A SVD-BASED WATERMARKING SCHEME FOR PROTECTING RIGHTFUL OWNERSHIP *

Transcription

1 SVD-BSED TERMRKIG SCEME OR PROTECTIG RIGTUL OERSIP * Ruzhen Lu and Tenu Tan atonal Lab of Pattern Recognton Insttute of utomaton, Chnese cademy of Scences P. O. Box 78, Bejng, 18, P. R. Chna Emal: {lurz, tnt}@nlpr.a.ac.cn BSTRCT Dgtal watermarkng has been proposed as a soluton to the problem of copyrght protecton of multmeda documents n networked envronments. There are two mportant ssues that watermarkng algorthms need to address. rstly, watermarkng schemes are requred to provde trustworthy evdence for protectng rghtful ownershp; Secondly, good watermarkng schemes should satsfy the requrement of robustness and resst dstortons due to common mage manpulatons (such as flterng, compresson, etc.). In ths paper, we propose a novel watermarkng algorthm based on sngular value decomposton (SVD). nalyss and expermental results show that the new watermarkng method performs well n both securty and robustness. 1. ITRODUCTIO The advent of the Internet and the wde avalablty of computers, scanners and prnters make dgtal data acquston, exchange and transmsson a smple task. owever, makng dgtal * Ths work s supported by the Chnese S (Grant o ) and the Chnese cademy of Scences. 1

2 data accessble to others through networks also creates opportuntes for malcous partes to make salable copes of copyrghted content wthout permsson of the content owner. Dgtal watermarkng technques have been proposed n recent years as methods to protect the copyrght of multmeda data [1,,3,4]. In general, an effectve watermarkng scheme should satsfy the followng basc requrements: 1. Imperceptblty: the perceptual dfference between the watermarked and the orgnal documents should be unnotceable to the human observer,.e., watermarks should not nterfere wth the meda beng protected.. Trustworthness [5,6,7,8]: a satsfactory watermarkng scheme should also guarantee that t s mpossble to generate counterfet watermarks, and should provde trustworthy evdence to protect the rghtful ownershp. 3. Robustness [9,1,11,1]: gven a watermarked document, an unauthorzed party should not be able to destroy the watermark wthout also makng the document useless,.e., watermarks should be robust to common sgnal processng and ntentonal attacks. In partcular, they should stll be detectable or extractable even after common sgnal processng operatons have been appled to the watermarked mage (such as dgtal-to-analog, analog-to-dgtal conversons, resamplng, flterng, compresson, geometrc transformaton, croppng, scalng, rotaton, etc.). Most exstng watermarkng schemes focus on robust means to make the watermark mperceptble rather than on addressng the mportant ssue of how to resolve the rghtful ownershp of an mage embedded wth multple sgnatures (or watermarks, labels, etc.) [5,8,13].

3 Craver et al [13] were among the frst to note that resolvng the rghtful ownershp of watermarked mages s a very mportant ssue. They smulated the cases of attackng exstng watermarkng technques by provdng counterfet watermarkng schemes that can be performed on a watermarked mage to allow multple clams of ownershp. Ther proposed attack s sometmes known as the IBM ambguty attack (or protocol level attack). n example s the nverson attack by Craver et al. that attempts to dscredt the authorty to the watermark by embeddng one or several addtonal watermarks such that t s unclear whch was the frst authortatve watermark embedded by the IPR owner. Currently only a few methods have been reported that try to solve the ownershp problem. The frst such method s probably the one presented by Craver et al. They desgn a non-nvertble scheme whch s a modfed verson of the watermarkng method proposed by Cox et al [9]. owever, the non-nvertblty of ther scheme s based on an nvald assumpton [8]. The second s based on tme-stampng as proposed by olfgang and Delp [14]. The owner wth the earlest tmestamp s the true owner of the watermarked documents. owever tme stampng has the dsadvantages of requrng ongong nvolvement of a thrd party and beng unsutable for tme senstve applcatons. In addton, tmestamps can be manpulated by anyone else besdes the true owners. Ths scheme can thus be easly defeated. The thrd method s proposed by Zeng et al [15]. Because ther watermarkng scheme detects the embedded watermark wthout usng the orgnal mage, t actually cannot resolve rghtful ownershp [8]. In ther algorthm, the watermarkng scheme protects the embedded watermark rather than the ownershp of dgtal mages. The key ssue les n that because watermark detecton n the ther algorthm does not need orgnal mages, an attacker can always 3

