SPATIO-FREQUENCY BASED IMAGE WATERMARKING

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1 STANBUL UNVERSTY JOURNAL OF ELECTRCAL & ELECTRONCS ENGNEERNG YEAR VOLUME NUMBER : 29 : 9 : (93-92) SPATO-FREQUENCY BASED MAGE WATERMARKNG Mahmut ÖZTÜRK Aydın AKAN 2 Yalçın ÇEKĐÇ Eletr-Eletron Mühendslğ Bölümü () Đstanbul Ünverstes, Avcılar, 3432, Đstanbul mahmutoz@stanbul.edu.tr aan@stanbul.edu.tr (2) Bahçeşehr Ünverstes, Beştaş, 34349, Đstanbul yalcn@bahcesehr.edu.tr ABSTRACT Watermarng technques are proposed as a soluton to copyrght protecton of dgtal meda fles. n ths or, a neand poerful atermarng method that s based on spatofrequency (SF) representatons s presented. We use the dscrete evolutonary transform calculated by the Gabor expanson to represent an mage n the SF doman. A atermar s embedded onto selected cells n the jont SF doman. Hence by combnng the advantages of spatal and spectral doman atermarng methods, a robust and perceptual method s presented. Keyords: mage atermarng, Tme-frequency analyss, Dscrete evolutonary transform.. NTRODUCTON n the past decade, the producton, dstrbuton, and use of dgtal meda has become very popular. Although these products have the advantages of hgh qualty, ease of modfcaton and qualty duplcaton, they ntroduce the problems of copyrght protecton ssues because they can be easly coped and altered. Watermarng technques are proposed as a soluton to copyrght protecton problems of dgtal meda fles. The basc dea n atermarng s embeddng a secret data nto a multmeda fle. n recent research, ne methods are proposed to atermar audo, mage and vdeo fles. n dgtal atermarng a specfc nformaton, hch s called atermar, s embedded n a multmeda fle n such a ay that t can be detected or extracted hen necessary. The atermar may contan nformaton about the dgtal object as ell as nformaton about the user or oner. As for mage and vdeo fles, the atermar may be another mage or sgnature logo. The atermar can be embedded so that t s ether vsble or nvsble. The prncple of atermarng s to embed a dgtal code (atermar) thn the host multmeda document, and to use such a code to prove onershp, to prevent llegal copyng, or smply to gve some ndcatons about the atermared data or to enable the access to enhanced versons of the content or to addtonal Receved Date: Accepted Date: 5..29

2 94 Spato-Frequency Based mage Watermarng servces. The atermar code s embedded by mang mperceptble modfcaton to the orgnal data. A atermarng algorthm n general conssts of three basc components: () atermar, () Encoder (atermarng algorthm), () Decoder (detecton or extracton algorthm). To be useful a dgtal atermarng system must satsfy same basc requrements. Frst of all, the embedded atermar should be perceptually nvsble. n other ords, ts presence should not affect the mage qualty. Moreover, the embedded atermar should be robust aganst the common sgnal processng manpulatons le, Salt&Pepper nose, flterng, JPEG Compresson, rotaton, and croppng. mage atermarng algorthms are manly concentrated on spatal or spectral domans. Although successful methods have been presented usng both approaches, they also have lmtatons and eanesses. n the spatal doman, the mage area here atermar s embedded s chosen based on the texture of the orgnal mage [, 2]. n the spectral approach, atermar s embedded n a transform doman usng dscrete cosne transform, dscrete avelet transform, etc. For an nvsble and robust atermarng, the atermar s embedded nto mddle frequences range [3, 4, 5]. Watermarng n the frequency doman has advantages n terms of robustness, but there are lmtatons as nvsble embeddng may be dffcult. Some ne technques are ntroduced by combnng the advantages of both spatal and spectral domans for robust and nvsble atermarng. Ths can be done usng jont SF representatons of mages [6, 7]. Watermarng n the jont SF doman provdes flexblty n terms of ho much atermar ll be embedded n hch mage regon, and n hat frequency band. n ths or, e present a ne mage atermarng algorthm based on a dscrete evolutonary transform (DET) hch provdes a tme-frequency (TF) representaton for sequences. We ntroduce atermar embeddng or encodng as ell as detecton and extracton algorthms n the SF doman. 