3D CAD DRAWING WATERMARKING BASED ON THREE COMPONENTS

-R I~ ~ 1 2 SekMo, SkHaLe3Ki-Ryong Kwon, Hey-Jung Chang, Gwang S. Jung, Kwang-Seok Moon,' Suk-Hwan Lee

IDivisiornof Electronic, Computer and Telecommuication Engineering, Pukyong National Univ.Departmeyt ofMathematics and Computer Science, Lehman College/CUNY

Department ofInformation Security, TongMyong Univ.

ABSTRACT

This paper proposed a watermarking for copyright protection of3D CAD design drawing based on 3 basic components that areLine, ARC, and 3DFACE. The watermark is embedded into thelength in Line, the radius of curvature in Arc, and the lengthratio of two sides in 3DFACE. Selecting the embeddingcomponent can be done by the distribution of 3D drawing orpreference of owners. By experimental result, we confirmed theinvisibility ofembedded watermarks as well as the robustness invarious attacks.

Index Terms CAD, Copyright Protection, Watermarking

This paper proposed the watermarking for 3D CAD drawingbased on 3D vector data, which is a public watermarking usingLine, Arc, and 3DFACE components in 3D CAD drawing. Thewatermark is embedded into the length of Line component inthe embedding primitives, the circular radius ofArc component,and the length ratio of two sides in 3DFACE component. Thus,according to the distribution of three components in 3D CADdrawing, the embedding component can be determined. Theresults of experiment verify that the proposed algorithm isimperceptible and robust against file format conversion, move,scaling, rotation, component cropping, and layer cropping.

2. THE PROPOSED 3D CAD WATERMARKING

1. INTRODUCTION )FAC\

A lot of research has been carried out to protect the copyrightprotection of image, video, and audio [1],[2]. Recently, 3Dgraphic models, such as VRML, MPEG-4, and 3D geometricalCAD, have become very popular leading the development of3D watermarking algorithms to protect the copyright of 3Dgraphic models with the extending technique of the imagewatermarking. The watermarking for 3D polygonal model and2D Vector data has begun to be studied. Ohbuchi et al.presented the watermarking for 3D polygonal model throughgeometric and topological modification [3]. Mao et al.presented the watermarking for 3D geometric model throughthe triangle subdivision [4]. Beneden et al. also presented analgorithm that adds a watermark by modifying the normaldistribution of the model geometry [5].Many design drawings in the industrial filed have been

designed by 3D CAD tools. However, because of the unlawfulreproduction of the architectural drawings, the constructionindustry has been financially damaged. Many researches havenot been carried out to protect the copyright of 3D CADcompared with 3D polygonal model. Unlike 3D polygonalmodel, 3D CAD drawings can be designed by the basiccomponents; LINE, ARC, CIRCLE, and 3DFACE. 3DFACE issimilar as polygon of 3D polygon model. We presented 2DCAD watermarking that the watermark is embedded into theposition of vertex in two components, LINE and Arc [6]. Thisalgorithm needs to know the original vertices for watermarkextracting and to extend 2D data to 3D CAD data.

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Figure 1. The structure of3D CAD data.

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2.1.3D CAD drawingThe basic system of3D CAD drawings consists ofHEADER,

TABLE, BLOCK, ENTITY, EOF sections. The shape ofdrawings is designed with the basic component of Line, Arc,Circle, and 3DFACE based on vector data in ENTITY sectionas shown in Fig. 1. A Line component has the start point v1 andthe end point v2. An Arc component has two points v0,v1, a

circle center point C, a circle radius R, a standard point ofangle P, two angles °0,°1-. O is an angle between v0 and Pand oe is an angle between v1 and P. A Circle component has aradius R and a circle center point C. A 3DFACE has pointsthat can represent the 3D surface of3D CAD. The watermark in

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CAD drawings must be robust against the various attacks suchas file format conversion, geometrical attack, layer cutting andso on. There are many editing operators in wide use CAD tools.This paper considers only the above attacks.