4 create hs counterfet orgnal mages and clam hs/her ownershp (see [8] further dscussons). Qao et al [8] proposed the fourth scheme to try to solve the ownershp problem. They combne ther scheme wth cryptography and use a standard encrypton algorthm (.e. DES) to generate the randomzed watermarks from the orgnal mage or vdeo chp. The embedded watermark s a functon of the encrypton key and the orgnal mage. n obvous drawback of ther scheme s that the algorthm cannot nsert semantcally meanngful watermarks and the capacty of watermarks s serously restrcted. In addton, t s a non-lnear watermarkng model, so t s dffcult to estmate the nserted watermark's energy and capacty and control the vsual qualty of the watermarked mages. In ths paper, we present a new dgtal mage watermarkng method based on sngular value decomposton. e wll show later that because SVD s n fact a one-way decomposton algorthm and s an optmal matrx decomposton n a least-square sense, the new method performs well both n resolvng rghtful ownershp and n resstng common attacks. The rest of ths paper s organzed as follows. Secton outlnes the problem of rghtful ownershp; Secton 3 descrbes the prncple of SVD and the proposed method; Secton 4 presents further analyss and dscusson on the method; Secton 5 dscusses expermental results. The paper s concluded n Secton 6.. PROBLEM O RIGTUL OERSIP One of the man purposes of a watermark s to protect the owner's copyrght. owever, for many exstng watermarkng schemes, an attacker can easly confuse one by manpulatng the watermarked mage (or vdeo, audo) and clam that he or she s the legtmate owner [13]. Some 4

5 watermarkng schemes requre the orgnal mage (or vdeo chp) to perform watermark verfcaton. owever even wth the presence of the orgnal mage, the rghtful ownershp problem stll exsts. The class of watermarkng schemes that can be attacked by creatng a "counterfet orgnal" s called nvertble. Craver et al [13] defne the concept of non-nvertblty to address the ssue of rghtful ownershp. Informally, non-nvertblty means that t s computatonally unfeasble for an attacker to fnd a faked mage and a watermark such that the par can result n the same watermarked mage created by the real owner. e wll revew the defnton of the class of nvertble watermarkng schemes n the followng. Suppose the orgnal mage s. The owner of uses the watermark (denoted as ) to make a watermarked mage. That s ( 1 ) or n functon representaton = E(, ) ( ) where functon E ( ) denotes the watermark embeddng algorthm. hen the attacker obtans the publshed and f wthout knowng, a counterfet watermark and a counterfet mage can be created to satsfy the followng equaton: = E, ) ( 3 ) ( then the attacker can use as hs "orgnal" to clam the ownershp of (suppose and are perceptually smlar). If Eq. (3) holds, the watermarkng scheme s called nvertble. Otherwse, t s called non-nvertble [7,8]. e regard Eq. () and (3) as the basc equatons to defne non-nvertble 5

6 watermarkng schemes (though there may be some alternatve defntons). Detaled descrptons can be found n [8,13]. 3. SVD-Based atermarkng Sngular value decomposton (SVD) s a numercal technque used to dagonalze matrces n numercal analyss. It s an algorthm developed for a varety of applcatons. The man propertes of SVD from the vewpont of mage processng applcatons are: (1) the sngular values (SVs) of an mage have very good stablty,.e., when a small perturbaton s added to an mage, ts SVs do not change sgnfcantly; () SVs represent ntrnsc algebrac mage propertes. In ths secton, we descrbe a watermark castng and detecton scheme based on the SVD.. SVD rom the vewpont of lnear algebra we can observe that a dscrete mage s an array of non-negatve scalar entres whch may be regarded as a matrx. Let such an mage be desgnated as. thout loss of generalty, we assume n the subsequent dscussons that s a square mage, denoted as, where represents ether the real number doman R or the complex number doman C. The SVD s defned as = USV ( 4 ) where U and V are untary matrces, and S s a dagonal matrx. e notce that the unque property of the SVD transform s that the potental degrees of freedom or samples n the orgnal mage now get mapped nto: S Degrees of freedom 6

