Research Article Hamming Code Based Watermarking Scheme for 3D Model Verification

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1 Mathematcal Problems n Engneerng, Artcle ID , 7 pages Research Artcle Hammng Code Based Watermarkng Scheme for 3D Model Verfcaton Jen-Tse Wang, 1 Y-Chng Chang, 2 Chun-Yuan Yu, 2,3 and Shyr-Shen Yu 2 1 Department of Informaton Management, Hsupng Unversty of Scence and Technology, 11 Gongye Road, Dal Dstrct, Tachung Cty 412, Tawan 2 Department of Computer Scence and Engneerng, Natonal Chung-Hsng Unversty, 250 Kuo-Kuang Road,Tachung 402, Tawan 3 Department of Dgtal Lvng Innovaton, Nan Ka Unversty of Technology, 568 Chung-Cheng Road, TsaoTun 542, Nantou County, Tawan Correspondence should be addressed to Shyr-Shen Yu; pyu@nchu.edu.tw Receved 25 February 2014; Accepted 13 Aprl 2014; Publshed 30 Aprl 2014 Academc Edtor: Her-Terng Yau Copyrght 2014 Jen-Tse Wang et al. Ths s an open access artcle dstrbuted under the Creatve Commons Attrbuton Lcense, whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded the orgnal work s properly cted. Due to the explosve growth of the Internet and maturng of 3D hardware technques, protectng 3D objects becomes a more and more mportant ssue. In ths paper, a publc hammng code based fragle watermarkng technque s proposed for 3D objects verfcaton. An adaptve watermark s generated from each cover model by usng the hammng code technque. A smple least sgnfcant bt (LSB) substtuton technque s employed for watermark embeddng. In the extracton stage, the hammng code based watermark can be verfed by usng the hammng code checkng wthout embeddng any verfcaton nformaton. Expermental results shows that 100% vertces of the cover model can be watermarked, extracted, and verfed. It also shows that the proposed method can mprove securty and acheve low dstorton of stego object. 1. Introducton The dgtal era already came to our lves thanks to the nterestngly sophstcated hardware and software technologes. Especally the nternet, t made our lfe more convenent and even changed our lfestyles. Tradtonal publshers, for nstance, gradually translated the products to onlnedgtalzed stores. Ths allowed any wrter s work to be searchedanddscoveredoncetheyuploadthemtothese onlne stores by publshers. Besdes ths, varous multmeda, bothaudoandvsual,alsotakepartnthsdgtalera. But everythng has ts pros and cons. Whle the nternet does make our lves easer, t also presents a rsk towards the copyrght or other personal nformaton. All of these lead to praces, tamperng, and stealng of data. In order to fx these leaks and mprove the data s securty, many experts and scholars endeavor n felds known as nformaton hdng research [1 6], anddgtalsgnature [7 10], dedcated tosolve these problems. Accordng to the dfference of applcaton purpose, nformaton hdng technques can be dvded nto data hdng and watermarkng. The former has another common termnology called steganography. The latter, watermarkng [11 13], s modeled to embed meanngful text or mages wth copyrght nformaton nto cover model to acheve copyrght protecton or mage authentcaton [14, 15]. Watermarkng technque [11 13] can be dvded nto vsble watermarkng and nvsble watermarkng by vsualzaton, or can be separated as blnd, semblnd, and nonblnd by extracton strateges, or can be dstngushed from specal doman [16 19] and frequency doman [19 24] by embeddng space, or can be dfferentated between robust watermarkng and fragle watermarkng accordng to applcaton purpose. The man goal of robust watermarkng s to make the embedded watermarks reman detectable after beng attacked. In contrast, the requrements of fragle watermarkng are to verfy the slghtest unauthorzed alteraton and be able to locate the changed regons. 2. Background and Related Works Among the dfferent meda types, watermarkng of 3D objects s comparatvely dffcult nherently. Intally, Ohbuch et al. [25 28] proposed a large varety of technques for embeddng

