A Robust Blind 3-D Mesh Watermarking based on Wavelet Transform for Copyright Protection
Mohamed Hamidi, Mohamed El Haziti, Hocine Cherifi, Driss Aboutajdine
AA Robust Blind 3-D Mesh Watermarking based onWavelet Transform for Copyright Protection
Mohamed HAMIDI ∗ , Mohamed EL HAZITI § , Hocine CHERIFI ∗∗ ,Driss ABOUTAJDINE ∗∗ Associated Unit to the CNRST-URAC N 29,Faculty of Sciences, University of Mohammed V,BP 1014 Rabat, [email protected] , [email protected] § Higher School of Technology, Sale, [email protected] ∗∗ Laboratoire Electronique, Informatique et Image (Le2i) UMR 6306 CNRS,University of Burgundy, Dijon, Francehocine.cherifi@u-bourgogne.fr
Abstract —Nowadays, three-dimensional meshes have been ex-tensively used in several applications such as, industrial, medical,computer-aided design (CAD) and entertainment due to theprocessing capability improvement of computers and the devel-opment of the network infrastructure. Unfortunately, like digitalimages and videos, 3-D meshes can be easily modified, duplicatedand redistributed by unauthorized users. Digital watermarkingcame up while trying to solve this problem.In this paper, we propose a blind robust watermarking scheme forthree-dimensional semiregular meshes for Copyright protection.The watermark is embedded by modifying the norm of thewavelet coefficient vectors associated with the lowest resolutionlevel using the edge normal norms as synchronizing primitives.The experimental results show that in comparison with alternative3-D mesh watermarking approaches, the proposed method canresist to a wide range of common attacks, such as similaritytransformations including translation, rotation, uniform scalingand their combination, noise addition, Laplacian smoothing,quantization, while preserving high imperceptibility.
Keywords — Three-dimensional meshes, digital watermarking,wavelet coefficient vectors, Copyright protection, synchronizingprimitives.
I. I
NTRODUCTION T HE majority of previous watermarking techniques havefocused on audio, image and video. Nowadays, 3-Dmeshes [1] are widely used in different fields such as virtualreality, computer aided design, medical imaging, video gamesand 3D movies, due to the high computational performance ofactual computers and the increasing needs of precision andrealism. Therefore, the necessity to protect their copyrightbecomes more crucial. Digital watermarking [2] has beenconsidered as an efficient solution that overcome this problem.Its underlying concept is to embed an information calledwatermark within a digital content. Three requirements mustbe satisfied in each watermarking system : imperceptibility,robustness and capacity [3]. The imperceptibility refers to theperceptual similarity between the original 3-D model and thewatermarked one while the robustness is the ability to resistagainst common signal processing attacks, such as spatialfiltering, lossy compression, and geometric distortions. Thecapacity refers to the number of bits that can be embeddedin the models. In image watermarking, pixels have an intrinsic order in the image such as the order established by columnor row scanning. The watermark bits synchronization is per-formed using this order. Nevertheless, there is no obviousrobust intrinsic ordering for mesh elements. Especially forirregular 3-D meshes, we can’t perform an effective spectralanalysis. Consequently, the existing successful spectral analy-sis watermarking techniques such as [4] can’t be applied on3-D meshes. Another issue is that the majority of intuitiveorders, (like the order of vertices obtained by ranking theirprojections on an axis of the objective Cartesian coordinatesystem), are very easy to be altered. Attacks on 3-D meshwatermarking can be divided into two types. Geometric at-tacks including similarity transformations, signal processing,and local deformation operations. Connectivity attacks whichinclude cropping, remeshing, subdivision and simplification.Generally, few watermarking schemes have been proposed for3D meshes in contrast with the maturity of image,video andaudio watermarking techniques. This situation is due to thedifficulties encountered while handling the arbitrary topologyand irregular representation of 3-D meshes, as well as thecomplexity of the existing possible attacks on watermarkedmeshes.Several robust watermarking techniques have been pro-posed for 3-D meshes using spatial primitives [5] [6], sta-tistical mesh descriptors [7] [8], content based [9] [10] andmultiresolution analysis [11] [12]. In the case of semiregularmeshes, the robust watermarking was first discussed by Kanai et al. [13], that proposed a nonblind method based on lazywavelet transform (see Fig. 1). Their scheme is robust againstsimilarity transformations. Uccheddu et al. [15] extended [13]to achieve a blind