2. TME-FREQUENCY ANALYSS BY DET n the follong e brefly explan the Dscrete Evolutonary Transform (DET) as a tool for the tme frequency representaton of mage sequences. A non-statonary sgnal, x(n), n N-, may be represented n terms of a tme-varyng ernel X(n,ω ). The TF dscrete evolutonary representaton of x(n) s gven by [8], x( n) K = = jω n X ( n, ω ) e () here ω = 2π / K, K-, K s the number of frequency samples, and X(n,ω ) s the evolutonary ernel. The evolutonary spectrum s obtaned from ths ernel as S(n,ω )= X(n,ω ) 2. The dscrete evolutonary transformaton s obtaned by expressng the ernel X(n,ω ) n terms of the sgnal. Ths s done by usng conventonal sgnal representatons [8]. Thus, for the representaton n (), the DET that provdes the evolutonary ernel X(n,ω ), s gven by, N ( ω ) = ( ) ( ) j X n, x W n, e ω l l l (2) l= here W ( n, l ) s, n general, a tme and frequency dependent ndo. Detals on ho the ndos can be obtaned from ether the Gabor expanson that uses non-orthogonal ndos or the Malvar avelets that uses orthogonal bass are gven n [8]. The mult ndo Gabor expanson s gven by, M K x ( n ) = a, m, h, m, ( n ) (3) = here { a m, } { } h m, m = =, are the Gabor coeffcents, and, are the Gabor bass functons defned as: h jωn, m, ( n) = h ( n ml) e (4)

3 Spato-Frequency Based mage Watermarng 95 and the synthess ndo h (n) s obtaned by scalng a unt energy mother ndo g(n) as 2 h ( n) = 2 g(2 n), =,,...,. The mult-ndo Gabor coeffcents are evaluated by N * jnω, m, = x( n) ( n ml) e n= a γ, (5) here the analyss ndo γ (n) s solved from the b-orthogonalty condton beteen (n) and γ (n) [8]. Hence by comparng the representatons of the sgnal n (3) and (), e obtan the DET ernel as M X ( n, ω ) = a, m, h ( n ml). (6) = m= a m, Substtutng for the coeffcents { } obtan that ( ω ) ( ) ( ) l= h,, e j X n, x W n, e ω l l l, (7) N = here e defned a tme-varyng ndo as M * W ( n, = γ ( l ml) h ( n ml). = m= We should menton that above evolutonary spectral estmate s alays non-negatve, and W n, l to unt energy, the total normalzng the ( ) energy of the sgnal s preserved, thus justfyng the use of S(n,ω ) as a TF energy densty for x(n). Furthermore, DET provdes a lnear sgnal representaton here the sequence may be obtaned from the TF representaton much easer than t s th the blnear TF representatons such as Wgner dstrbuton [8]. Hence DET s approprate for atermarng applcatons n the SF doman here embeddng and extractng a atermar ll be easly mplemented usng lnear operatons. 3. MAGE WATERMARKNG N SF DOMAN n our SF based atermarng approach, the ros of the mage to be atermared are consdered as one dmensonal sequences and transformed nto the jont SF doman. There are methods to represent to dmensonal mages n the SF doman, but computatonal complexty and the dmensonalty problems mae them dffcult to use n atermarng applcatons [6]. Recently ne methods are presented here TF dstrbutons (TFDs), usually the Wgner dstrbuton, of each ro of an mage s used for embeddng a atermar n the jont TF doman [7, 9]. Hoever, synthess of a sequence from ts modfed blnear TFD s generally a dffcult problem. Hence e propose a ne SF doman atermarng here e use the lnear DET explaned above to embed the atermar nto each ro of the mage. Then the atermared ros are easly obtaned by the nverse transformaton. Let (, x, y N, be the orgnal mage and (n), n N be the atermar sequence. Frst, the DET of the atermar sequence, X, ω ), s obtaned: X ( y N jωl ω ) = ( W( y, e. (8) l= Then, the DET of ro x of the mage, X N jωl ω ) = ( W e (9) l= y, N, s obtaned. Proposed atermar embeddng algorthm n the SF doman s done by addng a eghted DET ernel of the atermar onto X y, ω ) as, ( Xˆ ω ) = X ω ) + T ω ) X ω ) () Here T, ω ) represents the SF doman ( y eghtng matrx for the ro x [9], and t s calculated by:

