Reversble Data Hdng Explotng Varance n Wavelet Coeffcents Xu-Ren Luo Department of Electrcal and Electronc Engneerng, Cung Ceng Insttute of Tecnology, Natonal Defense Unversty, Tas, Taoyuan 33509, Tawan, Republc of Cna. and Te-Lung Yn Department of Computer Scence and Informaton Engneerng, Cna Unversty of Tecnology, Hukou, Hsncu 303, Tawan, Republc of Cna. ABSTRACT In ts paper, we present a new reversble data dng sceme tat utlzes te wavelet transform and better explots te large wavelet coeffcent varance to aceve g capacty and mperceptble embeddng. Our sceme dffers from tose of prevous studes n tat te wavelet coeffcents stogram rater tan te gray-level stogram s manpulated. In addton, we desgn ntellgent stogram-sftng rules to avod te decmal problem n grayscale pxel values after recovery process to aceve reversblty. Small canges n te wavelet coeffcents after embeddng process are mportant factors contrbutng to low vsual dstorton n te marked mage. Furtermore, an mportant property of our sceme s tat te use of tresold dffers greatly from prevous scemes. Te expermental results sow tat our sceme outperforms oter reversble data dng scemes. Keywords: reversblty, marked meda, wavelet transform, wavelet coeffcent, dstorton, stogram.. Introducton Reversble data dng, or so-called nvertble, dstortonfree data dng, s a branc of fragle tecnque manly used for qualty-senstve applcatons suc as multmeda content autentcaton, medcal magng systems, law enforcement, and mltary magery, etc. One of te most mportant requrements n tese felds s to recover te orgnal meda exactly durng analyss to enable te rgt decsons. Te oter sgnfcant necesstes of reversble data dng are te embeddng capacty and vsual qualty of te marked meda, snce tey are crtcally essental to acevng satsfactory performance n varous applcatons. [][2] Te sceme we present n ts paper s an attempt to aceve g-performance reversble data dng, n wc te embeddng and recoverng processes are devsed n te frequency doman. Te partculartes of large varance n wavelet coeffcents and mnor canges n wavelet coeffcents followng from te embeddng process n wavelet coeffcents are exploted to aceve g capacty and mperceptblty. Te rest of ts paper s organzed as follows. In Secton 2, prevous reversble data dng scemes and ter caracterstcs wll be brefly revewed n terms of embeddng capacty and vsual qualty. Our proposed sceme s ntroduced n Secton 3. Expermental results and comparatve analyses are presented n Secton 4. Fnally, some conclusons are drawn n Secton 5. 2. Related studes Nowadays, a number of researc works n ts feld can be classfed nto two major categores accordng to te embeddng strateges. Category-I reversble data dng scemes work on te transform doman. In 2002, Frdrc et al. [3][4] proposed a novel paradgm of lossless data embeddng. Te payload of ts so-called RS sceme s gly dependent on te compresson algortm and nsuffcent for some applcatons. Subsequently, Xuan et al. [5] presented a new sceme carred out n te nteger wavelet transform (IWT) doman. In ts sceme, one or multple mddle bt-plan(s) n te g-frequency subbands s(are) cosen to embed data bts. In 2003, Tan [6] proposed a dfference expanson (DE) sceme, wc exploted te DE tecnque to embed data bts nto te g-frequency coeffcents. However, ts sceme suffers from te