2 2 Mathematcal Problems n Engneerng data nto 3D polygonal models. In [26], Ohbuch et al. proposed a nonblnd algorthm that works n the transformaton doman. It embeds a watermark nto a 3D polygonal model by deformng the low-frequency components of the shape by usng the mesh spectral analyss. Cayre and Macq [29] descrbed a blnd data hdng scheme n the spatal doman. The key dea s to consder a trangle as a two-state geometrcal object. Each trangle that can be embedded s called an admssble trangle. In [30], Alface et al. presented a way to extend the robustness of blnd and robust 3D watermarkng schemes to the dffcult croppng attack. C.- M. Wang and P.-C. Wang [31, 32] proposeanovelscheme for dgtal steganography n the spatal doman. It employs a prncpal component analyss (PCA), resultng n a blnd approach. Kana et al. [33] were the frst to apply a transform doman watermarkng approach on 3D polygonal model. It s a nonblnd algorthm, whch frst decomposes an orgnal polygonal model by applyng wavelet transform several tmes. Ths algorthm embeds the watermarks nto the wavelet coeffcentvectorsandtsrobustaganstaffnetransformaton and random nose attacks. The exstng fragle watermarkng algorthms that are desgned for 3D models are relatvely few. In fragle watermarkng, the embedded watermark wll be modfed when the stego object s altered. Therefore, the fragle watermark canbeusedtoverfyastegoobject.yeoandyeung[19]frstly proposed a fragle watermarkng algorthm for authentcatng 3D polygonal meshes. Two ndces were calculated for every vertex: the locaton ndex and the value ndex. Accordng to the coordnates of t and ts neghborng vertces, the locaton ndex was calculated by a hash functon and the value ndex s calculated by another hash functon for each vertex. Then they slghtly perturbed every vertex to make these two hash functons equal. Ther scheme s both blnd and fragle, but there arse two problems: the causalty problem and the convergence problem. The causalty problem s that the locaton ndex of a former processed vertex wll be changed by the perturbng of later processed neghborng vertces. The convergence problem s that the user cannot control the dstorton nduced by the teratvely perturbng process. Fornaro and Sanna [17] proposed a publc key scheme to authentcatng constructve sold geometry (CSG) models whch has a serous drawback that t cannot locate the tampered regon(s). Yeo and Yeung [19] proposedtheuseof content-based sgnature to authentcate 3D volume data. Ln et al. [18] proposed a modfed fragle watermarkng scheme smlar to Yeo and Yeung s method [19]. The causalty problem s conquered n ths method by applyng two dfferent hash functons on the vertex coordnates, wthout consderng the neghborng vertces of a vertex. In the watermark embeddng stage, they slghtly perturbed every vertex makng these two hash functon values equal. However, the convergence problem stll occurs n ths scheme. To avod heavy dstorton due to vertex perturbng, they set a threshold and smply skp the vertces that could not meet the requrement under the threshold. Ths causes some embeddng holes whch cause false alarms n the watermark extracton stage. Chou and Tseng [16] proposedafraglewatermarkng scheme for authentcatng 3D mesh models. A watermark embedded by ths method s robust to translaton, rotaton, and unform scalng but s senstve to other operatons. The man dea of the method s to keep the rato between thedstancefromthemeshcentertoeachsurfacefaceand a quantzaton step remanng the same after the model s translated, rotated, or unformly scaled. There are two major drawbacks n ths scheme. Frstly, t s a sempublc watermarkng scheme snce the orgnal watermark s needed n the decodng stage to authentcate the watermarked model. But a publc watermarkng scheme s preferred n fragle watermarkng. Secondly, t fals n locatng the changed regons snce the center poston of the mesh wll be changed when any vertex has been changed. Chou and Tseng [34]proposeablndfraglewatermarkng technque whch can embed watermark nto at most half the number of total ponts. In [35], a publc fragle watermarkng scheme based on the senstvty of vertex geometry for 3D model authentcaton s proposed. In ths paper, Chou and Tseng propose a multfuncton vertex embeddng methodandanadjustng-vertexmethodtoovercomethe causalty problem and the convergence