4 96 Spato-Frequency Based mage Watermarng X ω ), ω ω ω T ) = max{ X )} 2 ω ω (), otherse The eghtng matrx s chosen such that the atermar s embedded nto the mddle frequences range. ω and ω 2 determne the range of frequences here the atermar s embedded, and they are chosen as.3π and.6π respectvely n ths or. Therefore, a robust and nvsble atermarng s acheved. Watermared mage ro, ˆ (, s obtaned from the atermar embedded SF matr Xˆ ω ), by the nverse DET (DET): ˆ( K = = Xˆ jω y ω ) e (2) On the other hand, substtutng () nto (2), the embeddng algorthm can be obtaned n the spatal doman as follos: ˆ( = K [ X( y, ω ) + T ω ) X( y, ω )] = = ( + K = T ω ) X ω ) e e jω y jω y (3) The second term of the last equaton can be veed as a ne mage hch s obtaned from the modfed DET ernel of the atermar ( K = = jω y T ω ) X ω ) e. (4) So, the embeddng algorthm can be consdered as the combnaton of to mages n the spatal doman: ˆ ( = ( + (. (5) As can be seen n (4), the SF dependence of the atermarng algorthm s ensured through the SF dependent eghtng matrx. The embeddng process can be repeated for all ros of the mage. Because of the securty reasons, e could choose some ros for embeddng the atermar. At ths method, e must use a securty ey hch contans the places of the atermared ros. 4. WATERMARK EXTRACTON n dgtal atermarng studes, methods have been presented for detecton and extracton of the atermar by assumng that some nformaton used n the embeddng s non to the detector [9]. Hoever, there are some or here blnd detecton s acheved thout usng any extra nformaton. n practcal applcatons such as copyrght protecton, the most mportant goal s the detecton of atermar exstence even after the atermared mage s attaced. At detecton or extracton stages of a copyrght protecton algorthm, the orgnal mage as ell as the atermared mage are non. n our study, e assume that e have the orgnal and the atermared mages and try to extract the atermar. t can be seen from (5), that the dfference beteen the atermared and orgnal mages gves us ( matrx. The eghtng matrx T, ω ) for any ro of the orgnal mage ( y can be obtaned at the detecton part as n (). The DET of the atermar can be extracted from equaton (), and then by usng the DET, the atermar s obtaned. By usng a correlaton based detector, the smlarty beteen the extracted atermar, ˆ( n ) and the seres of the possble atermars, (n), can be calculated to determne the embedded atermar. The correlaton t = ˆ ( n), ( n) s calculated and then a correlaton based detector s gven by t η true atermar t < η rong atermar (6) here η s a threshold hch may be derved by usng the Neyman-Pearson crteron: η ( t ) P F = f dt (7) and f (t) s the probablty densty of t. Assumng all atermars are zero mean and Gaussan dstrbuted, e have that

5 Spato-Frequency Based mage Watermarng 97 η µ t P F = Q σ t (8) here Q(.) s the standard error functon and µ t and σ t are the mean and standard devaton of t respectvely. From above, e can obtan that ( ) η = σ (9) tq P F n our smulatons, e tae σ t 2 =524, P F =., and η=.229. Any ro of the mage can be used for atermar detecton f the same atermar s embedded onto all ros of the mage. Ths maes the proposed method robust aganst attacs. f e prefer to choose some ros for embeddng, e may eep the atermared ro numbers n a sequence and use t as a securty ey n extracton stage. 