A New Watermarking Method of 3D Mesh Model

Transcription

1 TELKOMNIKA Indonesan Journal of Electrcal Engneerng Vol., No., Februar 4, pp. 6 ~ 67 DOI: 6 A New Watermarng Method of D Mesh Model Lu Jng*, Wang Ynghu, He Wenjuan, L Ye Facult of Computer Scence and Engneerng, X an Unverst of Technolog, X an 748, Chna *Correspondng author, e-mal: lujng@xaut.edu.cn Abstract A new watermarng method for D model robust to geometrc attacs s presented. The algorthm frstl uses average normal of the part wth the obvous geometrc feature n the D model to establsh coordnate sstem, whch s not affected b geometrc attacs such as translaton, rotaton and scalng; Embed the watermarng nformaton nto the approprate vertces selected accordng to area of - rng neghbours of each vertex; Embeddng strength adaptvel adjusted n terms of curvature of the model facet. The choce of embeddng poston and the embeddng strateg above effectvel guarantee good transparenc and maxmum robustness of the proposed algorthm. Smulaton results ndcate the ablt of the proposed method to deal wth the some attacs more than satsfactor results. Kewords: D model, geometrc feature, average normal, coordnate sstem, -rng neghbour Coprght 4 Insttute of Advanced Engneerng and Scence. All rghts reserved.. Introducton Wth man new technologes for representaton,storage and dstrbuton of dgtal meda nformaton becomng avalable, the applcatons of D model are qucl ncreasng n number and the necesst to protect coprghts of D model s becomng crucal. Watermarng has been consdered a potental effcent soluton for deterrng llegal copes of D model. In the last decades,numerous methods have been presented for the dgtal watermarng of D mage, successfull solvng a lot of dffcult problems. But few algorthms of D model have been developed and tested wth good performances. One of the man reasons s that man D mage processng algorthms are ver helpful to development of D mage watermarng technolog but these algorthms are not completel sutable for D model. At the same tme, compared wth D mage, D model data are ntrnscall complex to handle; There are more attacs to nterfere wth D model; There sn t a mathematcal framewor to provde an effcent tool for D model watermarng. So t s ver dffcult to develop robust watermarng algorthms for D model. At present, watermarng algorthms of D Model are dvded nto two categores accordng to the nserton area: spatal doman methods [-7] embed the watermar b drectl modfng nvarants of the orgnal model.for example, Ohbuch [] chose the rato between the heght of a trangle and ts opposte edge length as prmtve to construct a watermarng technque (TSQ). Benedens presented two technques for embeddng watermars whch are robust aganst remeshng and more specfcall trangle reducton attacs,named Normal Bn Encodng [5] and Affne Invarant Embeddng [6], respectvel. The frst method needs a model reorentaton to provde successful detecton. The second method wthstands geometrcal transforms but needs the orgnal model for the detecton. Whle n the frequenc doman methods [8-6], the watermarng nformaton s embedded b modfng coeffcents of frequenc doman whch s wavelet analss [8-], Laplace transforms [-] or other transforms [4-6]. Frequenc doman algorthms can provde better robustness ablt. In ths paper, we proposed a new method for embeddng watermar nto D model represented as trangular meshes. Frstl, establsh the reference frame b utlng average normal of the area whch has the obvous geometrc feature; Project each component of the vertex coordnate separatel onto the orthogonal coordnate axes n the reference frame; The postons embedded the watermarng nformaton were selected accordng to area of -rng neghbous of each vertex; Embeddng strength was adaptvel adjusted n terms of curvature of the model surface. These strateges grant the method robustness to rotaton, scalng and translaton attacs. Receved Jul 7, ; Revsed September, ; Accepted October,