problem. The average dstorton of the marked models s under user control wth proper key value settng, and ths scheme can detect and locate all unauthorzed modfcatons. But ths scheme stll has the embeddng holes problem. In [36], the coordnates of each vertex of the cover model are transformed to sphercal coordnates. The quantzaton ndex modulaton technque s employed to embed the watermark nto the r coordnates by usng the center of gravty of the cover model. The drawback of [36] s that the reference pont would be changed f any coordnate of the model s modfed. In [37], Wang et al. proposed a multple reference pont embeddng process to overcome the drawback of [36]. In ths paper, a hammng code based fragle watermark scheme s performed on 3D polygonal meshes n spatal doman. The proposed method can provde the capablty of accurately verfyng, locatng the tampered regon to protect the ntegrty of 3D objects and there has no embeddng holes problem. The remanng sectons of ths paper are organzed as follows. The proposed hammng code based fragle watermarkng scheme s descrbed n Secton 3. Expermental results and dscusson are presented n Secton 4. Fnally, conclusons are provded n Secton Proposed Hammng Code Based Fragle Watermark Algorthm In ths paper, a hammng code based fragle watermark scheme for 3D objects s proposed n spatal doman. It s publc and fragle. The logstc map [38]s utlzed to produce the ntermngled embeddng order of vertces. There does not need embeddng any verfcaton nformaton for tamperng detecton n the proposed method. An adaptve watermark s generated from each cover model by usng the hammng code technque [39 42]. Instead of the comparson of the hash functon, the hammng code based watermark can be verfed by usng the hammng code checkng n the extracton stage.

3 Mathematcal Problems n Engneerng 3 Table 1: Relatonshp between party check bts and data bts. D 1 D 2 D 3 D 4 P 1 P 2 P 3 Cover model Embeddng Secret key Stego model Hammng code s named after Rchard Hammng and s a lnear forward error correcton code whch works by addng party check bts at the output data stream. Because of the smplcty of hammng codes, they are wdely used n computer memory RAM [42]. The most wdely used hammng code s (7, 4) hammng code, whch encodes four data bts (D 1, D 2, D 3,andD 4 ) nto seven bts by addng three party check bts (P 1, P 2,and P 3 ). Each party check bt s created by ts assocated data bts. Table 1 llustrates the relatonshp between party check btsanddatabts,where ndcates the relatonshp exsts between party check bts and assocated data bts. As shown n Table 1,thepartycheckbtscanbecreated by usng the assocated date bts, and the results are shown n Table 2,where donates an exclusve or (XOR) operaton. The hammng code detects errors by ensurng each party check bt and ts correspondng data bts acheve the even party. Ths detecton procedure s called party checkng. In mathematcal pont of vew, hammng code s a class of bnary lnear block code. Regardless the form of H and G, H and G for lnear block codes must satsfy HG T = 0, where 0 s an all-zeros matrx due to [7, 4, 3] = [n, k, q] = [2 m 1,2 m m 1,m]. There s a code wth m party bts and 2 m m 1data bts for each nteger, where m must satsfy m 2.ThepartycheckmatrxH of a hammng code s constructed by lstng all columns of length m that are parwse ndependent. Gven a generator matrx G of the code, where G s that so-called systematc form. It means that the leftmost or rghtmost k columns of G form a k kdentty matrx I k. For the detaled formulas, one s referred to [43]. In ths paper, the party check matrx H and the code generator matrx G are: H=[ ], [ ]3,7 G= [ [ ] [ ]4,7 Accordng to the descrpton above, (1) are rewrtten as follows: H=[I n k,p T ], (2) G=[P,I k ]. After calculate (3), the matrces H and G used n ths paper satsfy the theory of hammng code.. (1) HG T =[I n k,p T ][ PT I k ]=P T P T =0. (3) Attacked stego model Extracton Recovery watermark Fgure 1: Proposed fragle watermarkng scheme. Addng the party bts allows the recever checkng and correctng f there are errors. The (7, 4) hammng codes can detect up to two-bt errors, and correct sngle-bt