5. SMULATONS The proposed atermarng method as tested on some commonly used test mages (Lena, Baboon, Boats, and Barbara) and the detecton performance as nvestgated. The szes of the mages are 52x52. Watermar s chosen as a zero mean normal dstrbuted random sequence. The atermared Boats mage and the dfference beteen the orgnal and the atermared mages can be seen n Fg.. The dfference, shon n Fg., s obtaned by magnfyng the real dfference mage by, so e can see the effects of the embeddng algorthm. Notce that the atermar embeddng algorthm does not cause any vsble changes on the mage. Pea sgnal to nose rato (PSNR) values are gven n Table for all test mages. The performance of the method as also tested under dfferent attacs for above mages. Addtve Whte Gaussan Nose (), Salt & Pepper (SP) Nose, Wener Flterng (WF), Medan Flterng (MF), JPEG Compresson, Rotaton, and Croppng attacs are used. The normalzed correlaton beteen the extracted and the orgnal atermars are calculated and presented for all mages n Table 2. Fgure 2 shos the correlatons beteen the extracted atermar and the all other possble atermars. t can be seen that, hen the orgnal atermar s tested th the extracted one, the correlaton value s the maxmum. t can be seen from the correlaton detector responses that our method s not successful at medan flterng and rotaton attacs, hoever e acheve outstandng performance for other attacs. 6. CONCLUSONS n ths or, a ne atermarng algorthm that s based on a spato-frequency transform s proposed. Dscrete evolutonary transform s used for the SF representaton of the ros of the mage. Watermar embeddng algorthm s developed to combne the advantages of both spatal and spectral doman atermarng technques. Thus, a better robustness than methods that use only spatal or spectral doman embeddng s acheved. At the detecton end, the atermar can be extracted by usng the orgnal mage. The performance of the method s tested under several attacs, and observed that t s very successful aganst addtve hte gaussan nose, salt&pepper nose, ener flterng, jpeg compresson, and croppng. Furthermore, the proposed algorthm hch s based on a lnear representaton s computatonally smpler than other blnear TFD based methods [7, 9]. 7. REFERENCES [] N.Nolads, and.ptas, Robust mage atermarng n the spatal doman, Sgnal Processng, vol.66, pp , 998. [2] O.Bruyndonc J.J.Qusquater, and B.Macq, Spatal method for copyrght labelng of dgtal mages, n Proc. EEE Worshop on Nonlnear Sgnal and mage Processng, June 995, pp [3] M.Barn, F.Bartoln, A. De Rosa, and A. Pva, Capacty of the atermar channel: Ho many bts can be hdden thn a dgtal mage?, n Proc. SPE, Jan. 999, vol. 3657, pp [4] J.J.K. O Ruanadh and T. Pun, Rotaton, scale and translaton nvarant dgtal mage atermarng, Sgnal Processng, vol.66, no.3, pp , May 998.

6 98 Spato-Frequency Based mage Watermarng [5] S.Perera, S.Voloshynosy, and T.Pun, Optmal transform doman atermar embeddng va lnear programmng, Sgnal Processng, vol.8, no.6, pp.25-26, June 2. Table. PSNR Values of the atermared mages. mage Lena Baboon Boats Barbara PSNR (db) [6] S. Stanovc,. Djurovc, and. Ptas, Watermarng n the space/spatal-frequency doman usng to dmensonal radon-gner dstrbuton, EEE Transactons on mage Processng, vol., pp , Aprl 2. [7] B.G. Mobasser, Dgtal atermarng n the jont tme frequency doman, n EEE nt. Conf. on mage Processng, 22, vol.3, pp [8] Suleesathra, R., Chaparro, L.F., and Aan, A., Dscrete Evolutonary Transform for Tme- Frequency Analyss, Journal of The Franln nsttute, Vol. 337, No. 4, pp , July 2. [9] M.Al-Khassaeneh and S.Avyente, A tmefrequency nspred robust mage atermarng, Thrty-Eghth Aslomar Conference on Sgnals, Systems and Computers 24, vol., pp , 24. (a) (b) Fgure. a) Watermared Boats mage, b) Dfference beteen the orgnal and the atermared Boats mages.

