Journal of VLSI Signal Processing 27, 35–53, 2001c© 2001 Kluwer Academic Publishers. Manufactured in The Netherlands.

An Integrated Approach to Image Watermarkingand JPEG-2000 Compression

PO-CHYI SU, HOUNG-JYH MIKE WANG∗ AND C.-C. JAY KUODepartment of Electrical Engineering-Systems, University of Southern California, Los Angeles, CA 90089, USA

Received August 2, 1999; Revised January 17, 2000

Abstract. A scheme which integrates image compression and image watermarking in an effective way is proposedin this research. The image compression scheme under consideration is EBCOT (Embedded Block Coding withOptimized Truncation) which has been adopted in the verification model (VM) of the emerging JPEG-2000 imagecompression standard. The watermark is embedded during the process when the compressed bit-stream is formed,and can be detected on the fly in image decoding. Thus, watermark embedding and retrieval can be done veryefficiently in comparison with other existing watermarking schemes. In addition to efficiency, the proposed schemehas many interesting features. The embedded watermark is robust against various signal processing attacks suchas coding and filtering while the watermarked image maintains good perceptual quality. The watermark retrievalprocedure does not require the knowledge of the original image. Furthermore, the watermark can be detectedprogressively and region of interest (ROI) watermarking can be accomplished easily.

Keywords: JPEG-2000, EBCOT, digital watermark, progressive watermark detection, ROI

1. Introduction

The need to facilitate transmission, storage and archiv-ing of multimedia data has led to great research inter-ests in the development of efficient coding schemes inthe last two decades. With the advance of compres-sion technologies, high quality digital media can becompacted into a small data stream and distributedwidely over the network in a fast speed. When peo-ple start to enjoy listening to network audio, watch-ing on-line video, reading web newspapers, magazines,or other electronic publications, content-providers areconcerned with the problem of copyright infringement.Unlike traditional analog copying with which the qual-ity of the duplicated content is degraded, powerful dig-ital facilities can produce a large amount of perfectcopies in a short period of time. Therefore, to de-velop an effective way to deter users from illegally

∗Present Address: Media Fair, Inc., Monterey Park, CA 91754, USA.

reproducing or misusing digital media becomes an ur-gent issue. Recently, researchers have considered em-bedding invisible or inaudible information into digitaldata for copyright/ownership verification and authenti-cation. The hidden information is known as the digitalwatermark.

To unambiguously identify the content source or des-tination for successful copyright protection for digitalmedia, a digital watermark has several requirements.First of all, a digital watermark should be robust againstintentional or unintentional attacks including compres-sion, filtering, and format conversion, etc. Besides, thewatermark must be imperceptible to human beings andable to convey enough information for different pur-poses. The watermark has to be secure enough to resistattempted attacks by knowledgeable persons. More-over, watermarking schemes should have a low com-plexity so that they can be applied to real-time applica-tions. It is also important that the probability of water-mark false detection should be kept as low as possible.Therefore, a lot of design tradeoffs must be taken into

36 Su, Wang and Kuo

account to develop a sound watermarking scheme. Theoverview of watermarking techniques in various typesof media can be found in [1–3].

In image watermarking, we classify watermarkingschemes into two categories depending on the domainof watermark insertion and retrieval, i.e. the luminanceintensity in the spatial domain [4–7] and the trans-form coefficient magnitude in the frequency domain[8–12]. Spatial-domain watermarking is to embed in-formation by modifying the value of image pixels di-rectly, e.g. replacing the least significant bit (LSB) ofimage pixels with a binary pseudo-random sequence aswatermark information. The basic idea of frequency-domain watermarking is to modify frequency coeffi-cients after a proper transform such as the DiscreteWavelet Transform (DWT), the Discrete Cosine Trans-form (DCT), or the Discrete Fourier Transform (DFT)is applied. Frequency-domain watermarking methodscan be further divided into two categories: visual-model based and energy based watermarking. Thevisual-model based watermarking decides the locationand the amount of the cast watermark by exploitingthe human visual system model. The energy based wa-termarking is done by examining coefficients with alarger energy amount and modifying them slightly. Be-cause frequency-domain watermarking schemes tendto achieve both perceptual transparency and robustnessbetter, a lot of related algorithms have been developed.

Most of frequency-domain watermarking schemesare based on the additive spread-spectrum method,which is inspired by the spread-spectrum modulationtechnique in the digital communication system. Thistechnique provides more security and resistance tochannel noise for digital communication. Similarly,the spread-spectrum watermarking scheme can resistmore serious content distortion. The watermark is usu-ally represented by a pseudo-random signal with a lowamplitude. The pseudo-random signal is either addedor subtracted from the host data and then detected laterby using a correlation receiver or matched filter. Anearly spread-spectrum frequency-domain watermark-ing method is proposed by Cox et al. [9]. Watermarksequence with lengthN is added onto the largestNcoefficients (except the DC coefficient) after the globalDCT transform is applied to the image. The water-mark is retrieved by subtracting the original coeffi-cients from the watermarked coefficients and then acorrelation detector is used to calculate the similaritybetween the original watermark sequence and the ex-tracted one. Piva et al. [8] examined another global

DCT-based method but no original image is requiredfor watermark detection. This is usually calledblindwatermark detection. The global DCT coefficients arereordered by using a zig-zag scan. Fixed DCT coef-ficients (e.g. 16000th to 25000th coefficients for animage with size larger than 256 by 256) are selectedfor watermark embedding and retrieval. The abovetwo watermarking methods share one common majordrawback. That is, the watermarking process is veryslow due to the high computational complexity in cal-culating global DCT coefficients. Xia et al. [10] con-sidered a multi-resolution watermarking method in thewavelet domain which requires the original image inwatermark retrieval. Wang et al. [12] investigated ablind wavelet-based watermarking scheme, in whichthe inserted watermark signal is adaptively scaled bydifferent threshold values to maintain perceptual in-tegrity of the watermarked image. These two wavelet-based watermarking methods are more robust againstwavelet-based coding in comparison with DCT-basedwatermarking schemes as given in [8, 9].