2 TELKOMNIKA ISSN: In the next secton, based on the analss of projectve transformaton, nsertng poston selecton and nsertng strength selecton, we wll ntroduce the embeddng and extractng watermar procedure of our watermarng algorthm. Secton shows some of our expermental results and analses. Fnall, concluson and some potental mprovements n future wor are gven n Secton 4.. A New Mesh Watermarng Algorthm.. A Projectve Transformaton D model watermarng requrements are smlar wth those for D mage watermarng. Such requrements nclude the non-perceptblt when watermar nformaton s nserted nto the D model.in addton, a watermar algorthm succesfull detects the watermar after the D model underwent geometrc attacs and topologcal attacs. Geometrcal attacs consst of rotaton, scalng and translaton. Topologcal attacs nclude changng the order of vertces n the D model, mesh smplfcaton, mesh alterng or croppng parts of the model. To settle above problems, numerous technques can be appled. But these approaches have not acheved the desred effect. Our strateg s to convert the D data to the space whch s nvarant to rotaton,translaton and scalng. Select a part wth the obvous geometrc feature n D model. The part s used to calculate the nvarant space and not nserted the watermar. The average normal of the part s computed and decomposed nto three components correspondng to the coordnate axes u,v and n of the new reference frame; The center of the part s calculated usng the followng Equaton (), whch s the orgn of the new coordnate sstem. v N N c v () Suppose the orgnal coordnate sstem s Ox, the new coordnate sstem s O uvn. To nvert the transformaton, the orthogonal transformaton M s computed as Equaton (): Ox Ouvn M Ox Ouvn u x v x n x u v n u v n v v v cx c c () Multpl each vertex of the model wth the matrx M Ox Ouvn to get the vertex coordnate n the coordnate sstem O uvn. The watermar nformaton s nserted n the coordnate sstem O uvn. Dvde the part nto two usng a plane whch s perpendcular to the u,v or n axs and passes through the orgn of the new coordnate sstem. Compute the mass center of each part Usng the Equaton (). Obtan the dstance between the mass center of the two part so as to acheve robustness aganst scalng attac... Embeddng Poston Selecton In a watermarng algorthm, watermar nformaton s added b modfng the vertex postons wthout causng the ee to perceve an change. The change s nfluenced b the surroundng geometr of the vertces. For example, perturbaton of an solated vertex n D model would not cause vsual degradaton n locaton of the vertex. However, f the solated vertex s n the bacdrop of a flat surface, the degradaton s more perceptble. If the same vertex s on a bump surface, the degradaton s nvsble. Thus, the absolute poston of the vertex s not mportant for watermarng, but ts poston relatve to the local geometr determnes whether the vertex s a good or bad canddate for watermar embeddng. In ths paper, the vertces to be nserted watermar nformaton are selected from the postons where the vertces are densel dstrbuted. Notce that the postons would not nclude the part of the D model whch s used to calculate the nvarant space n secton.. We selected -rng A New Watermarng Method of D Mesh Model (Lu Jng)

3 6 ISSN: -446 vertces [7] to represent the local set of each vertex.suppose V s a randoml vertex n the D model, f an edge exsts whch connects V and V, the vertex V s a neghbor of the vertex V. The set of all neghbors of the vertex V s called -rng of the vertex V. The set of all neghbors of the -rng neghbors of the vertex V and ts -rng neghbors are called -rng of the vertex V, whch s expressed as T V : TV V V V,,,, T () Fgure. Neghbors of the Vertex V : -rng Dsplaed b Whte Patch, -rng Dsplaed b Whte and Gra Patches Where V V represents the number between the vertex V and V, T expresses the valence of the vertex V. Fgure shows the -rng neghbours and the -rng neghbours of vertex V. The characterstcs of the hgh-curvature area n the D model are that trangular patch area s relatvel small and has relatvel more vertex number. If watermar nformaton s nserted n the neghborhood of the vertex located n the hgh-curvature area, the dstorton can be mased b the surroundng geometrc features. Suppose S s the local set area of the vertex V,and represents the average area of all the trangular meshes n -rng of the vertex V. We can measure whether the vertex V s sutable for embeddng watermar nformaton b usng the local set area S. S N N s (4) Where s s the area of the th trangular mesh n the -rng of the vertex V. Suppose that the three vertces of the th trangular mesh are P (x,, ),P (x,, ),P (x,, ), the area s s defne as: s P P x x P P sn x x x x x x (5) Set a threshold value S T, when S < S T, the vertex V s a good canddate for watermar nserton. Notce that the vetces later selected can t fall wthn -rng neghbor of the vertex V. TELKOMNIKA Vol., No., Februar 4: 6 67