7 U ( 1) / Degrees of freedom V ( 1) / Degrees of freedom totalng degrees of freedom. SVD has many good mathematcal characterstcs. or the sake of space, we wll not dscuss them n ths paper. urther detals on SVD may be found n [16,17]. B. atermark Castng and Detecton In watermark castng, the sngular value decomposton of an mage s computed to obtan two orthogonal matrces U and V and one dagonal matrx S. lthough we assume to be a square matrx (mage) for convenence, other non-square mages can be processed n exactly the same way. e mantan that ths s one of the advantages of the SVD method over some other popular watermarkng schemes whch cannot drectly handle non-square matrces [9,18,19]. e add a watermark (also represented as a matrx) nto matrx S and perform sngular value decomposton on the new matrx S + a to get U, S and V ( S + a = U S V ), where the postve constant a s the scale factor whch controls the strength of the watermark to be nserted. e then obtan the watermarked mage by multplyng matrces U, S, and T V. That s, f matrces and represent the orgnal mage and the watermark respectvely, we obtan the watermarked mage accordng to the followng three steps: => USV S + a => U S V ( 5 ) <= US V 7

8 In watermark detecton, gven matrces U, S, V and the possbly dstorted mage, one can extract a possbly corrupted watermark by essentally reversng the above steps. That s => U S V D <= U S V ( 6 ) 1 <= ( D S) a ote that the total number of degrees of freedom of matrces U, S and V s, whch s the same as that of a matrx. hle many exstng watermarkng algorthms requre the orgnal mage (whose degrees of freedom s also ) to extract the watermark, our method uses three matrces to extract the watermark and needs no addtonal nformaton. The smlarty between (the orgnal watermark) and (the extracted watermark) s measured by means of correlaton. or convenence we regard and as one-dmensonal vectors, and compute ther correlaton coeffcent c (, ) n the standard manner. or a -D watermark (such as the mage of a company logo), we can smply map the watermark nto a 1-D vector or compute the two-dmensonal correlaton coeffcent drectly. 4. LYSIS D DISCUSSIO. on-nvertble atermarkng Scheme If an attacker attempts to create a "counterfet orgnal" mage, Eq. () and (3) must be satsfed smultaneously by the watermarked mage and the created counterfet watermark. In the followng, we wll analyze the method presented n the precedng secton n order to show that t s a one-way and non-nvertble watermarkng algorthm. 8

9 Lemma 1: Suppose the SVD of mage R s performed as Eq. (4), then the mappng of matrx to S s many-to-one and non-lnear. Proof: Eq. (4) yelds 1 = [ ( )] ( 7 ) s ( ) λ where λ ( ) are the egenvalues of matrx, = 1,,...,. It s easy to prove that S = s, s,..., s } s unque for a gven. But the nverse s untrue. In fact there may exst many { 1 matrces whose sngular value matrces equal to S. or a gven S, we can llustrate ths by constructng another matrx ~ R as follows: ~ ~ ~ <= USV ( 8 ) If untary matrces ~ U U or/and ~ V V, then ~ s dfferent from. Eq. (7) also shows that s ( ) can be completely defned wth matrx egenvalues λ ( ). Because the computaton of λ ( ) n doman R s not n closed-form and the egenvalues cannot be obtaned n a fnte number of steps, we can conclude that the mappng of matrx to S s non-lnear. e are now n a poston to deduce one mportant result. Theorem 1: If watermarkng s carred out as Eq. (5), then we have the followng two equvalences: = E(, ) S + a = U S V = ( + = ( 9 ) E, ) S a U, SV, where S = dag( s, 1,..., s, ) and S = dag( s, 1,..., s, ) are the sngular value matrces of and respectvely, s the created counterfet watermark, a s the scale factor as 9