one-bit watermarking method for semi-regular meshes. The method is relatively robust against ge-ometric attacks. Similarly to [15], Kim et al. [11] proposeda robust watermarking correlation-based scheme to embedwatermark bits in groups of WCVs using irregular wavelettransform [16]. Their technique shows good robustness againstgeometric attacks and affine transformation, but their schemeis low robustness against connectivity attacks. Later, Kai Wang et al. proposed a hierarchical watermarking framework basedon wavelet transform for semiregular meshes [17].The authors embed robust, fragile and high capacity water- a r X i v : . [ c s . MM ] N ov ig. 1: One illustration of the lazy wavelet process applied totriangular semiregular mesh [13].marks in different resolution levels for Copyright protection,content authentication and content enrichment respectively.The robust watermark is able to resist common geometricattacks. In [18], Yesmine et al. proposed a blind robustwatermarking method for Copyright protection where thewatermark bits are embedded by quantizing the Euclideandistance between the mass center of the mesh and the selectedvertices. Recently, a robust blind 3-D watermarking methodbased on multiresolution adaptive parametrization of surfacehas been proposed [19]. This parametrization is used to selectthe vertices of the coarsest level in order to establish aninvariant space and some other vertices of the fine level usedas feature to embed the watermark.In this paper, we propose a blind robust 3-D watermarkingscheme for semiregular meshes. Our method is based on thequantization of the the norm of the wavelet coefficient vectors.The watermarking primitive is the ratio between the norm ofa wavelet coefficient vector and the norm of edge normalsin the coarsest-level. In addition, the edges in the coarsest-level mesh obtained after wavelet decomposition are sortedaccording to the norms of normals on vertices which representthe synchronizing primitives. This order is found to be robustto a wide range of attacks, including similarity transformations,quantization, Laplacian smoothing, etc.The rest of this paper is organized as follows. Section IIpresents the background. Section III develops the proposedwatermarking scheme. Section IV shows the experimentalresults and section V concludes the paper.II. B ACKGROUND
A. Multiresolution Wavelet Decomposition
Multiresolution analysis is a very useful tool which aimsto represent a signal at different levels of detail. It has beenapplied on different kinds of data, such as signals, images, 3-D models, etc. In this work, our interest is on 3D waveletsbased on subdivision surface of Lounsbery et al. [14]. Oneiteration of the lazy wavelet process, in which a group offour triangles ( t j , t j , t j and t j ) is merged in one triangle t j +11 at low-resolution level j + 1 , is illustrated in Fig. 1.The positions of the vertices v j , v j and v j are kept unchanged even at the low-resolution. Three of six initial vertices v j , v j and v j are conserved at the low-resolution. The waveletcoefficients W j +11 , W j +12 and W j +13 are considered as theprediction errors for the deleted vertices v j , v j and v j . Thusthe multiresolution representation of ( v j , v j , v j , v j , v j , v j ) canbe expressed as follows : V j +1 = A j +1 V j (1) W j +1 = B j +1 v j (2)Where V j = (cid:104) v j , v j , . . . , v jk (cid:105) T represents the vertex coor-dinates at resolution level j , k j is the number of verticesat level j and W j +1 = (cid:104) w j +11 , w j +12 , . . . , w j +1 t (cid:105) T refers towavelet coefficient vector at resolution level j + 1 . t j +1 is thenumber of wavelet coefficient vectors at resolution level j + 1 where t j +1 = k j − k j +1 . A j +1 is a non-square matrix whichillustrates the triangle reduction by merging four triangles intoone. B j +1 is a non square matrix which produces the waveletcoefficient vectors which start from the midpoint of the edgein the lower resolution j + 1 and ends at the vertices which arelost at the same level j + 1 .III. P ROPOSED SCHEME
In this paper, we propose a blind robust 3-D mesh water-marking scheme for Copyright protection. The chosen water-marking primitive are the WCV norms. In fact, the watermarkis embedded by quantifying the WCVs norms associated withthe coarsest-level mesh after performing a thorough waveletdecomposition. The reason behind inserting the watermarkin the low frequency is that they are supposed to be robustagainst several attacks, especially geometry attacks. For thesynchronization primitives, the edge normal norms are chosento synchronize the watermark bits. We find experimentally thatthis order is robust against various attacks. The watermark em-bedding and extracting are described in detail in the followingsections.