It is worthwhile to point out that image compressionand frequency-domain watermarking share some com-mon characteristics. In image compression, we encodesignificant frequency coefficients first because thesecoefficients convey more fundamental visual informa-tion about the image. In watermarking, we choose sig-nificant coefficients for watermark casting to enhanceits robustness since these coefficients often remain sta-ble after the attack. If they do change substantially, thereconstructed image will be perceptually different fromthe original one, and the value of protecting the intellec-tual property right of such a seriously degraded imagebecomes low. With this similarity, efficiency can beachieved by integrating frequency-domain watermark-ing procedures with compression processes, since themost expensive computation related to the image trans-form has been already computed as one part of com-pression and decompression algorithms.

In this research, we investigate an integrated ap-proach to image compression and watermarking.The image coding scheme under our considerationis EBCOT (Embedded Block Coding with OptimizedTruncation) [13, 14], which has been accepted inJPEG-2000 VM (Verification Model) and will be thebackbone of JPEG-2000 coding scheme. EBCOT hasseveral distinct advantages, including efficient rate con-trol, low computational complexity, low memory re-quirement, good error resilience and excellent codingefficiency. Besides, EBCOT supports region of interest

Integrated Approach to Image Watermarking and JPEG-2000 Compression 37

(ROI) coding, which allows users to select parts of animage to achieve higher fidelity. By integrating thewatermarking scheme with JPEG-2000, the proposedwatermark embedding and retrieval are more efficientin comparison with existing watermarking schemes.The watermark is embedded in the discretized host im-age coefficients by examining bit-planes. A binary orbi-polar watermark sequence is used, and the resultingwatermarked image coefficients also take only discretevalues. Therefore, both watermark embedding and de-tection occur directly in the compressed domain. Theintegrated scheme eliminates both the need to com-press the host image after watermark embedding andthe need to decompress the watermarked image beforewatermark detection. In addition to efficiency, the pro-posed scheme has quite a few interesting features. Theembedded watermark is robust against various signalprocessing attacks including compression and filter-ing while the resulting watermarked image maintainsgood perceptual quality. The progressive character-istic is essential for Internet applications since userscan get a coarse-resolution image after a small portionof the bit-stream is received. For the same reason, itis desirable that the embedded watermark can be de-tected progressively so that an operation, which is en-abled via watermark detection such as “never copy”,can be enforced earlier without waiting for the wholeimage to be downloaded. Furthermore, ROI water-marking can be easily coupled with ROI coding in theproposed scheme. In this case, when we receive ROIwithout the background, the watermark can still be de-tected without ambiguity. The embedded watermarkcan be detected without the knowledge of the originalimage so that it is a blind watermarking scheme. Ex-perimental results show that the proposed integratedJPEG-2000 watermarking performs very well and sup-ports all above claims.

This paper is organized as follows. A brief overviewof JPEG-2000 compression scheme is provided inSection 2. The integrated watermark embedding anddetection procedures are presented in Section 3. Thedecision and analysis of the threshold for watermark de-tection are discussed in Section 4. Experimental re-sults are illustrated in Section 5. Finally, concludingremarks are given in Section 6.

2. Brief Review of JPEG-2000

The current JPEG-2000 VM (Verification Model)[13, 14] is based on the Embedded Block Coding with

Optimized Truncation (EBCOT) scheme proposed byDr. Taubman. Basically, EBCOT can be viewed as ablock-based bit-plane coder. By the block-based coder,we mean that the basic coding unit is a block insteadof the whole image as used in coding schemes such asSPIHT [15] and EZW [16]. A bi-orthogonal wavelettransform is first applied to the image, and each sub-band of wavelet coefficients is divided into blocks ofsamples with the same dimension, except at imageboundaries where some blocks may have smaller di-mensions. Therefore, blocks in lower resolution sub-bands span a larger spatial region in the original im-age. Each block is then encoded independently byusing the same algorithm. That is, for each block, aseparate bit-stream is generated without resorting toany information from other blocks. The bit-stream canbe truncated to a variety of discrete lengths with re-spect to different distortion measures. Once the entireimage has been compressed, a post-processing opera-tion passes over all compressed blocks, and determinesthe extent to which each block’s embedded bit-streamshould be truncated to achieve the target bit-rate. Thefinal bit-stream is formed by concatenating the trun-cated bitstreams of all blocks together.

EBCOT is a bit-plane coding, i.e. the most signif-icant bits for all samples in the code block are sentfirst, then the next most significant bits and so onuntil all bit planes are sent. Previously encoded in-formation about the current sample and neighboringsamples are exploited for efficient block coding. Foreach bit-plane, the coding proceeds in a number ofdistinct passes. EBCOT provides many features, in-cluding random access, Signal to Noise Ratio (SNR)progressive, SNR parsable, resolution progressive, res-olution parsable and component parsable. The richbit-stream syntax makes EBCOT more attractive thanother wavelet-based coders. Region of interest (ROI)is one interesting feature that can be easily supportedby EBCOT. ROI coding makes it possible to encoderegions in which users are more interested with bet-ter quality than the rest of the image. For the extremecase, the specified ROI can be encoded losslessly whilethe remaining parts of the image are encoded with lowbit-rates. When ROI is small compared with the wholeimage, the transmission time and the storage space canbe greatly saved.

The implementation of EBCOT is a pipeline struc-ture, which attempts to minimize the internal memorysize. Thus, EBCOT can be implemented by hardwareconveniently. Two kernels are used in EBCOT. One

38 Su, Wang and Kuo

is reversible kernel for lossless compression, and theother is non-reversible kernel for lossy compression.Since the two kernels use different wavelet filters andnormalization strategies, encoding and decoding mustadopt the same kernel. For lossy compression, the orig-inal I -bit image samples are level shifted to a nominalrange of−2I−1 to 2I−1 and then shifted up byP− I−Gbits to fit within theP-bit implementation precision.Gis the number of guard bits, which is included to avoidthe occurrence of overflow so that the frequency coeffi-cients can be represented with the fixed-point precision.The wavelet transform kernels are then normalized sothat the low-pass analysis filters always have a unit DCgain and the high-pass analysis filters always have aunit Nyquist gain. This means that the nominal rangeof subband coefficients will be in the range of−2P−G−1

to 2P−G−1. The normalization of coefficients is a veryimportant step in the EBCOT implementation, whichturns out to facilitate the proposed watermarking pro-cess as described later.