10 descrbed n Eq. (5), U, and V, are untary matrces. Proof: The proof s smple and the above two equvalences are smlar. So we only need to prove one of them. rom the defnton of SVD and the proposed watermarkng algorthm, we have: = E(, ) = US V US V = UU, ( S + a ) V, S = U, ( S + a ) V, U S V = S + a,, S + a = U, SV, V Smlarly, t s obvous that the followng equvalence holds: = E(, ) S + a = U S V Based on the defnton of non-nvertblty and the concluson obtaned above, we can deduce that f the new method s non-nvertble, t should not satsfy the followng two condtons smultaneously: S + a = U S V ( 1 ) T S a = U, SV, + ( 11 ) where matrces S, S, and S are all dagonal and represent the orgnal mage, the "counterfet orgnal" mage and the watermarked mage respectvely. = { w j } and = w {, j} are watermarks. ere for smplcty and wthout loss of generalty, we neglect the scale factor a. In the followng, we wll show that for 1

11 our proposed method, a sutable "counterfet orgnal" mage and watermark can not be created f certan constrants on the watermarks are mposed. Proposton 1: (a) Gven S, Eq. (1) s an ll-posed problem, that s, t s mpossble to fnd the orgnal S and ; (b) Gven S and S, t s mpossble to obtan ; (c) Gven S and, t s computatonally unfeasble to obtan S. Proof: (a) It holds obvously because there s no unque soluton for S and f only S s gven. (b) Eq. (1) can be expanded nto a set of equatons. If we compute { w j } = wth unknowns, under the constrants provded by S and S, there s an nsuffcent number of constrants. Therefore the soluton for the orgnal watermark cannot be found. (c) Gven S and, we have enough constrants and the soluton of S n Eq. (1) s unque. Because U = U(, S) and V = V (, S) are all functons of S, Eq. (1) s a hgh-dmensonal and hghly non-lnear equaton. So t s computatonally almost unfeasble to obtan the soluton. Proposton : or Eq. (11), we have smlar observatons: (a) Gven S and, t s computatonally dffcult to create S that satsfes Eq. (11); (b) Gven S, S and by mposng some constrants on (but wthout knowng ), t s dffcult to fnd the soluton of. Proof: 11

12 (a) rom the concluson of Proposton 1(c), gven S and, there s a unque soluton for S, but t s dffcult to fnd t. (b) or gven S and S, f there s no constrant on watermark be satsfed easly, just as done n the followng:, then Eq. (11) can = U, SV, S S = U, SV, + ( 1 ) Ths makes t possble for an attacker to create counterfet watermarks. owever, f we mpose some constrants on, the real cannot be obtaned. In general, t s reasonable to requre the watermark to satsfy some condtons nstead of beng randomly selected. or example, we can requre that the watermarks are semantcally meanngful. or enough constrants on the watermarks, there s a unque soluton for, but fndng the soluton s computatonally almost mpossble. Proposton 1 shows that Eq. (1) s an ll-posed problem whch means that a unque soluton does not exst. rom the above dscusson, we can see that the new method s a safe watermarkng scheme, especally when compared wth many exstng watermarkng algorthms. In these watermarkng schemes, gven any two of, and, the thrd can easly be obtaned, whereas ths s not true for our method as Proposton 1 shows. urthermore, our method nvolves no cryptography (though cryptography can be ncorporated to further enhance safety). Proposton shows that an attacker can not create the counterfet mage and watermark whle satsfyng Eq. (11) under certan gven constrants on the watermark. or 1

13 example, we can requre that the watermark take values form {1,} or be semantcally meanngful. B. Error Estmaton hen we add a watermark nto an mage, two questons should be asked: what s the dfference between the orgnal mage and the watermarked mage, and how much energy or watermark nformaton can be nserted? These questons are not solated and all n fact related to error estmaton, a subject that has mostly been overlooked n the exstng lterature. Defnton 1: Suppose matrx = M { a j }, we defne ts spectral norm as follows: = λ = s ( 13 ) max max where λ max and s max denote the maxmum egenvalue of T and the maxmum sngular value of respectvely. Lemma : If U M M and V are orthogonal matrces, and M, then UV = ( 14 ) Lemma 3: Suppose, δ s the dsturbance on matrx, we denote = + δ. The -th sngular value n descendng order of and are s () and s ( ). Then s ( ) s ( ) δ ( 15 ) where = 1,,...,. The above conclusons can be found easly n many textbooks on matrx theory. Lemma 3 s also called the sngular value dsturbance theorem. Then t s easy for us to have the followng result: Theorem : If I,, and s ( ) are defned as above, then 13