A. Watermark embedding
Firstly, the wavelet decomposition applied to the originalsemiregular mesh M is carried out until we get a coarsest-level mesh M J and a set of WCVs associated to each edge inthis level. We note that the number of WCVs in the coarsest-level is equal to the number of edges in this level. Afterwards,the edges are sorted in the descending order according to thenorm of edge normals. We define the normal (cid:126)n , of an edge e as the average of the two vertices normals ( (cid:126)n , (cid:126)n ) composingthis edge. The first edge denoted by e J is the edge which hasthe biggest normal norm. The second is denotes by e J , etc.The wavelet coefficient vector associated with e J is denotedby W CV J , the wavelet coefficient vector associated with e J is denoted by W CV J , etc. The watermark bits are embeddedby quantifying the WCVs norms. The quantization step Q S isfixed to N av /λ , where λ is a parameter that controls the trade-off between imperceptibility and robustness. This parameteris chosen in such a way that gives good robustness whilemaintaining the imperceptibility of the proposed watermarkingsystem. The quantization of the WCV norms is performedusing the -symbol scalar Costa scheme (SCS) [20]. First, aandom code is established for each WCV norm using equation3. β x i ,t xi = (cid:91) l =0 (cid:26) u = zQ S + l Q S t x i (cid:27) (3)Where z ∈ Z + , l ∈ { , } denotes the watermark bit, Q S isthe quantization step, t x i is an additive pseudo-random dithersignal generated using a secret key K . We look for the nearestcodeword β JW CV i to W CV i J in the codebook which impliesthe correct watermark bit. The quantized value W CV (cid:48) Ji iscalculated according to (4). As detailed in [21], the perfectsecurity is achieved when γ = 1 / . W CV (cid:48) Ji = (cid:13)(cid:13) W CV Ji (cid:13)(cid:13) + γ ( β W CV Ji − (cid:13)(cid:13) W CV Ji (cid:13)(cid:13) ) (4)After the quantization process, we reconstruct the dense meshusing the modified WCVs after performing the wavelet synthe-sis. It is well known that the ratio between the norm of a WCVand the average length of all edges in the coarest-level meshis invariant to similarity transformations [17]. However, theedges in the coarsest-level have often the same length whichcan be a real limitation. To avoid this problem, we choose theaverage edge normals norms of all edges in the coarest-levelas synchronizing primitives. The embedding steps are furtherdescribed in Algorithm . Algorithm 1: Watermark embedding N Av of edge normals in thislevel and set the WCV norm quantization step as N av /λ .4- Calculate the norms of the WCVs and quantize them ac-cording to (3) using the -symbol scalar Costa quantizationscheme, keeping the same order of edges.5- Do mesh reconstruction starting from the modified WCVnorms in order to obtain the watermarked dense semi-regularmesh. B. Watermark extracting
The exacting process is blind so we don’t need the originalmesh. Only the secret key K is needed. First of all, weapply the wavelet analysis to the watermarked mesh until weget the coarsest-level. Then, we reestablish the edge order(the norm of normal edges sorted in the descending order).After, we recalculate the quantization step and reconstructthe codebook. Finally, we search the nearest codeword to thewavelet coefficient vector norm in the reconstructed codebookin order to find out the watermark bits. The extracting stepsare further described in Algorithm .IV. E XPERIMENTAL RESULTS
A. Experimental setup
Experiments were carried out on three 3-D semiregularmesh models: Bunny ( vertices), Horse ( ver-tices), Venus ( vertices) as depicted in Fig. 2 ((a), (b)and (c)). In the embedding process, bits of watermark are Algorithm 2: Watermark extracting (a) (b) (c)(d) (e) (f)
Fig. 2: Original 3-D models (Top) Venus, Rabbit, Horse andFeline and watermarked ones : (Bottom) Venus, Rabbit, Horseand Feline. (a) (b) (c) (d)
Fig. 3: Several attacks on Bunny: (a) Mesh simplification, (b)Quantization 7-bits , (c) Laplacian smoothing relaxation = 0 . ,(d) Noise addition intensity = 0 . .embedded into the mesh models. The capacity of the proposedscheme is one bit per WCV. We tested several values of λ andwe retained the value which ensures a good trade-off betweenrobustness and imperceptibility. B. Imperceptibility
TABLE I: Watermark imperceptibility measured in terms ofMRMS, HD and MSDM.