2.2. Watermark EmbeddingThe proposed watermarking embeds the watermark into the

components of Line, Arc, and 3DFACE respectively. Thecomponent for watermark embedding is selected by thestructure of3D CAD drawings or user preference.

Vo4. it, = 0- /f

e I- ft i/ 1 1i - ',I X:i s wJ I Z .s~

limiting regions of v1, v2 which can be changed invisibly aredetermined respectively to be below the coordinate values ofthe connected points. Thus, the limiting region of v = (x, y, z)

is [v -Av,v+Av] , Av =0.5xminjvt Iv$ C(x),t x, } where

C(v) represents the points that are connected to v. Two pointsare changed to v V1I ±a, v' v2 ±a alternatively

within the limiting regions until satisfies the condition asfollows;

mm lk0Ellk OelkO<£, '02ke2 02k 02k < £

COS1 VI 'V2 'VIVl 1 V Ik *V2 V2 2=COS

1 V2 1 k ) 02k =COS1 2 2 2k

|| VI V2 HH1 VI Vlk 11 || VI *V2 ||| V2 V2k 11

(1)

(2)

V3VI

RegLiontI I i0 0 \Od=1

V4Figure 2. Embedding a watermark bit into an embeddingprimitive among Line components.

In 3D CAD file, Line node has a number of the enumeratedpair of two points, the start point and the end point. A pair oftwo points represents a Line component. A line may be or notconnected to another lines, as shown in Fig. 3. If one point in aline is changed according to the watermark, the lines connectedto one point will be changed together. The lines connected to anembedding line must be not the embedding target. Theproposed algorithm uses the connected lines as the referenceline for the watermark embedding. Thus, the embeddingprimitive ei = Ili,lij j = [0, Ni]} consists of an arbitrary line 4iand the lines li,j connected to ii, where Ni is the number ofthe connected lines. Firstly, the set E = lei = [O,N]} of theembedding primitives is gathered from starting to an arbitrarypoint. N is the number of the embedding primitives. Thewatermark with n < N bit length is embedded into nembedding primitives that are randomly selected among the setE. A i th watermark bit wi is embedded into the length 4i ofcenter line as follows;

If wi = 1, then 1i 21Ii.-iN.Otherwise, 4i < Ii. where, 4i = E=0,i,j I Ni .

Ii is an average length of the connected lines li j. To changethe length of line according to the watermark, the coordinate ofthe point must be changed imperceptibly considering theconnected lines. Fig. 3 shows an embedding primitive with acenter line 4i = {V1V2} and 3 connected lines li jc[13] VO iSconnected to v1 and V3, V4 are connected to v2 The

and vlk E C(v1), v2k E C(v2). The index of the embeddingprimitives is stored to extract the watermark.

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CmcviV14i a ( ±

ii\ ah,-S1 C + a

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(a) (b)Figure 3. (a) the watermark embedding in an Arc component(b) by moving the center point C.

An Arc component has two points v0, v1, a circle centerpoint C, a circle radius R, a standard point of angle P, twoangles 00,0 1 between points and P as shown in Fig. 3 (a). Thewatermark bit can be embedded into all elements{vO,v1,C,R,P,00,01} of an Arc component. The proposedalgorithm embeds the watermark bit into a circle radius Rusing {vo, vl, C} in the randomly selected Arc component. Thus,i th watermark bit wi is embedded into Ri of i th randomlyselected Arc component as follows; R'i=Ri+ (2wi-1)a . Afactor a is determined by the differential ratio of the curvatureAK.