14 s ( ) s ( ) a, = 1,..., n ( 16 ) Proof: rom Eq. (5), (6), (14) and (15), we get s ( = s ( S ) s ( ) = s ( S + a ) s ( S) a ) s ( S) rom Eq. (16) we see that can be used as a measure to determne the error between I and Â. Therefore we can adjust the watermark's spectral norm to an acceptable level to trade-off between robustness and perceptblty. One smplest way s to adjust the value of scale factor a. Theorem provdes theoretcal gudance for us to select watermarks, control watermark locaton and determne the watermarkng energy nserted. Such nformaton s typcally unavalable n exstng watermarkng algorthms but s of great mportance n practcal applcatons. C. atermark Selecton rom Eq. (16), we can see that gven scale factor a, the error between the orgnal mage and the watermarked mage s controlled by the spectral norm of the watermark. In the vewpont of mperceptblty of watermark, we want to be as small as possble. Smaller value of suggests better smlarty between the orgnal mage and the watermarked mage. So how to select watermarks s an mportant ssue to be consdered. Many watermarkng algorthms select pseudo Gaussan random sequences as watermarks, and use them to prove the exstence of watermarks by means of correlaton detecton or by explotng the statstcal characterstcs [9]. owever they hardly consder semantcally meanngful vsual watermarks. In fact, such watermarks are more common n many practcal applcatons. 14

15 Suppose two watermark matrces = { a j } and B = { b j }, where j 1,...,, =. s a matrx wth ts elements beng real random numbers, whle B s a gray scale mage. If a j s Gaussan, e.g. a j ~ (,1) and b j [,1] s normalzed to the range of [,1], then n general we have B >> ( 17 ) or most mages, the energy s manly concentrated n a small number of large sngular values. rom Eq. (16), t s obvous that f we choose random matrx as the watermark, better results can be obtaned. or non-random meanngful watermarks, we can preprocess the watermark to reduce the value of the watermark's -norm. One effectve way s to randomze the watermark. 5. EXPERIMETL RESULTS In ths secton, we manly demonstrate the robustness of our watermarkng method. The resstance of the proposed watermarkng algorthm to varous dstortons was studed n a seres of experments on grayscale mages. e compare our method wth the Spread Spectrum Communcaton method proposed by Cox [9] n order to put the performance nvestgaton of our algorthm n proper context. The results show that our method s much more robust. The algorthm s tested wth a varety of mages, but for the sake of space, here we only gve the results of usng the -by- gray mage Lena and robustness test n sx aspects: addng nose, low pass flterng, JPEG compresson, scalng, mage croppng and rotaton. Smlar to the Cox method, the watermark used s a 5-by-1 vector consstng of pseudo 15

16 Gaussan random numbers. In watermark castng by the SVD method, we represent the watermark vector as a 5-by-5 matrx, whle n the Cox method, the watermark s drectly added nto the frst 5 hghest magntude DCT coeffcents of the mage. The value of the scalng factor a of the Cox method, whch controls the watermark energy to be nserted, s set to.1 (a typcal value used by Cox [9]). e use a set of 5 5-by-1 random vectors as watermarks for testng, and only the 1-th s the correct one. The smlarty of the orgnal mage and the watermarked one s evaluated by ther two-dmensonal correlaton coeffcent e c. The value of cox e c produced by the Cox method s (a) (b) (c) gure 1. Dgtal watermarkng for mage Lena by the SVD method. (a) Orgnal mage. (b) atermarked mage. (c) The absolute error mage (a) (b) gure. ose robustness of the SVD method. (a) The nosy mage. (b) atermark correlaton coeffcent. gure 1 shows the result of dgtal watermarkng on Lena by the SVD method. The orgnal mage Lena s n gure 1(a). The watermarked mage s shown n gure 1(b), and gure 1(c) s the absolute error mage scaled up by a factor of 64. The value of a s set to. to ensure that the two mages watermarked by the SVD method and the Cox method has comparable vsual appearances. The correlaton coeffcent value SVD e c s ote that the 16