Model MRMS ( − ) HD ( − ) MSDMHorse 0.26 0.5060 0.0708Venus 0.38 0.56 0.0105Bunny 0.05 0.67 0.0775 ABLE II: Comparison of watermark invisibility in terms ofMSDM.
Method Horse[17] 0.098[19] 0.21Proposed scheme
TABLE III: Comparison of watermark invisibility in terms ofMRMS ( − ). Method Bunny Horse[17] 0.20 0.64[18] 0.043 –[19] 0.28 0.32Proposed scheme
Several experiments was conducted before applying attackson the 3-D meshes using to evaluate the effectiveness of theproposed scheme in terms of imperceptibility. The distortionintroduced by the proposed technique is compared objectivelyand visually. The objective distortion between the originaland watermarked meshes is measured using the maximumroot mean square error (MRMS) proposed in [22] as thenumerical objective comparison measurement. The MRMS isthe maximum between the two root mean square error (RMS)distances calculated by: d MRMS = max ( d RMS ( M, M w ) , d RMS ( M w, M )) (5) d RMS ( M, M w ) = (cid:115) | M | (cid:90) (cid:90) p ∈ M d ( p, M w ) dM (6)Where p is a point on surface M , | M | denotes the area of M , and d ( p, M w ) is the point-to-surface distance between p and M w . It is well known that MRMS does not correctlyreflect the visual difference between two meshes [23]. Thus,another perceptual metric is needed to evaluate the visualdistortion. The mesh structural distortion measure (MSDM)proposed in [23] is chosen to measure the visual degradationthat the watermarked mesh has undergone. When the originaland watermarked meshes are identical the MSDM value isequal . Otherwise, the MSDM value is equal to when themeasured objects are visually different. The global MSDMdistance between the original mesh M and watermarked mesh M w having n vertices respectively is defined by : d MSDM ( M, M w ) = (cid:32) n n (cid:88) i =1 d LMSDM ( a i , b i ) (cid:33) ∈ [0 , (7) d LMSDM is the local MSDM distance between two mesh localwindows a and b (in mesh M and M w respectively) which isdefined by : d LMSDM ( a, b ) = (0 . × Curv ( a, b ) + 0 . × Cont ( a, b ) + 0 . × Surf ( a, b ) ) (8)Where Curv , Cont and
Surf are respectively curvature,contrast and structure comparison functions. Figure 2 shows the 3-D tested objects along with thecorresponding watermarked meshes. It can be observed fromthe same Figure that, for the same watermark capacity, thereare no perceptible distortions introduced by the watermarkembedding for all the three models. This observation is alsoconfirmed by the objective metrics. Thus, according to TableI, all the MSDM values are above . which illustrates thegood imperceptibility of the proposed method. Moreover, theMRMS values illustrate the better quality of the watermarkedmodels and the imperceptibility of the embedded watermark. Inorder to further evaluate the imperceptibility of our method, wecompare it with the scheme in [18]. The obtained results provethe high imperceptibility of the proposed technique comparedwith [17], [18] and [19]. Table II sketches the comparison ofimperceptibility in terms of MSDM for Horse. It can be seenthat the proposed method outperforms schemes in [17] and[19]. In addition, the obtained results depicted in Table IIIshow the superiority of the proposed technique compared with[17], [18] and [19]. C. Robustness