error, but cannot dentfy the error type. Therefore, hammng codes are an example of perfect codes whch exactly match the theoretcal upper bound on the number of dstnct code words for a gven number of bts and ablty to correct errors. Fgure 1 llustrates the outlne of ths proposed scheme. In ths paper, the hammng code technology s adopted as the premse of our 3D model fragle watermarkng scheme. A smple LSB substtuton technque s employed for watermark embeddng. Moreover, the hammng code based watermark can be verfed by usng the hammng code checkng wthout embeddng any verfcaton nformaton n the extracton stage. In summary, the proposed scheme has several advantages: (1) t s publc and blnd; (2) the verfcaton rate acheves 100% (watermarked vertces/total vertces); (3) the vertex based localzaton of unauthorzed modfcaton can be acheved; (4) the key sze used n the proposed scheme s small; (5) Fnally,theproposedmethodsmmunetothe causalty, convergence, and embeddng holes problems The Embeddng Process. Wthout loss of generalty, let each 3D object of nterest be descrbed by a sequence of coordnates P 0,P 1,P 2,...,P N 1, 0 N 1.Moreover,each vertex of the sequence s represented by ts 3D coordnates (x,y,z ). The embeddng algorthm takes two nputs: the cover model and the secret key to produce the stego model. As shown n Fgure 2, t embeds a watermark accordng to the followng four steps: Step 1 (normalzaton). The coordnates of each pont are normalzed nto the range 0 to 1. Consder q x = q y = q z = x orgnal q Mn (X orgnal) Max (X orgnal) Mn (X orgnal) y orgnal q Mn (Y orgnal) Max (Y orgnal) Mn (Y orgnal) z orgnal q Mn (Z orgnal) Max (Z orgnal) Mn (Z orgnal), where x, y, z denote the X, Y, Z axs; s the vertex 0 N 1; Max (X orgnal) denotes the maxmum value of the cover model at X axs, and so as Max (Y orgnal) and Max (Z orgnal), Mn (X orgnal) denotes the mnmum value (4)

4 4 Mathematcal Problems n Engneerng Table 2: Create party check bts. Party check bts Assocated date bts P 1 D 1 D 2 D 4 P 2 D 1 D 3 D 4 P 3 D 2 D 3 D 4 of the cover model at X axs, and so as Mn (Y orgnal) and Mn (Z orgnal). Step 2 (extracton of data bts). Wthout loss of generalty, suppose q r s the pont to be embedded, where r denotes the axs usedand 0 N 1.The4bts,whcharethe 4th least sgnfcant bt to 7th least sgnfcant bt of pont q r, are consdered as an nput data bts D 1, D 2, D 3,andD 4 of hammng procedure. Cover model Normalzaton Extracton of data bts Generaton of party check bts Watermark embeddng Secret key Step 3 (generaton of party check bts). Then, the hammng code procedure s performed to generate the party check bts. As shown n Table 1, the three party check bts P 1, P 2,andP 3 can be generated from the hammng procedure. Moreover, these three party check bts P 1, P 2,andP 3 are regarded as watermark w r n ths paper. Step 4 (watermark embeddng). For securty reasons, a secret key K s employed to generate a random sequence of ntegers. They represent the ndex orders for embeddng watermark to correspondng pont. The party bts are then embedded nto the 3 least sgnfcant bts (LSB) of pont q r by user least sgnfcant bt substtuton. Note that every numerc of random sequence wll never duplcate and only cooperate to one vertex of the cover model. Every vertex has ts own unque watermark. If any part of the stego model s modfed, then the tampered regon wll be verfed n extracton stage The Extracton Process. The watermark extracton process s performed to extract the embedded watermark and verfy the ntegrty of the stego model. The extracton process takes two nputs: the attacked stego model and the secret key K to extract the embedded watermark. As shown n Fgure 3, t extracts the watermark accordng to the followng fve steps: Step 1 (normalzaton). The coordnates of each pont are normalzed wthn the range 0 to 1. Step 2 (extracton of data bts). A secret key K s employed to generate a random sequence of ntegers. The random number generator s the same as that used n embeddng process. The 4 bts whch are the 4th least sgnfcant bt to 7th least sgnfcant bt of pont q r n stego model are extracted and consdered as nput data