17 absolute error mage shows the texture characterstcs of the orgnal mage. gure shows the result of addng Gaussan nose. e frst obtan the watermarked mage accordng to Eq. (5) and then add Gaussan nose to t. The mean of addtve Gaussan whte nose s zero, and ts varance s.5. By performng the watermark detecton, we obtan the corrupted watermark. Then the correlaton coeffcent (, ) c between (orgnal watermark) and s computed. The watermarked mage produced by the SVD method after addng nose s shown n gure (a). The response of watermark correlaton detecton s shown n gure (b). The ordnate axs represents the value of the correlaton coeffcents, and the abscssa axs represents a set of 5 5-by-1 watermarks. It s obvous that only the 1-th watermark (the correct one) acheves a meanngful correlaton value (about.7) (a) (b) gure 3. ose robustness of the Cox method. (a) The nosy mage. (b) atermark correlaton coeffcent. gure 3 shows smlar results of the Cox method for comparson. gan we frst add watermark to the orgnal mage, then corrupt t by addng the same nose descrbed above. The correlaton coeffcents c (, ) are also computed. The corrupted mage produced by the Cox method s shown n gure 3(a) and the response of watermark detecton s shown n gure 3(b). e note that although the correct watermark (the 1-th) shows the hghest response compared wth other watermarks, but the hghest value n ths case s only a mere.11. gure 4 shows the result of low pass flterng to the mage by the SVD method. The flter s a Gaussan low pass flter. Its sze s 16-by-16, and the varance σ s 4. e use the flter to 17

18 perform two-dmensonal IR flterng on the watermarked mage. fter flterng, the mage s heavy smoothed. The smoothed mage s shown n gure 4(a). The responses of watermark detecton from the blurred mage are shown n gure 4(b). e can see that after heavly smoothng, the SVD method can stll relably detect the correct watermark. The value of the correlaton coeffcent of the correct watermark s about.3 whch s much hgher than that of the Cox method where the result s almost meanngless (see gure 5). (a) (b) gure 4. Robustness test aganst low pass flterng for the SVD method. (a) The blurred mage. (b) atermark correlaton coeffcent (a) (b) gure 5. Robustness test aganst low pass flterng for the Cox method. (a) The blurred mage. (b) atermark correlaton coeffcent. e also perform lossy compresson for the watermarked mages. gure 6 shows the robustness test aganst JPEG compresson for the SVD method. e apply heavy compresson to the watermarked mage. The qualty of JPEG compresson s 5 wth a compresson rato of 18. gure 6(a) shows the compressed and then decompressed mage. gure 6(b) dsplays the responses of correlaton detecton. e can see that after heavy compresson, the watermark s almost unchanged. The value of c (, ) s.981, whch suggests that our method s extremely robust aganst mage compresson. 18

19 (a) (b) gure 6. Robustness test aganst JPEG compresson usng the SVD method. (a) The compressed-decompressed mage. (b) atermark correlaton coeffcent (a) (b) gure 7. Robustness test aganst JPEG compresson usng the Cox method. (a) The compressed-decompressed mage. (b) atermark correlaton coeffcent (a) (b) gure 8. Robustness test aganst mage rotaton for the SVD method. (a) The rotated mage. (b) atermark correlaton coeffcent. gure 7 shows the Cox method aganst JPEG under the same compresson condtons. gure 7(a) shows the resulted mage after JPEG compresson. gure 7(b) dsplays the responses of correlaton detecton. gan the result s almost of no use. gure 8 shows the robustness test of mage rotaton for the SVD method. e use blnear nterpolaton to perform the rotaton of watermarked mage. The rotaton angle s 3. fter rotaton, we crop the four corners of the rotated mage n order to keep the same sze as the orgnal mage. gure 8(a) shows the rotated mage. gure 8(b) dsplays the correlaton coeffcents of watermark detecton. ote that rotaton by angles of multples of 9 and mage 19