7 Spato-Frequency Based mage Watermarng Örne Damgalar (a) Örne Damgalar (e) Örne Damgalar (b) Örne Damgalar (f) Örne Damgalar Örne Damgalar (c) (g) Örne Damgalar (d) Fgure 2. Correlaton detector response under; a) ( Örne Damgalar (h) σ ), 2 σ =.85 ), b) ( 2 =. 25 c) SP nose (den.=.8), d) WF (6x6), e) MF (3x3), f) JPEG comp. (Q=%), g) Rotaton (5 o ), h) Croppng ( column).

8 92 Spato-Frequency Based mage Watermarng Table 2. Normalzed correlatons under dfferent attacs. Attacs Lena Baboon Boats Barbara ( σ 2 =. 5 ) ( σ 2 =. ) ( σ 2 =. 5 ) ( σ 2 =. 2 ) ( σ 2 =. 25 ) SP Nose (Den.=.2) SP Nose (Den. =.4) SP Nose (Den. =.6) SP Nose (Den. =.8) SP Nose (Den. =.) WF (3x3) WF (4x4) WF (5x5) WF (6x6) WF (7x7) MF (3x3) MF (6x6) MF (9x9) MF (2x2) MF (5x5) (Q=%9) (Q=%7) (Q=%5) (Q=%3) (Q=%) Rotaton (5 o ) Rotaton ( o ) Rotaton (5 o ) Rotaton (2 o ) Rotaton (25 o ) Croppng ( column) Croppng (25 column) Croppng (5 column) Croppng (75 column) Croppng ( column) Mahmut ÖZTÜRK as born n stanbul, Turey n 977. He receved the B.Sc. degree n 2 and the M.Sc. degree n 23 from stanbul Unversty, stanbul, Turey both n Electrcal Engneerng. He s currently a Ph.D. student at the same unversty. He s also a research assstant at the department of Electrcal and Electroncs Engneerng, stanbul Unversty. Hs research nterests are dgtal sgnal processng, tmefrequency sgnal analyss and ts applcatons. Aydın AKAN as born n Bursa, Turey n 967. He receved the B.Sc. degree n 988 from the Unversty of Uludag, Bursa, Turey, the M.Sc. degree from the Techncal Unversty of stanbul, stanbul, Turey n 99, and the Ph.D. degree from the Unversty of Pttsburgh, Pttsburgh, PA, USA, n 996 all n electrcal engneerng. He has been th the Department of Electrcal and Electroncs Engneerng, Unversty of stanbul snce 996 here he currently holds a Professor poston. Hs current research nterests are dgtal sgnal processng, statstcal sgnal processng, tme-frequency analyss methods and applcatons of tme-frequency methods to communcatons and boengneerng. Dr. Aan s a senor member of the EEE Sgnal Processng Socety. Yalçın Çeç as born stanbul n 97. He receved the B.Sc., M.Sc., Ph.D. degree n electrcal engneerng from stanbul Unversty n 993, 996, and 24 respectvely. He served as a Research Assstant at the Department of Electrcal and Electroncs Engneerng, stanbul Unversty from 996 to 2. He joned Bahcesehr Unversty n 2 became an Assstant Professor of electrcal and electroncs engneerng n 24. He s currently servng as an assocate char of Mechatroncs Engneerng. Hs research nterests are dgtal sgnal processng, fractonal sgnal representatons, and fractonal tme-frequency analyss technques.