The robustness of the proposed method has been tested underdifferent types of attacks including similarity transformations,noise addition, Laplacian smoothing, quantization, and subdi-vision in terms of correlation coefficient between the extractedwatermark bit sting w m and the original embedded one.A benchmarking system is used to evaluate the proposedmethod [24]. In order to further evaluate the robustness againstseveral attacks, we compare our proposed method with theperformance of the methods in [17] and [19]. Corr ( X, Y ) = (cid:80) n ( X − X )( Y e − Y ) (cid:112) ( (cid:80) n ( X − X ) )( (cid:80) n ( Y e − Y ) (9)Where X and Y are the averages of the watermark bit sequenceof X and Y respectively, and n is the watermark size. Wenote that the proposed technique is specific for semi-regularmeshes. So we aren’t obliged to take into account those attacksthat alter connectivity of the mesh such as simplifications,re-meshing, etc. The watermark can be fully extracted fromunattacked 3-D meshes ( Corr = 1 . ) with the proposedtechnique for all the 3-D test models.The watermarked 3-D meshes are exposed to similaritytransformations. The obtained results, as depicted in TableVII, show that the proposed approach ensures high resistanceto similarity transformations including (translation, rotation,scaling and their combination). To further demonstrate therobustness of the proposed method, we compare it with thescheme in [19]. From table VIII, it can be seen that the pro-posed method show relatively good robustness against rotationattack and outperforms the scheme in [19]. Furthermore, therobustness against uniform scaling has been carried out. TableIX illustrates the robustness of the proposed technique usingseveral scaling factors in terms of correlation. The obtainedresults sketch the relatively good resistance to this attack. It canalso be observed that, compared with scheme IX the proposedapproach is more robust.Table X shows the robustness obtained in terms of correla-tion, MRMS, hausdorff distance and MSDM after carrying outthe addition noise using several amplitudes. It can be observedhat the proposed method has a good robustness against noiseaddition. It can be concluded from Table IV that our methodshow high robustness and slightly outperforms the method in[17].For the smoothing attack, the Laplacian smoothing methodproposed in [25] is used. Table XI shows the performance ofthe watermarking method after smoothing attacks using , , and iterations while fixing the deformation factor as . . From the above table, it can be seen that the proposedapproach shows high robustness against Laplacian smoothingfor the three test models. Moreover, it can be observed fromTable VI that the robustness of the proposed method slightlyoutperforms the scheme in [17].Our method is tested also under quantization attack using , , and bits. Table XII sketches the obtained resultsin terms of correlation, MRMS, HD, and MSDM. Accordingto these results, it is clear that the proposed method is robustagainst this attack regardless of the used 3-D mesh. Table Villustrates the superiority of our scheme compared with [17].In addition, the proposed technique is tested under subdi-vision attacks, especially for two typical subdivision schemes,with one iteration: the simple midpoint scheme and the Loopscheme [26]. As depicted in Table XIII, the obtained resultsin terms of correlation and MRMS are encouraging.To summarize, the proposed method shows good robust-ness against Laplacian smoothing, quantization and similaritytransformations, but it appears less robust under noise additionand subdivision attacks.TABLE IV: Robustness and quality comparison with schemein [17] against noise attack measured in terms of correlationand MRMS, HD and MSDM. Model Amplitude Corr MRMS HD MSDM( % ) ( − ) ( − )0.05 /0.85 /0.17 /0.62 /0.28Venus 0.25 /0.59 /0.84 /3.15 /0.700.50 /0.31 /1.67 /6.25 /0.830.05 /0.96 /0.11 /0.41 /0.23Horse 0.25 /0.50 /0.55 /2.03 /0.640.5 /0.08 /1.10 /4.07 /0.78 TABLE V: Robustness and quality comparison with schemein [17] against quantization measured in terms of correlationand MRMS, HD and MSDM.