locaton map problem tat t s dffcult to aceve capacty control. Alattar [7][8] extended Tan s sceme by generalzng te DE tecnque to te trplets and quads of adjacent pxels. Kamstra et al. [9][0] mproved te DE sceme by predctng te expandable locatons n te g-pass band. Ts sceme mproves te effcency of lossless compresson, altoug te embeddng capacty s small. In 2007, Tod et al. [] proposed a new sceme combnng stogram sftng and predcton-error expanson approaces to remedy te problems of Tan s sceme. In category-ii, scemes are performed n te spatal doman. Frdrc et al. [2] presented te jont b-level mage experts group (JBIG) lossless compresson tecnque to save space for data embeddng. However, te payload s gly dependent on te lossless compresson algortm. Celk et al. [3][4] employed te generalzed least-sgnfcant-bt (G-LSB) tecnque and te contextbased adaptve lossless mage codng (CALIC) to aceve lossless data dng. In 2006, N et al. [5] utlzed te pars of maxmum and mnmum ponts of a gven mage stogram to aceve reversblty. In ts sceme, te pxels between eac par are modfed for data embeddng and extracton. However, suc a strategy may lead to sgnfcant overead and nsuffcent vsual qualty. In [6][7], Hwang et al. and Kuo et al. extend N s sceme by usng a locaton map to aceve reversblty. Altoug te sceme s smple, te sgnfcant overead and nsuffcent vsual qualty are crtcal problems. In 2009, Km et al. [8] exploted te feature of g spatal correlaton between negborng pxels to aceve g- 27
performance data dng. Te embeddng capacty n te paper ranges from 6 to 20 k. For all of te above reversble data dng scemes, te requrement of addtonal overead s one of te tornest problems n te restore process. Ts paper presents a novel metod and enances te embeddng performance recently proposed by Luo et al. [9] n te frequency doman to aceve g-performance lossless data dng. 3.2. Data embeddng algortm We assume tat te embedded message s a random bnary sequence. Te stograms of te sub-band dfferences between te reference sub-band and te oter destnaton sub-bands are sfted to embed te secret message. Fg. 3 depcts te overall data embeddng process, wc s descrbed n detal below. 3. Proposed sceme Te proposed sceme combnes te two-level Haar dscrete wavelet transform (HDWT) algortm and a new stogram sftng tecnque to aceve reversble data dng. In our sceme, a gven mage s frst transformed nto a frequency doman and sub-bands n te mddle- and g-frequency ranges are ten used to create sub-band dfferences. Eac stogram of tese sub-band dfferences s ten sfted accordng to a selected tresold. Message bts can ten be embedded n te empty space of te sfted stograms. Fnally, te marked mage s reconstructed wt te sub-bands carryng and noncarryng dden message by performng te nverse HDWT algortm to complete te embeddng process. As to te extractng process, te correspondng nverse operatons can be performed to recover te dden nformaton and te orgnal mage. Te new sceme dffers from our prevous study [9] n tat sx rater tan four of te wavelet sub-bands are manpulated. 