sized at

kB or at a compression ratio of 80:1 (0.4517:37).

IV. EXPERIMENTAL RESULTS AND DISCUSSIONS

In this section, experimental results are given to illustratethe transparency, robustness against JPEG compression andfragility against malicious manipulation of the proposed wa-termarking scheme. The perceptual quality of images afterthe watermarking insertion is showed. The tolerance of thescheme against compressions and the fragility to the variousmalicious manipulations is experimented. Table II and Fig. 2give the respective results. From the Table II and Fig. 2, it can


TABLE IVCOMPARISONS BETWEEN THE PROPOSED METHOD AND WAVELET BASED WATERMARKING SCHEMES ON 512 � 512 IMAGES: BER OF THE EXTRACTED

WATERMARK CORRESPONDING TO SEVERAL JPEG COMPRESSION RATIOS, RESPECTIVELY

Fig. 3. (a)–(b) Watermarked image Lena when S is set to 64 and 32,respectively. (c)–(d) Peppers when S is set to 64 and 32, respectively.(e)–(f) Baboon when S is set to 64 and 32, respectively. (a) S = 64,PSNR = 38:7383. (b) S = 32, PSNR = 38:6065. (c) S = 64,PSNR = 38:8181. (d) S = 32, PSNR = 38:7204. (e) S = 64,PSNR = 37:0850. (f) S = 32, PSNR = 36:9575.

be observed that the proposed hybrid wavelet domain SVDwatermarking scheme preserves not only the high perceptualquality of the watermarked image, but also possesses an ex-cellent robustness against the JPEG compression with variouscompression ratios. Compared with the spatial domain SVDscheme, the proposed scheme achieves extremely low BERswhile retaining high PSNRs even against a compression ratioas low as 20%. For example, for image Shore, the wavelet SVD

produces virtually no errors for the extracted watermark whilethe simple SVD scheme has a BER between 1.87 and 15.24. Forthe compression ratios at 40% or lower, the proposed schemestarts to generate some errors for the extracted watermarksbut by varying the weight parameters and , we couldminimize the BER for a given PSNR range. Table III shows thePSNR measurement of the watermarked images at 40% JPEGcompression and different BERs corresponding to differentvalues of parameter and , respectively, where the optimalBERs are boldfaced.

Obviously, the transparency of the watermarked imagesand the robustness against JPEG compression are closelyrelated to the number of the embedded bits, thus the sizeof blocks. The larger is set, the fewer bits are embeddedresulting in thebetter transparency(higherPSNR)androbustness(lower BER). Table IV gives some results when is setto 8 and the watermark bits are only inserted into the LLsubband, in comparisons with other watermarking schemes[3], [11]. It can be seen that the proposed scheme significantlyoutperforms the simple SVD scheme [11] in BER for variouscompression ratios while achieving better visual perceptionsof the watermarked images. And the proposed method alsooutperforms the two wavelet-based watermarking schemes [3]and the QIM method [13] in BERs for various compressionratios with comparable PSNRs. Note that the PSNR valuesachieved are lower compared to those by the wavelet schemesbut the perceptual differences are unnoticeable (PSNRs at 40dB or higher usually lead to excellent visual perceptions).Table IV also shows that the proposed scheme could achievea higher embedding rates than SVD-based, wavelet-based andQIM watermarking schemes. It should be clarified that inTable IV, the data by the proposed method and the simple SVDmethod are produced by experiment but the correspondingdata by the wavelet and QIM methods are taken directlyfrom [3], [13]. The PSNR measurements and the robustness(BER) against JPEG compressions may vary for differentwavelets and thus the comparison should be served as areference.

It is also shown that in the proposed scheme the watermarkextracted is very fragile to the malicious manipulations suchas cropping, random noising (Gaussian), and filtering, etc.


Fig. 4. (a1)–(a2) Modified watermarked images. (b1)–(b2) Detected watermark images corresponding to the LL band. (c1)–(c2) Enlarged detected watermarkimages for detecting the malicious modification operation.

Fig. 4 shows that the proposed wavelet domain SVD-basedwatermarking scheme can effectively detect the maliciousmanipulations made on the watermarked image, includingcropping, Gaussian and , and medianfilters (3 3) and (4 4), where the watermarks extracted areseriously damaged for all the manipulations. Thus any attemptto manipulating the watermarked images would be detectedand the content associated with the images would be effectivelyauthenticated.

V. CONCLUSION

In this letter, a novel, yet simple, hybrid wavelet domainSVD-based watermarking scheme for image authenticationis presented, where the watermark bits are embedded on theSV (luminance) of the blocks within each wavelet subband ofthe original image. The quantization parameters of the water-marking are modeled based on the statistics of block imageswithin different subbands in wavelet domain thus adaptive tothe individual image. The parameters can be automaticallydetermined for the enhanced perceptual quality of the water-marked images. While the proposed scheme preserves highperceptual quality of the watermarked image (high PSNR)and possesses an excellent robustness to JPEG compression(low BER), it also possesses an excellent fragility to variousmalicious manipulations, thus enabling a variety of the au-thenticated networked multimedia applications. The watermarkdetection is also efficient and blind, i.e., only the compressedquantization parameters but not the original image are needed.Since the watermark embedding is solely determined by thequantization parameters, the malicious detection of the water-mark would not be possible without knowing the quantizationparameters. The scheme also achieve higher embedding ratesthan other methods.

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