3. Watermark Embedding and Retrival

3.1. Framework for Watermarking

Before presenting the implementation of the proposedwatermarking scheme, we briefly describe the basicframework of the watermarking method to be adopted.Similar to most robust watermarking schemes given inSection 1, the additive spread-spectrum watermarkingmethod is chosen due to its decent characteristics in ro-bustness, unobtrusiveness and security to watermark-ing applications. After a proper transform (the wavelettransform in our scheme) is applied to the image, thewatermark is added onto the selected frequency coef-ficient by

I ′(x, y) = I (x, y)+ α(x, y)×W(x, y), (1)

where I ′(x, y) is the watermarked coefficient andI (x, y) is the original coefficient with the coordinate(x,y) in the spatial position.I (x, y) is chosen based onits magnitude, i.e. the coefficient with the large magni-tude is selected for watermark embedding.W(x, y) isthe corresponding watermark symbol, which can be areal number or only take values, 1 and−1. The weight-ing factorα(x, y) is a positive number used to adjustthe amount of added watermark energy. The valueof α is usually adjusted according to the magnitudeof the frequency coefficients or the different subband

characteristics so that the balance between robustnessand fidelity of the resulting watermarked image can beachieved. The inverse transform is then applied to formthe watermarked image.

In watermark detection, a correlation detector is usedto determine if the watermark exists in the tested im-age. It is based on the fact that if the coefficients and thewatermark sequence are independent, the inner productof the watermark and the coefficient sequences will beclose to 0. If the target watermark sequence is added tothe coefficient sequence, we will get a peak responsefrom the inner product. We show this basic idea asfollows; I ∗(x, y) is the wavelet coefficient of the sus-pected image. We make use of the correlation detectorto determine if the wavelet coefficients are embeddedwith a specific watermark sequenceW∗(x, y). Thecorrelation responseρ of the watermark detector canbe expressed as

ρ =∑(x,y)

(I ∗(x, y)×W∗(x, y)) (2)

By assuming thatI ∗(x, y) is formed by casting wa-termark symbolW(x, y) onto the original coefficientI (x, y) without any modification, then we can expressρ as

ρ =∑(x,y)

((I (x, y)+α(x, y)×W(x, y))×W∗(x, y))

(3)

=∑(x,y)

(I (x, y)×W∗(x, y))

+∑(x,y)

(α(x, y)×W(x, y)×W∗(x, y)) (4)

After calculating the expected value of both sides,we get

E [ρ] = E[∑(x,y)

(I (x, y)×W∗(x, y))

]

+ E[∑(x,y)

(α(x, y)×W(x, y)×W∗(x, y))

],

(5)

whereE [·] is the expected value. The first term onthe right-hand side of (5) is zero if the tested water-mark sequenceW∗(x, y) and the coefficientsI (x, y)are independent. Similarly, the second term is also zeroif W(x, y) andW∗(x, y) are independent orW(x, y)

Integrated Approach to Image Watermarking and JPEG-2000 Compression 39

does not exist. If the image is embedded withW∗(x, y),i.e. W(x, y) = W∗(x, y), then the expected value ofthe correlation responseE [ρ] will be close to

E [ρ] = E[∑(x,y)

α(x, y)×W∗2(x, y)

], (6)

which is much larger than zero. Therefore, we cansimply examine the peak response and compare it witha threshold value to determine the existence of water-mark without any difficulty.

3.2. Implementation of the Integrated WatermarkingScheme

In the proposed system, the watermark is embeddedafter coefficients are quantized so that the watermarkcan be easily embedded into the bitstream. Watermarkdetection is done before the dequantization stage. Wechoose the non-reversible kernel for watermark embed-ding and detection in the following discussion sincelossy compression offers a broader application scopethan the lossless one. The same idea can however beapplied to the reversible kernel without modification.

3.2.1. Watermark Embedding. To make the embed-ded watermark robust against attacks, significant coef-ficients are chosen for watermark casting. Significantcoefficients are those with a larger magnitude. Becausecoefficients in each subband have been normalized tohave unit gain in EBCOT implementation, the signif-icant coefficients in each subband tend to have theirhighest non-zero bit in the same bit-plane. Therefore,we can apply the same watermark embedding rule ineach subband. EBCOT divides the subband into blockswhich is the basic coding unit so that we also use thecoding block as the basic unit for watermarking.

In EBCOT implementation, the Most Significant Bit(MSB) of the coefficient indicates the sign value andthe remainingP − 1 bits represent the absolute mag-nitude of the coefficient. This simplifies the case whenthe magnitude is required only, because we can avoidthe calculation of the absolute value. We select signifi-cant coefficients by examining the highest non-zero bit(not including the sign bit) that is higher than a certainbit-plane with indexq. That is, coefficientIbs(x, y) inthe blockbs of subbands with the coordinate(x, y)will be chosen for watermark embedding if

‖Ibs(x, y)‖ ≥ 2q, (7)

where we define that the Least Significant Bit (LSB)of coefficients form the bit-plane with index “0”. Thestrategy to select coefficients matches the bit-plane cod-ing well since coefficients to be coded earlier will becast with the watermark first. The watermark in ourscheme is a random number sequence taking two val-ues 1 and−1. First, a seed, which can be viewed asa user ID number, is used to generate the watermarksequence with the length equal to the number of co-efficients in a coding block. The sequence forms awatermark map with a dimension equal to that of ablock. For a block of sizeγ × γ , the watermark mapis Wbs(x, y), wherex, y ∈ [0, γ ), and the coefficientIbs(x, y) that satisfies (7) is modified toI ′bs