20 transpose have no effect on the method. gure 9 shows the Cox method aganst mage rotaton. The watermarked mage s also rotated for 3. gure 9(a) s the rotated mage. gure 9(b) dsplays the responses of correlaton detecton. e can see that the watermark s destroyed completely after mage rotaton. In fact, the Cox method has lttle resstance to mage rotaton (a) (b) gure 9. Robustness test aganst mage rotaton for the Cox method. (a) The rotated mage. (b) atermark correlaton coeffcent (a) (b) gure 1. Robustness test aganst mage croppng for the SVD method. (a) The clpped mage. (b) atermark correlaton coeffcent (a) (b) gure 11. Robustness test aganst mage croppng for the Cox method. (a) The clpped mage. (b) atermark correlaton coeffcent. gure 1 shows the robustness test of mage croppng. e remove the left half of the watermarked mage produced by the SVD method and then detect exstence of the watermark from the remanng data. gure 1(a) s the clpped mage. gure 1(b) dsplays detecton results. e can see that the correct watermark can stll be relably detected. The correlaton

21 coeffcent value s One nterestng thng s that we also perform the test of removng the mage's rght half. The correlaton coeffcent value becomes.1548, whch means that the mage's rght half contans more nformaton than the left half as far as mage watermarkng s concerned. gure 11 s the same robustness test for the Cox method. gure 11(a) s the clpped mage. gure 11(b) shows the responses of correlaton detecton. The correlaton coeffcent value s.877. ote that the Cox method requres the orgnal mage to extract the watermark. So f we replace the watermarked mage's left part wth the correspondng part of the orgnal mage, much better result can be obtaned. The correlaton coeffcent value becomes.7178, whle f the same processng s appled to our method, the correlaton coeffcent value becomes gure 1. Robustness test aganst rescalng and resamplng of the Cox method and the SVD method, rescalng and resamplng factor are. (a) Test result of the SVD method. (b) Test result of the Cox method. gure 1 shows the results of robustness test aganst rescalng and resamplng. By comparng the correlaton coeffcent values of the SVD method (.9) and the Cox method (.5), we can see that our method s more robust aganst rescalng and resamplng attacks. nally we demonstrate the results of usng vsual watermarks. In our method, the added watermark s represented by a matrx, so t s convenent for us to embed a vsual watermark drectly nto the mage wthout extra processng. ere we add a 5-by-5 gray scale mage nto mage Lena. The watermark s shown n gure 14 (a). The value of scalng factor a s also., 1

22 and the error value SVD e c s gure 13 shows the expermental results. (a) (b) (c) gure 13. Embeddng vsual watermarks by the SVD method. (a) Orgnal mage. (b) atermarked mage. (c) The absolute error of the two mages scaled up by 64. (a) (b) (c) (d) (e) (f) gure 14. Robustness test of vsual watermark. The correspondng Lena mages of (b)~(f) are shown on the top row. Robustness tests have also been done for the watermarked mage wth a vsual watermark. gure 14 shows the test results. (a) s the orgnal watermark. (b) s the extracted watermark after the watermarked mage s contamnated by whte nose. The nose's mean s and ts varance s.5. The error value (.e. the value of two-dmensonal correlaton coeffcent of the orgnal watermark and the corrupted watermark) s.75. (c) shows the result of low pass flterng. The flter s 16-by-16 Gaussan flter, wth ts varance beng 4. The error value s.153. (d) s the JPEG compresson result. The JPEG compresson qualty s 5. The correlaton coeffcent s.945. e can see that heavy compresson has nearly no effect on our method. (e) s the corrupted watermark extracted after we rotate the watermarked mage for 3, wth blnear nterpolaton and croppng. The correlaton coeffcent s.95. (f) shows the croppng robustness test. The mage's left half part s removed. But the logo can stll be dentfed. The correlaton coeffcent s.33.

23 These expermental results show that even f the watermarked mage has undergone severe physcal dstortons, the SVD method can stll detect the correct watermark and determne the exstence of the watermark. The results also clearly demonstrate that the novel method s consderably more robust than the popular Cox method. 6. COCLUSIOS In ths paper, a new watermarkng method for dgtal mages has been presented. The watermark s added to the SVD doman of the orgnal mage. The mathematcal background of ths method s very clear, and the error between the orgnal mage and the watermarked mage can be estmated. s a result, mportant questons such as how to determne the locaton of the watermark and how much energy to be nserted can be answered easly. Unlke some other untary transformatons whch adopt fxed orthogonal bases (such as dscrete ourer transform, dscrete cosne transform etc.), SVD uses non-fxed orthogonal bases. It s a one-way, non-symmetrcal decomposton. These propertes lead to the good performance of the novel algorthm n both securty and robustness. urthermore, the algorthm does not requre encrypton to resolve rghtful ownershp and can provde more powerful securty for rghtful ownershp f combned wth encrypton. Extensve experments and comparsons wth the Cox method have been made. Results show that the new method s very robust aganst mage dstorton and s consderably more robust than the Cox method. 7. CKOLGEMET Some parts of the work dscussed n ths paper have been fled for patent (Patent umber: ). The authors would lke to thank the anonymous referees for ther thorough revew 3