4 TELKOMNIKA ISSN: In fact,we calculate the local set area of all vertces and order them from small to large accordng to ther value and nsert the watermar nformaton nto those vetces wth smaller area of -rng. The capact of the watermar nformaton determnes the threshold value S T... Embeddng Strength Selecton Once vertces are selected for watermarng, the strength of watermar to be nserted n the vertex poston depends on f there s perceptble degradaton for the vertex. If a smaller watermar s nserted b modfng fewer bts n the vertex poston, the watermar could be easl destroed wth watermarng attacs. If a hgher number of bts are moded, the watermared vertex could potentall cause perceptble degradaton. Thus, the watermarng algorthm needs to be able to mae a determnaton as to the maxmum amount of watermar or bts to modf n the vertex wthout causng perceptble degradaton. Curved surface s more curved, more the watermar nformaton ma be nserted. Curved surface consst of a number of smaller trangles. Normal varaton usuall gves a good ndcaton of the surface curvature. For example, f the surface s flat, all the surface normals are parallel to each other and there s ero devaton of the average normal from each of the surface normals; If the surface s smooth, the devaton of the surface normal from the average normal s consstent wth the devaton of the other surface normals from the average normal; If the surface has uneven curvature, the devaton of the surface normals from the average normal could be erratc [7]. In the paper,we are gong to use curvature of the model surface to determne the ampltude of embeddng watermar. We frstl calculate the average normal of the -rng and the -rng of the vertex V, respectvel; Then, calculate the devaton angle β of the average normal of the -rng ( N, see Fgure ) from the average normal of the -rng ( N,see Fgure ); At last, use the parameter sn( ) to modulate the embeddng watermar ampltude.in fact,when the devaton angle β s larger, t ndcates that the surface s more curved, more the watermar capact ma be nserted..4. Embeddng Watermar The watermarng algorthm of ths paper embeds watermar b modfng the poston of the vertces selected b usng local set area. The data fomat of the D model to be embedded the watermar s trangle mesh, we assume that the watermar s a bt vector b ( b b, b, b, bm, b (,), m ),and a seed number (stego-e w ) generates pseudo random numbers b ( b b, b, b, b m, b (,), m). Let us now consder modfng one component u of the vertex coordnate and modfcaton processes for the other two components are dentcal. Let V u, be the th vertex pror to watermarng correspondng to the coordnate axs u, b (, ) be the pseudorandom number sequence, and sn( ) ( sn( ) >) be the modulaton ampltude. Watermared th vertex V u, s computed b the followng Equaton (6): V u, V V u, u, ( sn( abs ( ))) ( sn( abs ( ))) f ( b f ( b ) ) (6) The extracton algorthm requres the same stego-e, whch s a seed for the pseudo random number sequence used for the embeddng. Applng the same procedure to v and n components of the vertex produces a set of watermared vertces V V, V V. u,, v, n, Inverse-transformng the set of vertces ( O uvn ) bac nto the orgnal doman of vertex coordnates V V, V mesh. V b usng the Equaton () produces a watermared trangular x,,,, A New Watermarng Method of D Mesh Model (Lu Jng)

5 64 ISSN: Extractng Watermar In ths paper, watermar extracton s non-blnd, that s, the detecton procedure requres the orgnal model. The extracton starts wth searchng the coordnate sstem b usng the method presented n Secton.. The tested model and the orgnal model are separatel projected onto ther correspondng to coordnate sstem; Calculate the local set area of -rng of all vertces, and the devaton angle β of the average normal of the -rng from the average normal of the -rng n the orgnal D model. Then, produce two sets of vertces b choosng the smaller local set area. Compare the value of the two sets of vervces, get the dfference ( u, V u, V ), sum over all of the three axes, and produce the overall sum : ( V r{ u, v, n} r, V r, ) (7) b f ( / sn( abs ( )) ) f ( / sn( abs ( )) ) (8) Where V u, and V u, are the coordnate of the vertex V n the u axs of the orgnal D model and the tested D model, respectvel. b expresses the watermar bt to be detected. Multpl wth the same the pseudorandom number sequence b as s used for the embeddng, and produce the overall correlaton b the followng Equaton (9): ( b, b ) m m b b b m b (9) When. 5, the watermar embedded s succesfull extracted.. Experments and Results In ths secton, we show some expermental results to verf the detecton performance and robustness of the proposed method aganst varous dsturbances, ncludng nose,smoothng, mesh smplfcaton and smlart transformaton (translaton, rotaton and scalng) [8]. The models used for testng were Cow (486 vertces, 84 facets), Standford Bunn (484 vertces, 6945 facets)... Watermar Invsblt Fgure shows the model before and after embeddng the watermar. The watermar s embedded n the D trangular mesh model. Fgure (d), Fgure (e) and Fgure (f) are the renderng effect correspondng to ther trangular mesh model (Fgure (a), Fgure (b) and Fgure (c)), respectvel. Fgure llustrates the perceptblt of a watermar depends not onl on the ampltude ( sn( ) ),but also on the watermar capact to be nserted. If we choose large embeddng capact, the dfference of the orgnal and watermared model would be vsble.in Fgure, the % of vertces watermared are less notceable than the 5% of vertces watermared... Nose and Smoothng Attacs As dscussed n Secton, the choce of embeddng poston and embeddng ampltude strateg meet several dfferent robustness requrements, e.g., robustness aganst nose and robustness aganst smoothng. The embeddng ampltude strateg maes the watermar more resstant to random nose added to vertex coordnates.however, the method of the local set TELKOMNIKA Vol., No., Februar 4: 6 67