(x, y) by

I ′bs(x, y) = Ibs(x, y)+ (Wbs(x, y)× 2δbs

)(8)

whereWbs(x, y) = ±1 is the watermark element in theposition(x, y) on the watermark map associated withblockbs andδbs is the number of bit-shift that dependson the implementation precisionP and the watermarkenergy. In general, the shifted number is chosen to be

δbs = P − I − G+ αbs. (9)

As mentioned earlier,P, G andI are the implemen-tation precision, the guard bit, and the image sampleprecision, respectively, andαbs is the watermark scal-ing factor. We may increase the embedded watermarkenergy by shifting the watermark a few bits to the left.It should be noted thatαbs can vary in different sub-bands or blocks so that we can adjust it according todifferent subband or block characteristics. Generally,only bitplanes aroundP− I −G+αbs will be affectedby watermark embedding so the bitplane-based water-mark embedding method does not affect the codingefficiency much. Besides, by experiments, the settingof δbs achieves a pretty good balance between imagequality and robustness of the watermark. Special caremust be taken that we do not cast the watermark inblocks of the DC band since it may lead to seriousfidelity degradation in the watermarked image.

3.2.2. Watermark Detection. As done in the embed-ding procedure, we only pick coefficients that satisfy(7) for watermark detection. We use the same bit-planeas a reference so that only the coefficients that are pos-sibly embedded with watermark are taken into consid-eration. A similar objective might be achieved if weembed and detect the watermark in all of the wavelet

40 Su, Wang and Kuo

coefficients. However, the watermarking process willbe less efficient because the computational load willincrease significantly especially when we have to testa lot of watermark sequences to see which one is em-bedded in the image.

However, we have to take the significance of differ-ent subbands into account during watermark detection.A value called “extra LSB” and denoted byβbs is de-termined along with the EBCOT normalization processand can be interpreted as the number of insignificantbit-planes in the coding blockbs. βbs is smaller in sub-bands that need better precision and larger in high-frequency subbands. Thus, the calculation of correla-tion response is done as

ρ =∑s

∑bs

∑(x,y)

(‖I ∗bs(x,y)‖≥2q ).

(I ∗bs(x, y)× 2−βbs

)×(Wbs(x, y)× 2(δbs−βbs )

)∑

s

∑bs

∑(x,y)

(‖I ∗bs(x,y)‖≥2q )

2(2δbs−2βbs)

,

(10)

whereδbs is defined in (9). I ∗bsis the coefficient of

the investigated image. Note that there is a differencebetween (2) and (10). In (10), we normalize the corre-lation response by the sum of squares of selected wa-termark symbols. Since the watermark symbol takesvalue 1 or−1, W2

bs(x, y) is equal to 1 and omitted in

the denominator. There are a couple of reasons thatwe decide to normalize the correlation response. Firstof all, the value of the response will not be affectedby the number of selected coefficients. Consequently,the same correlation response can be used in differentscenarios, e.g. normal watermark detection and pro-gressive watermark detection, which will be discussedin Section 3.3. Second, this normalization process willhelp in explaining the high value of the correlation re-sponse of the watermarked image in our scheme. Thatis, the value of (2) in a watermarked image will be evenlarger than (6). This phenomenon will be discussed inSection 4.

3.3. Progressive Watermark Detection

Progressive watermark detection is one of the mostattractive features for watermarking in JPEG-2000compressed images. When a large image is being de-compressed, it is not efficient to detect the watermarkafter the whole image is formed. This is especiallytrue for Internet applications. A fully-embedded com-

pression scheme lets the user truncate the image at anytime to get his or her “best” image. Thus, it is de-sirable that the watermark can also be detected pro-gressively. EBCOT is a bit-plane coder which cansupport the fully-embedded feature. Significant coeffi-cients, which have been embedded with the watermarkin our scheme, will be encoded and decoded first sothat progressive watermark detection can be achievedeasily. However, we should set a threshold valueη toindicate the minimum number of coefficients neededfor watermark detection. If the correlation responseis higher than the current threshold, which is used todecide the existence of watermark, but the selected co-efficients are less thanη, the detection process shouldcontinue in other blocks to avoid possible false alarm.The derivation of the threshold in the proposed water-marking scheme will be discussed in Section 4.

3.4. Region of Interest Watermark

There are two types of ROI functionality. The first oneis “ROI during encoding”, in which ROI is specifiedwhen the image is compressed. The other one is “ROIduring decoding” that supports interactive browsing.In JPEG-2000 VM, the “ROI during encoding” modeis implemented. In the encoder part, coefficients thatbelong to ROI remain unchanged while other coeffi-cients which do not belong to ROI are scaled downby a few bits. The encoding process is done as usualwhile the coordinates of ROI and scaling values areput in the bitstream header for transmission. When theSNR progressive mode is used, ROI will be sent beforethe background. The decoder can detect ROI by exam-ining the magnitude of received coefficients since allROI coefficients are larger than other coefficients out-side ROI. The decoder may have to upshift the receivedcoefficients when necessary.

Under this scenario, we do not have to change theproposed algorithm because only coefficients in ROIwith a larger magnitude will be embedded with thewatermark. All coefficients outside ROI will be down-shifted so that they will not satisfy the criterion in (7)for watermark embedding and retrieval. To conclude,our scheme can support ROI watermarking automati-cally.

4. Threshold Decision and Analysis

It is essential to determine a threshold value so that theexistence of a watermark sequence can be detected by

Integrated Approach to Image Watermarking and JPEG-2000 Compression 41

comparing the value of the correlation response withthe selected threshold value. There are two main partsin this section. First of all, we determine the thresh-old value to decrease the possibility of false positivedetection. False positive detection occurs when thewatermark is falsely detected in an image that con-tains no watermark or the wrong watermark ID is de-tected. Since the usage of the image will be limitedonce a certain watermark is found, false positive detec-tion will bring much more inconvenience to the legit-imate users. Therefore, the threshold value should bedecided carefully. Second, we examine the peak cor-relation response of the watermarked image and showthat the existence of the watermark can generate a largecorrelation response.