3.. Segmentaton algortm Te two-level HDWT algortm utlzes te four-band sub-band codng system to decompose an mage nto a set of dfferent frequency sub-bands. As llustrated n Fgs. and 2, te sze of eac sub-band s one egt of te orgnal mage n te spatal doman. Te egt dfferent sub-bands can be classfed nto te low-, mddle-, and g-frequency sub-bands. Snce te low-frequency subband of an mage ncorporates more energy tan te oter sub-bands, ts coeffcents are te most fragle tat f any of tem are manpulated, a suspect can vsbly detect te canges on te spatal doman mage. In contrast, f te coeffcents n te mddle- and/or g-frequency subbands are altered, canges n te spatal doman mage are mperceptble to uman eyes. As a result, ts feature s generally exploted to conceal secret messages. Fg.. Te two-level segmentaton process. Fg. 2. A tow-level HDWT four-band splt of Lena. Fg. 3. Flowcart of data embeddng process. Embeddng_process, T, Input:, te orgnal mage; T, te tresold accordng to wc te empty bns n eac stogram are prepared;, te secret message. Output:, te marked mage, f, te mark of embeddng status. Advan Proceedngs: Step : Create sub-bands by performng two-level HDWT four-band sub-band codng system on an nput mage. Sx of te sub-bands to be utlzed are denoted by L H ( x, y ), H L( x, y ), H H ( x, y ), L H 2( x, y ), H H 2 and H L2( x, y ), were ndcates te coordnate of te coeffcents n eac sub-band. Step 2: Create sub-band dfferences D, D, 2 D and 3 D between te reference sub-bands L H, L H 2 and 4 te oter destnaton sub-bands HL, HH, HL2 and HH 2 by te followng formulas: x y LH x y HL x y, () 2 x y LH x y HH x y, (2) D3 HL2, (3) D4 HH 2. (4) Step 3: Denote te stograms of D as, were 28
, 2, 3 and 4. Step 4: Sft stogram accordng to te tresold T selected. Te sfted can be calculated as follows: j 8, f j T, j 8, f j ( T ), (5) were, 2, 3, 4 and j ndcates te value of eac bn. Tese can also be obtaned by te followng formulas: x y LH x y HL x y, (6) 2 x y LH x y HH x y, (7) 3 x y LH x y HL x y, (8) 4 x y LH x y HH x y. (9) were HL (, x y), HH (, xy), HL (, ) 2 xy and HH (, ) 2 xy can be expressed as: HL( x, y ) 8, f j T, HL HL( x, y ) 8, f j T. (0) HH( x, y ) 8, f 2 j T, HH HH( x, y ) 8, f 2 j T. () HL2( x, y ) 8, f 3 j T, HL2( x, y) HL2( x, y ) 8, f 3 j T. (2) HH2( x, y ) 8, f 4 j T, HH2( x, y) HH2( x, y ) 8, f 4 j T. (3) Embeddng Data: Step 5: We frst set an nteraton ndex to T and ten embed message bts sequentally by modfyng. Eac s sfted to become, were, 2, 3 and 4 by te followng rules: j 8, f j, ( 0, j 4, f j, (, j j for 0. 8, 4, f f j j,, ( 0, (, (4) j 8, f j 0, ( 0, j 4, f j 0, (, (5) for 0. Te canges n te dfference stograms above result n canges n te coeffcents. Ts mples tat D( xy, ) s scanned and modfed agan. Once te value of D( xy, ) s equal to, te message bt s embedded. Ts process s repeated untl tere are no D ( xy, ) wt te value of. We ten decrease by and repeat te step untl 0. Tese steps can be formulated as follows: x y LH x y HL x y, (6) 2 x y LH x y HH x y, (7) 3 x y LH x y HL x y, (8) 4 x y LH x y HH x y. (9) f 0, HL( x, y ) 4, f j, (, HL( x, y ) 4, f j, (, HL HL( x, y ) 8, f j, ( 0, HL( x, y ) 8, f j, ( 0. HH ( x, y ) 4, f 2 j, (, HH ( x, y ) 4, f 2 j, (, HH HH ( x, y ) 8, f 2 j, ( 0, HH ( x, y ) 8, f 2 j, ( 0. HL2 ( x, y ) 4, f 3 j, (, HL2 ( x, y ) 4, f 3 j, (, HL2( x, y) HL2 ( x, y ) 8, f 3 j, ( 0, HL2 ( x, y ) 8, f 3 j, ( 0. HH 2 ( x, y ) 4, f 4 j, (, HH 2 ( x, y ) 4, f 4 j, (, HH 2( x, y) HH 2 ( x, y ) 8, f 4 j, ( 0, HH 2 ( x, y ) 8, f 4 j, ( 0. f 0, HL(, x y) HH(, x