Aic= ii i'i1= I I 1= (2w1 -1)aR1 R'I Ri(R +(2wi1 )a)

1(2wi -1)a < c Ri(Ri + (2wi - I)a) l,

(3)

If we consider a > O,R > a , a is 0 < a < eR2/(1I+ R)

Therefore, a is determined to half value R2/2(1 + ?R). Tochange a circle radius R , a circle center point C must bemoved forward or backward to m = (v0 + v1 ) / 2 as follows;

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t -V21 Ctitrol ct, xvithin

A-< j< A,7 & - J<A

I'j > 11 ,w = 1

P1 < li,w 0

V'2 = V2 + p

Figure 4. Embedding a watermark bit by using the ratio of twodistances in 4faces in 3DFACE component.

including the original intersection points v; and vj1±1 Thusy ...v

Sj=O-Ie Vi j- j+l j ) O-1( Vi+lVj+l *V jVj+i-O1 Cos 1 j1=o ('1 1j)vivj 1Vj+i Vj1H1 H1Vi+1Vj+ 1 VjVj+11

Furthermore, 0'j and 0'j1± are the angles of two vectorsincluding the changed points v'j and v'j+1I Thus

0ij = COS-1( aii).v1v' 1 jl1 ) Thea 1 viv'j1 fiP 1vi+lv'+l 11

second condition can be represented as follows;

C'= C + (2wi - )ca, n = Cm/ Cm I. (4)

n bit watermark is embedded into n 3FACE components thatare selected randomly among 3DFACEs over 4 faces(quadrilateral). To embed a watermark bit wi, the distance set

L = '11zr2, IN, } is obtained in a selected 3DFACE component

with Ni points. lic[4 Nil is the distance vivi+l between two

points vi,vi+l. An then, an arbitrary distance pair {l,ij~}Iij, Ij E L, i < j, Ii - Ij < A with no shared points is randomlyselected. Ii =1viv+1 and Ij =1vjvj+I can be used as thereference distance and the changeable distance. A watermark bitwi is embedded into the ratio li 11j of distance pair; li 11j >1 ifw =1 and lillj < 1, otherwise. To change the distance ratioaccording to the watermark bit, two points vj,vj+1 in thechangeable distance Ij must be changed to be parallel thereference distance li within the invisible range as shown in Fig.5.

If wi = 1, then v'j= vj +a,v'j+l= vj+l -.Otherwise, v'j = vj - c, v'j+l = v+l +1

where, c = aii,, 8fi, and ii = vjvj+l vjvj+1

Displacement vectors a, p are controlled by two conditions. Thefirst condition is to satisfy the distance ratio according to thewatermark as follows;

il' vj'V'j+l ij+a +,8>i, a+fl>l i- for wi =1 (5)

ij v' v'j+l Ij+±a l<Ii, a+/J<li -I for wi =0 (6)

The second condition is to satisfy the invisible ranges of twopoints vj , vj+1. The invisible ranges are determined by using

the angles of two lines as follows; 0j - Oj j< A and

I0±1 -0j+j j< A and 0j+j are the angles of two vectors

I v,v01 - A < cos- (n f(a)) < 01 + A, f(a) = ,

1viV'j1

02 -A <cos- (ii.f(f))<02 + A, f(fC8)vi+lV,'

(7)

(8)

2.3. Watermark ExtractingFrom each of components in the watermarked drawing, the

watermark can be extracted respectively by using the storedinformation in the embedding process. The information is theindex of the embedded Line component, circle radius of theembedded Arc components, the index of the embedded3DFACE component, and an average I of length of allembedded Line components. The extracting process is similaras the embedding process. In 3D drawing that is uniformlyscaled to an arbitrary factor, the re-scaling processing must beperformed by using l* before the watermark extracting. The re-

scaling process is to re-scale all components by dilating or

shrinking until 1 is 1. 1 is an average length of Linecomponents in the attacked drawing. It takes long time to re-

scale closely to original scale factor.

3. EXPERIMENTAL RESULTS

In our experiment, we evaluate the performance ofthe proposedalgorithm by using 3D CAD drawings, Campusl, Campus2,and Watch designed by AutoCAD and 3DS-MAX. There are a

lot of Line (1,130 Lines) in Campusl, Arc (1,770 Arcs) inWatch, and 3DFACE (551 faces) in Campus2. Thus we

embedded the binary watermark into Lines in Campus 1, Arcs inWatch, and 3DFACE in Campus2. The embedding primitiveswere randomly selected as 500 components among thesecomponents in each drawing. The 3D CAD drawings that are

watermarked by the proposed algorithm are shown in Fig. 6. Inthis figure, a subjective evaluation was used to verify that thewatermark was invisible.