In watermark detection, we compute the sum of mul-tiplications of the shifted coefficients with the corre-sponding watermark symbol in the watermark map, andthen divide it by a weighting factor, i.e. the weightednorm of the watermark sequence as indicated in (10).Here, we assume that the correlation responseρ fol-lows the Gaussian distribution due to the Central LimitTheorem.

The variableρ in (10) has a mean equal to zero ifthe watermark does not exist. The variance ofρ can beestimated by

σ 2ρ '

∑s

∑bs

∑(x,y)

(‖I ∗bs(x,y)‖≥2q )

I ∗2

bs(x, y)× 2(2δbs−4βbs)

∑

s

∑bs

∑(x,y)

(‖I ∗bs(x,y)‖≥2q )

2(2δbs−2βbs)

2 , (11)

where all entities in above are the same as those in (10).By definition, the Gaussian Integral Function [17]

(or simply theQ function) can be written as

Q(z) =∫ ∞

z

1√2π

e−x2

2 dx. (12)

If random variableY(u) follows the Gaussian distri-bution with meanm and varianceσ 2, the probabilitythatY(u) > a can be expressed as

Pr{Y(u) > a} = Q

(a−m

σ

). (13)

We should set up the threshold value according totheQ function so that the false alarm rate is lower than

a given probability. As a result, the threshold valueis actually a function of the variance ofρ. Here, wesimply define the threshold as

T = τ × σ, (14)

whereτ is a scaling parameter. On one hand, we canlower the false alarm rate by raising theτ value. Onthe other hand, we can reduce theτ value so that de-tection of the embedded watermark can be more easilyachieved even under very serious attacks at the expenseof a higher false alarm rate. For example, if the desiredfalse alarm rate is around 10−12, we should choose thethreshold value asT = 7σ since

Pr{Y(u) > T} = Q

(T

σ

)= Q(7) = 1.28× 10−12.

(15)

In progressive watermark detection, the probabilityof false alarm can be larger because the number ofthe selected coefficients may not be large enough. Wechoose a largerτ to get a higher threshold to lower theprobability of false alarm as much as possible. It isalso possible to adjust theτ value to adapt to differentdetection situations.

After setting up the threshold, we would like to an-alyze the peak value of the correlation response whena certain watermark is found to exist in an image. Tosimplify the analysis, it is assumed that the extra LSBβbs and the bit-shift numberδbs are both equal toδ in allblocks. If the watermark exists, (10) can be modifiedas

ρ =∑{(Id+Wd× 2δ)× 2−δ ×Wd}∑

(Wd×Wd)

=∑(Id×Wd)∑(Wd×Wd)

× 2−δ + 1, (16)

whereWd and Id are the watermark symbol and theoriginal coefficient selected by the watermark detector.To be more precise, we calculate the expected value onboth sides as

E [ρ] = E[ ∑

(Id×Wd)∑(Wd×Wd)

]× 2−δ + 1. (17)

As discussed in Section 3.1, one may think that thefirst term on the right-hand side of (17) is zero so that theexpected value of the maximal correlation peak is unity.However, the peak can be substantially larger than 1 if acertain watermark exists in the image as argued below.

42 Su, Wang and Kuo

Let Ie denote the original coefficient selected by thewatermark embedder, i.e. the coefficient satisfies (7),and We be its respective watermark symbol, i.e. thewatermark symbol to be cast on the selected coefficient.First, we calculate the expected cumulative sum ofIe×We:

E [Re] = E[∑

(Ie×We)]. (18)

Note thatE [Re] = 0 becauseIe andWe are indepen-dent. Let us divideE [Re] into two parts, i.e.

E [Re] = E [Re1] + E [Re2]

= E[∑

(Ie1 ×We1)]+ E

[∑(Ie2 ×We2)

].

(19)

Ie2 is the coefficient satisfying both of the followingconditions:

2q ≤ ‖Ie2‖ < 2q + 2δ, q > δ, (20)

and

Ie2 ×We2 < 0, (21)

whereWe2 is the respective watermark symbol ofIe2.Obviously,E [Re2] is a negative number so thatE [Re1]has to be positive to makeE [Re] equal to 0. However,owing to the process of watermark detection, coeffi-cients Ie2 in Re2 will not be picked by the detectionprocess in watermark retrieval since its highest non-zero bit isq− 1, which is lower thanq. Therefore, theexpected value of the correlation response calculatedin the detection process is equal to

E [ρ] = E [Re] − E [Re2]

E[∑

W2e2

] × 2−δ + 1

= E [Re1]

E[∑

W2e2

] × 2−δ + 1> 1 (22)

The number of coefficientsIe2 is quite large so thatthe first term of the right-hand side in (22) can be largerthan 1 to generate a peak valueρ that could be evenequal to 2 when the watermark exists in the image.Therefore, the first term of the right-hand side in (17)is positive and does make a contribution to the peakcorrelation response when a watermark is embedded.

One main concern of the correlation-based water-mark detection is the efficiency issue. To determinewhich watermark ID number is embedded, we mayhave to check all possible ID numbers. By assuming

the total number of users is 232, it is not practical totry from ID number 0 to 232− 1 to determine the ex-actly embedded watermark ID number. Thanks to theblock coding of EBCOT, we can simplify the detec-tion structure. We first divide all coding blocks inton subsetSi , i = 1, . . . ,n. We can embedk bits ineach of the subsetSi . Therefore, the total number ofbits that can be embedded in the image isk × n. Inwatermark detection, we only need to check 2k dif-ferent watermark candidates in each subset to decidethe k-bit value. k × n bits can be decoded correctlyaftern subsets are processed. If we also consider thesign of the correlation response, we can check only2k−1 watermark candidates in each block. For largerimages, we are able to have more divided subsets toallow a larger watermark capacity. However, becausespread-spectrum watermarking is adopted in the sys-tem, a spreading gain must be maintained to reliablyembed and retrieve the watermark. Therefore, thereexists a tradeoff between robustness and capacity.