y) HL2( x, y) (20) (2) (22) (23) HL( x, y ) 4, f j = 0, ( =, HL( x, y ) 8, f j = 0, ( = 0. (24) HH( x, y ) 4, f 2 j = 0, ( =, HH( x, y ) 8, f 2j = 0, ( = 0. (25) HL2( x, y ) 4, f 3 j = 0, ( =, HL2( x, y ) 8, f 3j = 0, ( = 0. (26) 4 4 HH2( x, y ) 4, f j = 0, ( =, HH2( x, y) HH2( x, y ) 8, f j = 0, ( = 0. (27) Centralzng Hstogram Step 6: Wen all te bns n te dfference stogram are exausted, egt bns, valued from 4 to 3, wll become empty. In ts case, te mark f s set to be and all bns on te rgt sde wll be moved left 4 bns, and tose on te left wll be moved rgt 4 bns n order to mprove te vsual qualty by decreasng te varance of te dfferences n te coeffcents. Oterwse, te mark f s set to be 0. Eac s sfted to become by te followng rules: ( j ) 4, f ( j) 0, j ( j ) 4, f ( j) 0, (28) were, 2, 3 and 4. Sftng stograms as above creates coeffcent canges, wc can be formulated as follows: x y LH x y HL x y, (29) 2 x y LH x y HH x y, (30) 29
3 x y LH x y HL x y, (3) 4 x y LH x y HH x y, (32) were HL (, xy), HH (, x y), HL (, x y) 2 and HH (, x y) 2 can be expressed as: HL( x, y ) 4, f j 0, HL HL( x, y ) 4, f j 0. (33) HH( x, y ) 4, f 2 j 0, HH(, x y) HH( x, y ) 4, f 2 j 0. HL2 HH 2(, x y) (34) HL2 ( x, y ) 4, f 3 j 0, HL2 ( x, y ) 4, f 3 j 0. (35) HH 2 ( x, y ) 4, f 4 j 0, HH 2 ( x, y ) 4, f 4 j 0. (36) Step 7: Usng te sub-bands HL and HL2 wt te dden message as te reference sub-bands, and ten fft and sxt dfference stogram s created wt te orgnal sub-bands LH and LH2. Te secret message s ten dden nto tese dfference stograms accordng to steps to 6; as a result, LH x, yand LH2 x, y wll be created. Ts completes te embeddng process. Obtanng Marked Image: Step 8: Reconstruct te marked mage by utlzng te nverse of te two-level HDWT four-band sub-band codng on tese sub-bands. We frst reconstruct te LL sub-band and ten reconstruct te marked mage. Ts procedure can be formulated as follows: LL IDWT ( LL2,, HL2, HH 2 ), (37) IDWT ( LL, L H, H L, H H ). (38) Preventon of overlap and over/underflow A flag-bt s used to ndcate weter te bn n te dfferent stograms s overlap or not. Te flag-bt s set to f a bn value sfted by 8 overlaps wt one sfted by 4. Te flag-bt s set to 0 f no overlap occurs. Tese flag-bts and te values of T and f n te btmap wll ultmately all be compressed wt an effcent compresson tool based on te LZMA algortm. Te compressed result s ten dden nto te reserved nonoverlappng bns. Accordng to expermental results, ts process results n less tan 2.92% overead n entre embeddng capacty for many dfferent types of mages. Toug te generated pxel values n te marked mage may be outsde te allowable range, te metod n [2][8] could be used to deal wt te problem. Te nterval range s dynamcally selected wt te mage caracterstcs tat t wll reduce dstortons to mnmum. 3.3 Data extractng and recoverng algortm Before extractng te dden message, recever needs to verfy weter or not te marked mage as been modfed. If tere s more tan one occurrence at j, we can conclude tat te marked mage as been tampered wt. Te proposed sceme ten stops te followng extracton steps mmedately. Te extracton and recovery process s scematzed n Fg. 4. Fg. 4. Flowcart of extracton and recovery process. Te detaled extracton and recovery process ncludes te followng steps: Extractng_process, T, f Input:, te marked