6 TELKOMNIKA ISSN: area for choce that resulted from the embeddng poston would reduce the watermar s robustness aganst mesh smoothng. Fgure shows the Bunn whose vertex coordnates are added wth Gaussan nose wth the dfferent ampltude factor. The watermar could stll be extracted despte the slght dstorton of qualt of the D model (see Fgure (b)), But the watermars faled to be extracted when the ampltude factor of Gaussan nose s more than.5 ( ) so that the degradatons of qualt s vsble (see Fgure (c)). Fgure 4 shows the method can resst aganst mesh smoothng as far as the smoothng does not degrade shape of the mesh too much. After an applcaton of the Taubn s smoothng flter, the Bunn model loos smoother. Despte the changes( ), the watermars embedded nto these models could be extracted. (a) The orgnal D mesh model (b) % of vertces watermared (c) 5% of vertces watermared (d) Renderng effect of (a) (e) Renderng effect of (b) (f) Renderng effect of (c) Fgure. Vsblt Tests of D Watermarng Method (a) The orgnal Bunn (b) The nose Bunn (σ=.) Fgure. The Nose Attacs on Bunn (c) The nose Bunn (σ=.5) A New Watermarng Method of D Mesh Model (Lu Jng)

7 66 ISSN: -446 (a) The Smooth Bunn (=.8) (b) The Smooth Bunn (=.)) (c) The Smooth Bunn (=.4) Fgure 4. The Smooth Attacs on Bunn (a) Bunn (% reducton) (b) Bunn (5% reducton) (c) Bunn (% reducton) Fgure 5. The Smplfcaton Attacs on Bunn.. Mesh Smplfcaton As far as the mesh smplfcaton attac, the algorthm maes full use of the average normal drecton of a group of facets and the dstances of a group of vertces to the mesh centre to resst t. Of course, the method s less robust because the geometrc postons of the vertex are changed and the snchronaton nformaton s dscarded. Fgure 5 llustrates that the method can extract the watermar when less than 5% of meshes are smplfed..4. Smlart Transformatons Watermars embedded b usng the proposed method are robust aganst smlart transformaton, for the transformaton can be dentfed and nverted b usng the method descrbed n Secton.. Table shows that the algorthm s able to extract the watermar when the tested models (Cow and Bunn) are subjected to mld acceptable scalng, rotaton or translaton attacs. Table. The Correlaton Value (ρ) of Extracton Watermar from the Varous Attacs Rotaton Scale Translaton ρ>.95 ρ>.89 ρ>.66 ρ<.4 ρ<.5 ρ>.7 ρ>.8 ρ< Concluson A novel D model watermarng method was proposed n the paper. The transfomaton maes the method resst the geometrc attacs such as rotaton,translaton and scalng. The choce of embeddng poston and the embeddng strateg used n the paper help to guarantee good transparenc and maxmum robustness of the watermar. Smulaton results demonstrate that the proposed method can gve good results even for small values of the embeddng power and deal wth the geometrc attacs more than satsfactor results. In the future, we would le to TELKOMNIKA Vol., No., Februar 4: 6 67