5. Experimental Results

In this section, we show some experimental re-sults to demonstrate the robustness of the proposedwatermarking scheme. The embedded watermark hasan ID number 500, which is actually the seed to gen-erate the random watermark sequence. The watermarkis embedded when the image is compressed. It can bedetected when the EBCOT bit-stream is expanded. Wetest 1000 watermark ID numbers to see if the correctone is detected without ambiguity. A threshold valuecalculated with (14) is used to determine if there existsa certain watermark in the image.

First of all, we examine the parameters to be usedin the experiments. In EBCOT implementation, thecoefficient precisionP can be either 32 or 16. Wechoose 32 since it is commonly used in software orhardware designs today. The guard bitG is chosenas 2, which has been shown a reasonable number toavoid the overflow problem. Therefore, the nominalrange of subband coefficients will be in(−229, 229).The image sample precisionI is equal to 8 for gray-level images. In the experiments, we letq in (7) beequal to 24 so that if a coefficient that has the non-zero bit higher than or equal to 24 will be viewed asa significant coefficient for watermark embedding orretrieval. The watermark sequenceWbs, which takesvalue 1 or−1, is left-shifted by 22+ αbs bits and thenadded to the selected coefficients to form watermarked

Integrated Approach to Image Watermarking and JPEG-2000 Compression 43

Figure 1. Original images v.s. compressed/watermarked images: (a) original “Bike”, (b) watermarked “Bike” (PSNR:32.49 dB), (c) orig-inal “Woman” and (d) watermarked “Woman” (PSNR:33.09 dB). Both images are with size 2048× 2560 and are compressed with0.5 bpp.

coefficients as indicated in (9). The value of “extraLSB”, which indicates the number of insignificant bit-planes in a coding block, is determined by EBCOT. Wedo not make any change on it. In watermark detection,our algorithm tends to generate a very high correlationresponse if the watermark exists. This allows us to set ahigher threshold value to avoid any possibility of falsealarm. The threshold scaling parameterτ in (14) is setto 7. If the progressive watermark detection is used, wechooseτ to be 8.5. As mentioned in Section 3.3, weshould define the minimum numberη of the selected

coefficients to claim the existence of watermark. In theexperiment,η is chosen to be 500.

Two JPEG-2000 test images, “Bike” and “Woman”,with size 2048 by 2560, as shown in Fig. 1(a) and (c),respectively, are used to demonstrate the invisibility ofthe embedded watermark. Because of the large sizeof the images, we encode them with a lower bit rateequal to 0.5 bpp so that they can be stored and trans-mitted efficiently. The SNR progressive mode is en-abled to demonstrate the fully-embedded feature andprogressive watermark detection. When the watermark

44 Su, Wang and Kuo

function is disabled, the peak signal to noise ratio(PSNR) between the original and the compressed im-ages of “Bike” and “Woman” are 33.54 dB and 33.70dB, respectively. The PSNR values between the origi-nal and watermarked/compressed images are 32.49 dBand 33.09 dB, respectively. It is clear that the qualitydegradation resulting from watermark insertion is verylittle. The watermarked images are shown in Fig. 1(b)and (d).

Next, we demonstrate the correlation response inthe watermark detection process. Detection results areshown in Fig. 2. We can see clearly that there exists apeak with the watermark ID number 500 in both cases.The peak value of the correlation response is muchlarger than the threshold valueT , which is shown asthe break line in the figures. The responses of other wa-termarks are much lower thanT . The target watermarkcan thus be determined unambiguously.

It usually takes a while to decode such large imagescompletely from the entire bit-stream. Furthermore,

Figure 2. Watermark detection results for (a) “Bike” and (b) “Woman” with 1000 watermark sequences tested.

Figure 3. Progressive watermark detection: (a) watermark detection by using the progressive mode and (b) watermark detection of the imagedecoded at a bit rate of 0.01 bpp.

watermark detection may involve a lot of coefficients sothat the watermarking process is also time-consuming.We take the “Woman” image for example. There areover 400K coefficients selected for watermark detec-tion. Actually, the number of the selected coefficientsnecessary for watermark detection can be reduced. Weuse progressive watermark detection by taking advan-tage of the fully-embedded feature of JPEG-2000 tospeed up the watermarking process. There are twoways to demonstrate this property. The first one isto adopt progressive watermark detection. During thedecoding process, whenever the correlation responseis larger than the thresholdT and the number ofthe selected coefficients is larger thanη, we stopwatermark detection and claim the existence of wa-termark. We test “Woman” image in progressive wa-termark detection. The result is shown in Fig. 3(a). Thenumber of selected coefficients is 32,611. The valueis still large because we set up a conservative thresh-old to avoid false alarm. In the second approach, we

Integrated Approach to Image Watermarking and JPEG-2000 Compression 45

Figure 4. Postprocessing: (a) part of the “Bike” image before postprocessing, (b) part of the “Bike” image after postprocessing and (c) thewatermark detection result.

do not use progressive detection but specify the decod-ing rate of the image. Fig. 3(b) shows the detectionresult when the image is decoded at a bit rate equal to0.01 bpp. In this case, the number of selected coeffi-cients is 6,511. The existence of watermark with IDnumber 500 is detected in both cases, yet the speed ofwatermark detection is greatly improved.

Although wavelet-based coding schemes have theadvantages over the block DCT-based coding methodin terms of the rate-distortion tradeoff performance,reconstructed images still suffer from various codingartifacts such as ringing effect, graininess, and blotch-iness, etc. In JPEG-2000 VM, a postprocessing tech-nique is used to reduce these artifacts so that the overallvisual quality of decoded images can be improved sub-stantially. Therefore, we apply the JPEG-2000 post-processing technique [14, 18] to the decoded imageand then test the performance of watermark detection.

We decode the “Bike” image with 0.125 bpp and thenfeed it to the postprocessing stage with three iterations.The effect of the postprocessing can be understood bycomparing the two images, before and after postpro-cessing. Fig. 4(a) and (b) show only part of the “Bike”image. The ringing artifact around the bike handler inFig. 4(a) is greatly reduced in Fig. 4(b) so that the visualquality is improved. The watermark detection resultdemonstrated in Fig. 4(c) indicates that our watermark-ing scheme can be coupled very well with JPEG-2000including the postprocessing procedure.