bts for hammng code. Step 3 (calculaton of party check bts). After hammng code encodng, the three output party bts are regarded as watermark w r. Step 4 (extracton of watermark). The embedded watermark h r can be extracted from the 3 least sgnfcant bts of pont n stego model. q r Stego model Fgure 2: The flow chart of embeddng process. Step 5 (verfcaton). The verfcaton s acheved when the watermark w r s equal to the embedded watermark h r. R(w r no tempered, )={ modfed, w r =h r w r =h r. Note that ths process s a publc blnd fragle watermark scheme whch does not need orgnal model and orgnal watermark for verfy forgery. 4. Expermental Results and Dscussons The proposed publc hammng code based fragle watermarkng method was mplemented usng Mcrosoft Vsual C++ programmng language. A seres of experments were conducted to test the performance of the proposed fragle watermarkng method. We shall present a set of vsualzaton results that can demonstrate the performance of the proposed method and valdate the feasblty of our algorthms. Table 3 shows the cover models of experments n ths paper and the vsual effect of the stego models. No vsual dstorton can be perceved between the cover models and stego models. Moreover, the precson level s used for these experments. No vsual dstorton can be perceved between the cover models and stego models. The drawback of spatal doman s that t has poor resstancetodstortoncompresson.therearesomeapproaches for measure dstorton, such as sgnal-to-nose (SNR), the Haussdorff dstance, Laplacan [44], and root mean square (RMS) rato [31, 32]. SNR used only on the stll mages. The HaussdorffdstanceandLaplacanwereusedtoevaluatethe dstorton of 3D polygonal models. But for a zoomed model, to measure RMS of dstorton s a better choce. Here,weusedRMSbyformula(7) andrmsratoby formula (6) to present the comparson of dstorton control. The RMS rato conssts of the RMS values over the dagonal (5)

5 Mathematcal Problems n Engneerng 5 Table 3: The cover model used n ths paper. Model (sze) Cover model Stego model Model (sze) Cover model Stego model Angelfsh (19724) Teapot (28922) Bunny (34837) Venus (33591) Lon (17352) Wolf (30084) Table 4: The comparson of RMS and RMS rato of dstorton control. Methods Models RMS RMS rato Yang s method Wang s method Proposed Yang s method Wang s method Proposed Anglefsh Bunny Lon Teapot Venus Wolf length of the boundng volume for a 3D stego model. The small RMS ratos ndcate nsgnfcant postonal changes durng the watermark embeddng. Consder where RMS = N 1 =0 RMS Rato = ((q x q x orgnal RMS Dagonal Length, (6) ) 2 +(q y q +(q z z orgnal q ) 2 ) 1/2 (N) 1, y orgnal ) 2 where q x denotes the x coordnate of the pont n stego model, so as q y and q z, 0 N 1, (7) Dagonal Length = X sze 2 +Y sze 2 +Z sze 2. (8) The RMS and the RMS rato comparson results of [36, 37] and the proposed method are as shown n Table 4. In ths paper, a publc hammng code based fragle watermarkng technque s proposed for 3D objects verfcaton. An adaptve watermark of each cover model can be generated from tself by usng the hammng code technque. In the embeddng stage, a smple least sgnfcant bt substtuton technque s employed for watermark embeddng. In the extracton stage, the hammng code based watermark can be verfed by usng the hammng code checkng wthout embeddng any verfcaton nformaton. The verfcaton nformaton should be embedded for achevng the verfcaton tasks n all the prevously mentoned 3D fragle watermarkng schemes. A comparson of the proposed scheme wth Ln s method [18], Yeo and Yeung s method [19], and Chou and Tseng s methods [34, 35] s gven n Table 5, where ndcates that the relatonshp exsts between methods and comparson tems and ndcates there s no relatonshp between methods and comparson tems. 5. Conclusons The proposed publc hammng code based fragle watermarkng s a blnd approach n spatal doman. It s smple to mplement and t does not need the orgnal model or the watermark for verfcaton and localzaton of tamperng detecton of 3D objects. Furthermore, the causalty problem, convergence problem, and embeddng holes problem can be overcome by the proposed scheme.