mage; T, te tresold; f, te mark, accordng to wc te embeddng status s determned. Output:, te secret message;, te orgnal mage. Advan Proceedngs: Step : Create sub-bands by performng two-level HDWT four-band codng on te marked mage. Sx of te sub-bands to be utlzed are denoted by ( x LH, y ), HL ( x, y), HL ( x, y), (, ) x y, (, ) HL2 x y and (, ) HH 2 x y, were x, y ndcates te coordnate of te coeffcents n eac sub-band. Recoverng LL Sub-band Step 2: Create sub-band dfference D (, x y) between te reference sub-band and te destnaton sub-band HL2 accordng to te followng formulas: D HL2. (39) Step 3: Denote te stogram of D as j, were j ndcates te value of eac bn. Step 4: Ceck te dstrbuton of te stogram j. If tere s more tan one occurrence at j, te 30
subsequent steps wll be stopped mmedately. Step 5: Ceck te embeddng status. Once te value of f s equal to, t can be concluded tat te sub-band s completely flled wt dden message bts. Subsequently, restore te orgnal dfference stogram. Te bns greater tan or equal to zero wll be sfted to te rgt by 4 and tose less tan zero to te left by 4. Te restored j can be calculated as follows: j 4, f j 0, j j4, f j 0. (40) Tese can also be obtaned by te followng formulas: D HL2 LH 2, (4) were (, ) LH 2 x y can be expressed as: ( xy, ) 4, f ( j) 0, LH 2 (42) ( xy, ) 4, f ( j) < 0. Extractng Data: Step 6: Extract te dden message (, were n denotes te ndex of a message bt, by sftng j wt reference to te btmap and nvertng te embeddng process. Frst, te teraton ndex s set to 0. Once a j wt a value of ( 4) s encountered, a bnary bt s retreved. On te oter and, a bnary bt 0 s retreved f j as a value of ( 8). Ts procedure s repeated untl tere are no j values of ( 4) or ( 8). Subsequently, s ncreased by. Te same procedures as descrbed above are repeated untl reaces T+. Te retrevng rule s as follows: j 8, f j = 8, j 4, f j = 4, (43) for 0. j 8, f j 8, j 4, f j 4, j j 8, f j ( 8), j 4, f j ( 4), for T. (44) Step 7: At te same tme, te modfed sub-band dfference D s also scanned and modfed. Te extractng operaton can be expressed as te followng formula: ( 0, f D ( 8 ),, f (, ) ( 4 ). D x y Ts procedure s executed untl = T+. (45) Step 8: Remove te dden message bts ( 0, from te sub-band dfference. Te removng rule s gven by D HL2 LH 2, (46) were (, ) LH 2 x y can be expressed as LH 2( xy, ) 8, f j8, n0, (47) LH 2( xy, ) 4, f j4, n, for = 0, and LH 2( xy, ) 8 f j 8, n0, LH 2( xy, ) 4 f j 4, n, (48) LH 2( xy, ) LH 2( xy, ) 8 f j( 8), n0, LH 2( xy, ) 4 f j( 4), n, for T. Step 9: Restore te orgnal stogram. Te orgnal stogram can be calculated accordng to te followng rules: j 8 f j T, j j 8 f j ( T). (4) for L. Te restoraton of te stogram as descrbed above results n canges n te coeffcents. Ts can be descrbed by te followng formula: D ( xy, ) HL2( xy, ) LH 2( xy, ). (42) Here, (, ) 2 x y can be expressed as: LH LH ( xy, ) 8, f j T, LH 2(, xy) LH 2( xy, ) 8, f j ( T). 2 (43) Step 0: After recoverng te LH2 sub-band, steps to 9 are repeated to recover te rest of HL2 and HH2 subbands as (, ) 2 x y and (, ) 2 x y. HL HH Obtanng te LL Sub-band: Step : Recover te orgnal Sub-band LL troug te nverse operaton of te HDWT algortm wt (, ) 2 x y, (, ) LH 2 x y, (, ) HL 2 x y, and (, ) HH 2 x y. Ts procedure can be formulated as follows: LL IDWT ( LL2, LH 2, HL 2, HH 2). (44) Recoverng LH, HL and HH Sub-bands: Step 2: After recoverng te LL sub-band, steps to 9 are also repeated to recover te LH, HL and HH subbands. Obtanng Orgnal Image: Step 3: Recover te orgnal mage troug te nverse operaton of te HDWT algortm wt te LH, HL and HH sub-bands. Ts procedure can be formulated as follows: IDWT ( LL, LH, HL, HH). (45) Tese steps fns te extracton and recoverng process. LL 3