The next example is ROI watermarking. ROI codingis especially useful for large images. We use the otherJPEG-2000 test image, “Aerial2” (2048×2048), as anexample because application of ROI is important foraerophotography. We assign two rectangular regionswhich cover two constructions in image “Aerial2” asthe desired ROI. We then enable the SNR progressive

46 Su, Wang and Kuo

Figure 5. ROI watermarking: (a) the fully reconstructed image from ROI coding bitstream, (b) the decoded image with a bit rate of 0.4 bpp,(c) the spatial difference of these two images (the lighter the pixel is, the larger the difference and the two black rectangles are the assigned ROI)and (d) the watermark detection result.

mode to encode the image, and then decode it with alower bit rate. We see that the two regions are wellreconstructed while other parts of the image remainblurred. The ROI coding can be verified by the spatialdifference of the transmitted image and the roughly de-coded image as shown in Fig. 5(c) where the lighterthe pixel is, the larger the difference between the twoimages. The detection result shown in Fig. 5(d) indi-cates that the proposed watermarking scheme matchesthe ROI feature of EBCOT, and the embedded water-mark can be detected without any difficulty. Besides,with ROI watermarking, it is also possible to embeddifferent watermark ID numbers into different objectsin the same image. In this case, the watermark canbe viewed as a function of data labeling, which may

benefit content-based retrieval in the management ofmultimedia databases [19].

We then apply a series of attacks to show the robust-ness of the proposed watermarking schemes. First,we consider compression attacks, i.e. to compress theimage with other schemes at low bit rates. The well-known DCT-based codec, JPEG, and the wavelet-basedcodec, SPIHT, are the two compression attacks undertest. The attacked image is encoded into the EBCOTbitstream for watermark detection. Since perceptualloss caused by compression varies in different images,some images can be compressed with a higher com-pression ratio yet preserving good image quality. Toverify that the watermark is robust against JPEG andSPIHT attacks, we choose to compress the image with

Integrated Approach to Image Watermarking and JPEG-2000 Compression 47

Figure 6. Compression attacks: (a) the watermarked “Woman” image compressed by JPEG with quality factor equal to 1 (PSNR: 22.61 dB),(b) the watermark detection result of the JPEG-attacked image, (c) the watermarked “Woman” image compressed with SPIHT at a bit rate of0.005 bpp (PSNR: 22.50 dB) and (d) the watermark detection result of the SPIHT-attacked image.

extremely low bit rates. That is, the “Woman” imageis compressed by JPEG with quality factor equal to 1and by SPIHT with a bit rate of 0.005 bpp. The result-ing images and detection results are shown in Fig. 6.In the JPEG-attacked image as shown in Fig. 6(a), avery serious blocking artifact appears since JPEG en-codes an image block by block. The SPIHT-attackedimage, as shown in Fig. 6(c), is blurred very muchsince only a few coefficients are used to reconstructthe whole image. The PSNR values of the JPEG- andSPIHT-attacked images are 22.61 dB and 22.50 dB,

respectively. Although the two images are compressedto an unacceptable degree, the embedded watermarkstill survives well as shown in Fig. 6(b) and (d).

GIF is a popular file format for graphics. UnlikeJPEG, the maximum number of colors that can be usedfor a picture is 256. For some images, annoying vi-sual degradation may not be generated when they areconverted to the GIF format. Thus, color reduction isanother important type of attack that a watermark mustresist. We have tested three kinds of color-related at-tacks. The first one is to reduce the number of colors

48 Su, Wang and Kuo

from 256 to 4 for a gray-level image. The second oneis image halftoning that is used quite often in FAX,newspapers, or other publications. The third one ishistogram equalization which tends to stretch the dy-namic range of the gray-level distribution of an image.

Figure 7. Color-based attacks.

Detection results of these attacks and attacked imagesare shown in Fig. 7. The distinctive peak of the corre-lation response indicates the survival of the watermarkeven though the attacked image is visually differentfrom the original one.

Integrated Approach to Image Watermarking and JPEG-2000 Compression 49

We then test the performance of our watermarkingscheme when the protected image is resized or cropped.We reduce the watermarked “Woman” image from asize of 2048× 2560 to a size of 256× 320 and theninterpolate it back to the original size, as shown inFig. 8(a). The finer detail of the image is lost due tothe resizing process. The detection result is shown inFig. 8(b), which indicates the watermark survives afterthe resizing operation. We also crop the lower 3/4 ofthe image and fill it with a constant gray level of 128 as

Figure 8. Robustness test against cropping and resizing attacks: (a) resizing “Woman” from 2048× 2560 to 256× 320 and then interpolatingit back to 2048× 2560, (b) the watermark detection result of the resized image, (c) cropping the lower 3/4 of the watermarked image and fillingit with gray level 128, and (d) the watermark detection result of the cropped image.

shown in Fig. 8(c) for the watermark robustness test.The result is shown in Fig. 8(d). Again, the watermarkcan be easily detected. However, the pre-registrationprocess must be done before detecting watermark fromthese two attacked images so some information of theoriginal image is required.

With the advances of graphical tools, users may editan image with some artwork. Thus, it is interestingto test the robustness of the proposed watermark-ing scheme by using a popular editing tool, e.g. the

50 Su, Wang and Kuo

Paint Shop Pro. In order to demonstrate the attackeffects, we choose a smaller image, “Rodeo” pro-vided by Corel Corporation. The image has size768 by 512 and is compressed with bit-rate equal to0.75 bpp. The PSNR between the original imageand compressed/watermarked image is 39.83 dB. The

Figure 9. Extensive watermark testing on the watermarked “Rodeo” (768× 512).

attacks tested include blurring, sharpening, edge en-hancement, eroding, dilating, median filtering, aver-aging, 25% random noise adding, 25% uniform noiseadding, softening, and mosaic. The attacked imagesand detection results are shown in Fig. 9. We can seethat the watermark is very robust under these attacks

Integrated Approach to Image Watermarking and JPEG-2000 Compression 51

because the watermark is embedded in significant co-efficients that usually remain stable after most imageprocessing operations.