6 6 Mathematcal Problems n Engneerng Comparson tems Table 5: Comparson of prevous methods and the proposed method. Yeo and Yeung s method Ln et al. s method Methods Chou and Tseng s method (2006) Chou and Tseng s method (2009) Proposed method No verfcaton nformaton No causalty problem No convergence problem No embeddng holes Verfcaton rate 42% 12% 16% 100% Data hdng rate (bts/vertex) <1 <1 <1.5 <1.5 3 Tamperng detecton Localzaton of tampered regon Dstorton control Attacked stego model Normalzaton Extracton of data bts Calculaton of party check bts Extracton of watermark Verfcaton Recovery watermark Secret key Fgure 3: The flow chart of extracton process. The man purpose n ths paper s to authentcate the ntegrty of 3D polygonal messes n the spatal doman. The dstorton rate can be controlled below Theverfcaton rate acheves 100%. Consequently, every regon of the 3D model can be embedded n the embeddng stage and can be verfed n the extracton stage. Conflct of Interests The authors declare that there s no conflct of nterests regardng the publcaton of ths paper. Acknowledgments Ths research was supported by the Natonal Scence Councl, Tawan, under the Grants NSC E and NSC E References [1] B. Pftzmann, Informaton hdng termnology results of an nformal plenary meetng and addtonal proposals, n Proceedngs of the 1st Internatonal Workshop on Informaton Hdng,pp , [2] F. A. P. Pettcolas, R. J. Anderson, and M. G. Kuhn, Informaton hdng a survey, Proceedngs of the IEEE, vol. 87, no. 7, pp , [3] N.F.Johnson,Z.Durc,andS.Jajoda,Informaton Hdng: Steganography and Watermarkng Attacks and Countermeasures, Kluwer Academc Publshers, London, UK, [4] P. Wayner, Dsappearng Cryptography Informaton Hdng: Steganography & Watermarkng, Morgan Kaufmann, San Francsco, Calf, USA, 2nd edton, [5] S. Katzenbesser and F. A. P. Pettcolas, Informaton Hdng Technques for Steganography and Dgtal Watermarkng, Artech House, London, UK, [6] F. Daraee and S. Mozaffar, Watermarkng n bnary document mages usng fractal codes, Pattern Recognton Letters,vol.35, pp ,2014. [7] J.L.Hernandez-Ardeta,A.I.Gonzalez-Tablas,J.M.deFuentes, and B. Ramos, A taxonomy and survey of attacks on dgtal sgnatures, Computers & Securty,vol.34,pp ,2013. [8] C.-F.Chou,W.C.Cheng,andL.Golubchk, Performancestudy of onlne batch-based dgtal sgnature schemes, Network and Computer Applcatons, vol. 33, no. 2, pp , [9] J. Zhang, A knd of message-recoverable farness blnd dgtal sgnature scheme, Proceda Engneerng, vol.15,pp , [10] D.-R. Ln, C.-I. Wang, Z.-K. Zhang, and D. J. Guan, A dgtal sgnature wth multple sublmnal channels and ts applcatons, Computers and Mathematcs wth Applcatons,vol.60, no. 2, pp , [11] I. Cox, M. Mller, and J. Bloom, Dgtal Watermarkng,Morgan Kauffman Publshers, San Francsco, Calf, USA, [12] J. Setz, Dgtal Watermarkng for Dgtal Meda, Informaton Scence Publshers, Hershey, Pa, USA, [13] M. Arnold, S. D. Wolthusen, and M. Schmucker, Technques and Applcatons of Dgtal Watermarkng and Content Protecton, Artech House Publshers, Morwood, Mass, USA, 2003.

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