4. Expermental results and comparson In ts secton, a seres of experments are performed to evaluate of our sceme. For tese experments, we used many dfferent types of mages, ncludng some commonly used ones and two medcal mages (Fg. 5). Te message bts to be embedded n our experments are randomly generated by a pseudo-random bnary generator. Te tresold ranges from 0 to 00. wavelet transform. Gven tat te mddle/g-frequency sub-bands ncorporate less energy, te test mages wt larger varance between mddle and g-wavelet coeffcents suc as MRI and MRI 2 can aceve ger vsual qualty tan Baboon at te tresold 0. Fg. 5. 8-bt 52 52 mages(a)lena, (b)baboon, (c)boat, (d)arplane, (e)aeral, (f)tank, (g)trucks, ()Medcal mage, () Medcal mage2. Capacty versus Tresold Te relatonsp between te capacty (n bpp) and te tresold s presented n Fg. 6. Te embeddng rate almost reaces 0.8 bpp at tresold 00 for most te test mages. As expected te capacty s nearly proportonal to te tresold at te begnnng and saturates wen te tresold s suffcently g. Fg. 7. PSNR at varous tresolds. Comparson of vsual qualty wt oter scemes To address te great contrbuton of our sceme, analyses n terms of actual embeddng capacty and vsual qualty were performed. Te proposed sceme was compared wt te DE sceme [4], G-LSB sceme [5], Km et al. s sceme [9], and N et al. s sceme [6] for te Lena, Baboon, Boat, and Arplane mages as sown n Fg. 8. Te embeddng capacty s te amount of embedded bts wt overead subtracted. It s observed tat our proposed tecnque as aceved te gest PSNR at te same bpp. Fg. 6. Embeddng capacty at varous tresolds. Vsual Qualty versus Tresold Fg. 7 depcts te vsual qualty n PSNR of te marked mage versus tresold varyng from 0 to 00 for test mages on te premse tat maxmal bts are embedded. Te expermental result ndcates tat te PSNR rses as te tresold ncreases and ts s not te case for te prevous studes. Te marked mage can aceve 43 db at te tresold 0, and above 46 db at te tresold of 00 for most test mages. It s noteworty tat larger values of tresold contrbute less varaton to te stogram of te 32
Fg. 8. Comparson of embeddng capacty n bpp versus dstorton wt exstng reversble scemes: DE sceme, G-LSB sceme, Km et al. s sceme, and N et al s sceme: (A) Baboon; (B) Lena; (C) Boat; (D) Arplane. 5. Concluson In ts paper, a reversble data dng sceme explotng te large varance of wavelet coeffcents and clever stogram sftng rules s presented. Te proposed sceme, compared wt prevous ones, can obtan better vsual qualty of te marked mage gven te same payload. Te man reason s tat te vsual qualty of our sceme does not decay wt ncreasng tresold as n te oter scemes. In addton, our sceme provdes te greatest embeddng capacty and s even better tan te one publsed recently [9]. It may be of nterest for future researc tat te tresold predctons, mult-round scemes, and fast algortms wll be explored