Model Quantization Corr MRMS HD MSDM( − ) ( − )9-bit /0.93 /0.17 /0.62 /0.28Venus 8-bit /0.59 /0.84 /3.15 /0.707-bit /0.63 /1.67 /6.25 /0.839-bit /0.61 /0.11 /0.41 /0.23Horse 8-bit /0.50 /0.55 /2.03 /0.647-bit /0.08 /3.144 /4.07 /0.78 V. C
ONCLUSION AND FUTURE WORK
A blind robust 3-D semiregular meshes watermarkingtechnique for Copyright protection has been presented in thispaper. The Wavelet coefficient vector is used as watermark-ing primitive, whereas the norm of edge normal is used assynchronizing primitive. The experimental results show the TABLE VI: Robustness and quality comparison with schemein [17] against Laplacian smoothing ( γ = 0 . ) measured interms of correlation and MRMS, HD and MSDM. Model Iterations Corr MRMS HD ) MSDM( − ) ( − )10 /0.74 /0.27 /5.65 /0.15Venus 30 /0.71 /0.68 /9.75 /0.2750 /0.62 /1.01 /12.20 /0.3410 /0.95 /0.21 /5.67 /0.15Horse 30 /0.50 /0.54 /9.97 /0.2350 /0.35 /0.80 /12.95 /0.28 TABLE VII: Robustness evaluation of 3-D watermarked mod-els after similarity transformations and their combination interms of correlation
Model Translation Rotation Uniform scaling Trans+Rot+Scal( ◦ ) ( . )Venus 1.0 0.9875 0.9731 0.9831Horse 0.9975 0.9943 0.9581 0.9758Bunny 0.9981 0.9897 0.9873 0.9856 TABLE VIII: Robustness comparison against rotation in termsof correlation
Model Rotation angle Scheme in [19] Proposed method ◦ Bunny ◦ ◦ ◦ Horse ◦ ◦ TABLE IX: Robustness comparison against uniform scalingmeasured in terms of correlation
Model Uniform scaling Scheme in [19] Proposed method0.8 0.70
Bunny 1.1 0.83
Horse 1.1 0.72
TABLE X: Robustness and quality against noise additionmeasured in terms of correlation and MRMS, HD and MSDM.
Model Amplitude Corr MRMS HD MSDM( % ) ( − ) ( − )0.05 0.89 0.265 0.283 0.0114Venus 0.1 0.73 0.468 0.517 0.01060.3 0.63 1.50 1.785 0.01870.5 0.58 3.066 2.815 0.03380.05 0.8362 0.308 0.512 0.0796Horse 0.1 0.8452 0.424 0.433 0.07080.3 0.7526 1.214 1.296 0.07070.5 0.7606 2.129 2.188 0.07490.05 0.92 0.513 0.593 0.0773Bunny 0.1 0.8819 0.566 0.672 0.07790.3 0.8758 1.591 1.689 0.07920.5 0.71 2.615 2.708 0.0815 high imperceptibility of the proposed scheme. Furthermore, therobustness evaluation shows its good resistance against a widerang of attacks including, similarity transformations, additiveABLE XI: Robustness and quality against Laplacian smooth-ing ( γ = 0 . ) measured in terms of correlation and MRMS,HD and MSDM. Model Iteration Corr MRMS HD MSDM( % ) ( − ) ( − )5 0.9133 0.153 0.3741 0.19Venus 10 0.8360 0.264 5.632 0.2530 0.7841 0.675 7.75 0.1750 0.7321 0.978 10.38 0.235 0.7891 0.135 1.78 0.20Horse 10 0.7538 0.208 5.654 0.2430 0.6854 0.527 7.48 0.14950 0.6534 0.785 10.63 0.215 0.9341 0.135 1.984 0.12Bunny 10 0.8362 0.242 1.829 0.1430 0.7890 0.655 4.84 0.2250 0.6299 1.012 8.722 0.29 TABLE XII: Robustness and quality against quantization at-tack measured in terms of correlation and MRMS, HD andMSDM.
Model Quantization Corr MRMS HD MSDM( % ) ( − ) ( − )10-bits 0.92 0.549 0.57 0.1065Venus 9-bits 0.9103 0.927 1.255 0.10768-bits 0.7108 1.280 2.144 0.10697-bits 0.5854 2.357 4.322 0.116410-bits 0.9436 0.481 0.715 0.0731Horse 9-bits 0.8758 0.591 1.131 0.07138-bits 0.7526 1.310 1.899 0.07447-bits 0.7500 3.144 4.202 0.103810-bits 0.90 0.792 0.840 0.0118Bunny 9-bits 0.8362 0.980 1.146 0.01708-bits 0.8094 2.130 2.293 0.03657-bits 0.7139 3.874 4.289 0.0642 TABLE XIII: Robustness and quality against subdivision
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