Finally, we would like to measure the false positiverate of the proposed system. As mentioned in Section 4,there are two cases in false positive detection: (1) thewatermark is detected in an un-watermarked image and(2) the wrong watermark ID is detected. In the firstcase, i.e. the watermark is found in an un-watermarkedimage, the best method to measure the probability offalse positive detection is to detect watermarks in nu-merous clear (un-watermarked) images by using theproposed watermarking scheme. This part is difficultto achieve due to the shortage of content sources. How-ever, we believe that the Gaussian assumption shouldhold in this case so that the false positive rate shouldbe covered by our analysis. The major concern of theaccuracy of the Gaussian assumption comes from thesecond case, i.e. a wrong watermark is detected froma watermarked image with different ID. At this point,we would like to verify it by experimental data. To doso, we generated 100000 watermark sequences, con-structed the watermarked image by embedding one ofthe watermark sequences and used 100000 watermarks(one correct watermark and the other 99999 incorrectwatermarks) for detection. We counted the number oftested watermarks with a correlation response higherthan the threshold value set according to the allowablefalse positive rate. We tested the false positive ratefrom 5× 10−3 to 10−5. We measured more pointsaround 10−4 to 10−5 because these measurements maybe more correct and important. The results are shownin Table 1. We see that the number of false detectionmatches pretty well with the predicted false detection

Table 1. The number of false positive detectionsmeasured from 100000 tested watermark sequences v.s.estimated number of false positive detections based on Gaussianassumption.

Error Number of wrong Expected number ofrate watermark detected false detection

5× 10−3 525 500

10−3 99 100

5× 10−4 55 50

10−4 12 10

8× 10−5 10 8

5× 10−5 7 5

3× 10−5 3 3

10−5 1 1

based on the Gaussian assumption. Table 1 verifies thesuitability of our analysis. By following this trend, weexpect that the false positive analysis will work when ahigher threshold value (with lower false positive rate)is set.

6. Conclusion

We presented an integrated approach to image com-pression and watermarking in this paper. EBCOT,which is the basis of JPEG-2000 VM, provides variousfeatures for different applications and the proposed wa-termarking method can be coupled with EBCOT to pro-vide a way to assert copyright information for JPEG-2000 compressed images. The watermark sequence isembedded on significant wavelet coefficients so that itis robust against general signal processing attacks. Thedetection process does not resort to the help from theoriginal image. Progressive watermark detection canbe supported so that the watermark retrieval process canbe done faster. ROI watermarking can also be achievedeasily under the same framework. One may view thisintegrated scheme as a base-line watermarking schemefor copyright protection. Other variants can be easilyderived based on this basic scheme. Future work will beto build an anti-geometric watermarking scheme uponthis basic scheme to make the watermarking systemmore robust.

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Mr. Po-Chyi Su was born in Taipei, Taiwan in 1973. He receivedthe B.S. degree from the National Taiwan University, Taipei, Taiwan,in 1995 and M.S. degree from the University of Southern California,

Los Angeles, in 1997, both in Electrical Engineering. He is cur-rently pursuing the Ph.D. degree at the Signal and Image Process-ing Institute, University of Southern California. His research inter-ests include digital watermarking, data compression and detectiontheory.pochyisu@sipi.usc.edu

Dr. Houng-Jyh Mike Wang received the M.S. and Ph.D. degreesfrom the University of Southern California, Los Angeles, in 1994and 1998 respectively, all in Electrical Engineering. He has authoredmore than 20 technical publications in international conferences andjournals. Dr. Wang’s research interests include multimedia compres-sion, digital watermarking, cryptography, and signal detection.

Dr. Wang worked at the Chung-Shan Institute of Science andTechnology (CSIST), a research institute of the Department of Na-tional Defense in Taiwan, from 1988 to 1993, where he obtainedthe Award of Excellent Staff of CSIST. He is the National HonoraryCivilian of Taiwan.

He is a member of the Institute of Electrical and Electronics En-gineering (IEEE), the International Society for Optical Engineer-ing (SPIE) and the International Standard Organization-Joint PictureExpert Group (ISO-JPEG). He is the vice president and the chiefof technology office in Media Fair, Inc., USA and working on theInternet multimedia researches and applications.mikewang@mediafair.com

Dr. C.-C. Jay Kuo received the B.S. degree from the Na-tional Taiwan University, Taipei, in 1980 and the M.S. and

Integrated Approach to Image Watermarking and JPEG-2000 Compression 53

Ph.D. degrees from the Massachusetts Institute of Technology,Cambridge, in 1985 and 1987, respectively, all in Electrical En-gineering.

Dr. Kuo was Computational and Applied Mathematics (CAM) Re-search Assistant Professor in the Department of Mathematics at theUniversity of California, Los Angeles, from October 1987 toDecember 1988. Since January 1989, he has been with the Depart-ment of Electrical Engineering-Systems and the Signal and ImageProcessing Insitute at the University of Southern California, where hecurrently has a joint appointment as Professor of Electrical Engineer-ing and Mathematics. His research interests are in the areas of digitalsignal and image processing, audio and video coding, wavelet theory

and applications, multimedia technologies and large-scale scientificcomputing. He has authored around 400 technical publications ininternational conferences and journals.

Dr. Kuo is a member of SIAM, ACM, a Fellow of IEEE and SPIE.He is the Editor-in-Chief for the journal of Visual Communicationand Image Representation, and served as Associate Editor for IEEETransaction on Image Processing in 1995–98 and IEEE Transactionon Circuits and Systems for Video Technology in 1995–1997. Dr.Kuo received the National Science Foundation Young InvestigatorAward (NYI) and Presidential Faculty Fellow (PFF) Award in 1992and 1993, respectively.cckuo@sipi.usc.edu