to meet real-tme applcaton requrements. References [] W. Bender, D. Grul, N. Mormoto, and A. Lu, Tecnques for data dng, IBM Systems Journal, vol.35, no.3, pp.33 336, 996. [2] M. Awrangjeb, An overvew of reversble data dng, Proc. Sxt Internatonal Conf. on Computer and Informaton Tecnology, Jaangrnagar Unversty, Banglades, pp. 75 79, December 2003. [3] J. Frdrc, M. Goljan, and R. Du, Dstorton-free data embeddng, Proc. 4t Informaton Hdng Worksop, New York, vol.237, pp.27 4, Lecture Notes n Computer Scence, 200. [4] J. Frdrc, M. Goljan, and R. Du, Lossless data embeddng new paradgm n dgtal watermarkng, EURASIP J. Appl. Sgnal Process. vol.2, pp.85 96, 2002. [5] G.. Xuan, Y.Q. S, J. Cen, J. Zu, and Z. N, W. Su, Lossless data dng based on nteger wavelet transform, IEEE Internatonal Worksop on Multmeda Sgnal Processng, St. Tomas, Vrgn Islands, USA, December 9-, 2002. [6] J. Tan, Reversble data embeddng usng a dfference expanson, IEEE Trans. on Crcuts and Systems for Vdeo Tecnology vol.3, no.8, pp.890 896, 2003. [7] A.M. Alattar, Reversble watermark usng dfference expanson of trplets, Proc. IEEE Internatonal Conference on Image Processng, vol., Barcelona, Span, pp. 50 504, September 2003. [8] A.M. Alattar, Reversble watermark usng dfference expanson of quads, Proc. IEEE Internatonal Conference on Acoustcs, Speec, and Sgnal Processng, Montreal, Canada, vol.3, pp.377 380, May 2004. [9] L. Kamstra and H.J.A.M. Hejmans, Wavelet tecnques for reversble data embeddng nto mages, Centrum voorwskunde en Informatca Rep. August 2004. [0] L. Kamstra and H.J.A.M. Hejmans, Reversble data embeddng nto mages usng wavelet tecnques and sortng, IEEE Trans. on Image Processng vol.4, no.2, pp.2082 2090, December 2005. [] D.M. Tod, J.J. Rodrguez, Expanson embeddng tecnques for reversble watermarkng, IEEE Trans. on Image Processng vol.6, no.3, pp.72 730, 2007. [2] J. Frdrc, M. Goljan, and R. Du, Invertble autentcaton, Proc. of te SPIE, Securty and Watermarkng of Multmeda Contents, vol.434, San Jose, CA, pp.97 208, January 200. [3] M.U. Celk, G. Sarma, and A.M. Tekalp, Reversble data dng, Proc. IEEE Internatonal Conf. on Image Processng, Rocester, NY, pp.57 60, 2002. [4] M.U. Celk, G. Sarma, A.M. Tekalp, and E. Saber, Lossless generalzed-lsb data embeddng, IEEE Trans. on Image Proc. vol.4, no.2, pp.253 266, February 2005. [5] Z. N, Y.Q. S, N. Ansar, and W. Su, Reversble data dng, IEEE Transactons on Crcuts and Systems for Vdeo Tecnology vol.6, no.3, pp.354 362, Marc 2006. [6] J. Hwang, J.W. Km, and J.U. Co, A reversble watermarkng based on stogram sftng, Internatonal Worksop on Dgtal Watermarkng, Lecture Notes n Computer Scence, Sprnger-Verlag, Jeju Island, Korea, vol.4283, pp.348 36, 2006. [7] W.-C. Kuo, D.-J. Jang, and Y.-C. Huang, Reversble data dng based on stogram, Internatonal Conf. on Intellgent Computng, Lecture Notes n Artfcal Intellgence, Sprnger- Verlag, Qng Dao, Cna, vol.4682, pp.52 6, 2007. [8] K.-S. Km, M.-J. Lee, H.-Y. Lee, and H.-K. Lee, Reversble data dng explotng spatal correlaton between subsampled mages, Pattern Recognton, vol.42, pp.3083-3096, 2009. [9] X.-R. Luo, C.-H. Jerry Ln, and T.-L. Yn, Reversble data dng based on two-level HDWT coeffcent stograms, Advanced Computng: An Internatonal Journal, vol.2, no., pp.-6, January 20. 33