24 of the paper and many constructve comments. 8. REERECES [1] B.R.Macq and I.Ptas, Specal ssue on watermarkng, Sgnal Processng, Vol.66, o.3, pp.81-8, [] M.D.Swanson, M.Kobayash and..tewfk, Multmeda data-embeddng and watermarkng technologes, Proceedngs of the IEEE, Vol.86, o.6, pp , [3] S..Low,..Maxemchuk and.m.lapone, Document dentfcaton for copyrght protecton usng centrod detecton, IEEE Trans. on Communcatons, Vol.46, o.3, pp , [4] J.M.cken, ow watermarkng adds value to dgtal content, Communcatons of the CM, Vol.41, o.7, pp.74-77, [5] J. Zhao, E. Koch and C. Luo, Dgtal watermarkng n busness today and tomorrow, Communcatons of CM, Vol.41, o.7, pp.67-7, [6]. Zeng, Dgtal watermarkng and data hdng: technologes and applcatons, Proc. of ICISS 98, Vol.3, pp.3-9, [7] S. Craver,. Memon, B. L. Yeo and M. M. Yeung, Resolvng rghtful ownershps wth nvsble watermarkng technques: Lmtatons, attacks, and mplcatons, IEEE Journal on Selected reas n Communcatons, Vol.16, o.4, pp , [8] L. T. Qao and K. ahrstedt, atermarkng schemes and protocols for protectng rghtful ownershp and customer's rghts, Journal of Vsual Communcaton and Image Representaton, Vol.9, o.3, pp.194-1, [9] I. J. Cox, J. Klan,. T. Leghton and T. Shamoon, Secure Spread Spectrum atermarkng for Multmeda, IEEE Trans. on Image Processng, Vol.6, o.1, pp , [1]. kolads and I. Ptas, Copyrght protecton of mages usng robust dgtal sgnatures, Proc. of ICSSP 96, Vol. 4, pp , May [11]. kolads and I. Ptas, Robust mage watermarkng n the spatal doman, Sgnal Processng, Vol.66, o.3, pp , [1] M. Barn,. Bartoln, V. Cappelln and. Pva, DCT-doman system for robust mage watermarkng, Sgnal Processng, Vol.66, o.3, pp , [13] S. Craver,. Memon, B. Yeo and M. Yeung, Can nvsble watermarks resolve rghtful ownershp, Techncal Report RC 59, IBM Research Dvson, July [14] R. B. olfgang and E. J. Delp, " watermark technque for dgtal magery: further studes", Proc. of Internatonal Conference on Imagng Scence, Systems, and Technology, Las Vegas, evada, [15]. Zeng and B. Lu, " statstcal watermark detecton technque wthout usng orgnal mages for resolvng rghtful ownershps of dgtal mages", IEEE Trans. Image Processng, 8(11), pp , [16]. C. ndrews and C. L. Patterson, Sngular Value Decomposton (SVD) mage codng, IEEE Trans. on Communcatons, pp , prl

25 [17] G.. Golub and C. Rensch, Sngular value decomposton and least squares solutons, umer. Math., Vol. 14, pp. 43-4, 197. [18] C. T. su and J. L. u, Multresoluton watermarkng for dgtal mages, IEEE Trans. on Crcuts and Systems II-nalog and Dgtal Sgnal Processng, Vol.45, o.8, pp , [19] J. J. K. O'Ruanadh and T. Pun, Rotaton, scale and translaton nvarant spread spectrum dgtal mage watermarkng, Sgnal Processng, Vol.66, o.3, pp ,