8 TELKOMNIKA ISSN: research mesh watermarng based on geometrc feature whch mght allow the watermar method more robust et less perceptble. Future wor wll also address the possblt of retrevng the watermar after that the mesh has been processed b re-trangulaton or resamplng. Acnowledgements Project supported b the Scentfc Research Program of Shaanx Provncal Educaton Department (No. JK74) and X an Scence and Technolog project (No. CX56(4)) and Beln of X an Scence and Technolog project (No. GX7). References [] Ohbuch R, Masuda H, Aono M. Watermarng Three Dmensonal Polgonal Models. Proceedngs of the Ffth ACM Internatonal Conference on Multmeda. Seattle, Washngton. 997: 6-7. [] Ohbuch R, Masuda H, Aono M. Embeddng Data n D Models. Proceedngs of the European Worshop on Interactve Dstrbuted Multmeda Sstems and Telecommuncaton Servces. Darmstadt. 997: -. [] Ohbuch R, Masuda H, Aono M. Watermarng Three-dmensonal Polgonal Models Through Geometrc and Topologcal Modfcatons. IEEE Journal on Selected Areas n Communcaton. 998; 6(4): [4] Ohbuch R, Masuda H, Aono M. Data Embeddng Agorthms for Geometrcal and on Geometrcal Targets n Three-dmensonal Polgonal Models.Computer Communcatons. 998; (5): [5] Benedens O, Busch C. Towards Blnd Detecton of Robust Watermars n Polgonal Models. Proceedngs of Eurographcs. Interlaen. : [6] Benedens O. Affne Invarant Watermars for D Polgonal and NURBS Based Models. Proceedngs of the rd Internatonal Worshop Informaton Securt, Wollongong. : 5-9. [7] Cho JW, Prost R, Jung HY. An Oblvous Watermarng for D Polgonal Meshes Usng Dstrbuton of Vertex Norms. IEEE Transactons on Sgnal Processng. 7; 55(): [8] Kana S, Date H, Kshnam T. Dgtal Watermarng for D Polgons Usng Multresoluton Wavelet Decomposton. Proceedngs of Internatonal Worshop on Geometrc Modelng. Too.998: [9] Uccheddu F, Corsn M, Barn M. Wavelet-based Blnd Watermarng of D Models. Proceedngs of the 4 Multmeda and Securt Worshop. Magdeburg. 4: [] Ohbuch R, Muaama A, Taahash S. Watermarng D Polgonal Meshes n the Mesh Spectral Doman. Proceedngs of Euro graphcs. Saarbrucen. : 7-8. [] Hung-Kuang Chen, Yung-Hung Chen. Progressve Watermarng on D Meshes. In Broadband Multmeda Sstems and Broadcastng (BMSB). IEEE Internatonal Smposum. Shangha. : -7. [] Care F, Rondao-Alface P, Schmtt F, et al. Applcaton of Spectral Decomposton to Compresson and Watermarng of D Trangle Mesh Geometr. Sgnal Processng. ; 8(4): 9-9. [] Care F, Devller O, Schmtt F, Matre H. Watermarng D Trangle Meshed for Authentcaton and Integrt. INRIA Research. Report number: [4] Praun E, Hoppe H, Fnelsten A. Robust Mesh Watermarng. Proceedngs of the 6th ACM Internatonal Conference on Computer Graphcs. Los Angeles. 999: 5-4. [5] Ka Wang, Lavoue G, Dens F, Basurt A. A Comprehensve Surve on Three-dmensonal Mesh Watermarng. IEEE Transactons on Multmeda. 8; (8): [6] Hu R, Rondao-Alface P, Macq B. Constraned Optmsaton of D Polgonal Mesh Watermarng B Quadratc Programmng. Proceedngs of the IEEE Internatonal Conference on Acoustcs, Speech, and Sgnal Processng.Tape. 9: [7] Muesh-Motwan. Thrd Generaton D Watermarng: Appled Computatonal Intellgence. PhD Thess. Unverst of Nevada, Reno.. [8] Ka Wang, Gullaume Lavou e, Florence Dens, Atlla Basurt, Xan He. A Benchmar for D Mesh Watermarng. Proceedngs of Shape Modelng Internatonal Conference Curves and Surfaces. Avgnon. : -5. A New Watermarng Method of D Mesh Model (Lu Jng)