In the robustness experiment, we attacked the watermarkeddrawings by using format conversion (DWS, DWG, DWT,DWS), RST (rotation, scaling, translation), layer cutting inAutoCAD and vertex deletion, twist, taper, and surface smoothin 3DS-MAX tools. The results are shown in table 2 thatrepresents BER of the extracted watermark in attackeddrawings. As shown in table 2, the watermark in any file format

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and RST geometrical attacks can be extracted without bit error.The proposed watermarking doesn't be influenced by

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(a) (b)

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cs(c) (d)

Figure 5. (a) Watch, (b) Campus2, (c) watermarked Watch, and(d) watermarked Campus2 drawings.

This work was supported by the Korea Research FoundationGrant funded by the Korean Government (MOEHRD)" (KRF-2005-042-D00225) and Technology Information (KISTI) andby the Program for the Training of Graduate Students inRegional Innovation which was conducted by the Ministry ofCommerce Industry and Energy ofthe Korean Government.

Table 2. BER ofthe extracted watermark.est drawin Campusl Watch Campus2

Format conversion | |RST - - -

Vertex deletion 0.11 0.10 0.18Layer cutting 0.24 0.14 0.25

Vertex deletion + RST 0.15 0.12 0.20Twist 0.05 0.07 0.07Taper 0.06 0.07 0.09

Surface smooth 0.02 0.03 0.05

file conversion with data lossless and rotation and translationsince the proposed algorithm embeds the watermark into thelength in Line, the radius of curvature in Arc, and the lengthratio of two sides in 3DFACE. But in scaling, the rescalingprocess has to be taken long time. In vertex deletion, we removerandomly 30% of vertices in drawings. BER of the extractedwatermark is about 0.10-0.18O% according to the percentage ofdeletion. Furthermore, we cut an arbitrary layer in thewatermarked drawings. In this case, the bit error occurred about0.14-0.25 that effects on the number of the embeddingcomponents in a layer. We tapered the watermarked drawingsbased on z primary axis with 1.0 amount and twisted based on zaxis with 10 angle. BER of the extracted watermark is about0.05-0.09. And we made the watermarked drawings to besmoothed by using turbo smooth in 3DS-MAX. In this case, thewatermark can be extracted with 0.02-0.05 BER. The aboveresults verified that the watermark still alive above 75% in anyattacks.

4. CONCLUSIONS

This paper presented a watermarking for 3D CAD drawingsusing Line, Arc, and 3DFACE components. The embeddingcomponents can be selected randomly or by the componentdistribution in drawing. The watermark is embedded into thelength in Line component, the radius of curvature in Arc, andthe length ratio of two sides in 3DFACE. Experimental resultsverified that the proposed watermarking has the robustnessagainst Format conversion, layer cutting and geometricalattacks. 3D CAD watermarking will be very importanttechnique in industrial field that manage architectural drawingswith great care.

(a) (b)Figure 6. (a) Watermarked Watch with rotation and vertexdeletion (30%) and (b) watermarked Campus with 3 layercutting.

6. REFERENCES

[1] I.J.Cox, J.Kilian, T.Leighton, and T.Shamoon, "Secure SpreadSpectrum Watermarking for Multimedia," NEC Research InstituteTech Rep. 95-10, 1995.

[2] C. Podilchuk and W.Zeng., "Image Adaptive Watermarking UsingVisual Models," IEEE Journal on Selected Areas inCommunication, Vol. 16, No.4. pp. 525-539,1998.

[3] R. Ohbuchi, H. Masuda, and M. Aono, "Watermarking Three-Dimensional Polygonal Models Through Geometric andTopological Modification," IEEE JSAC, pp. 551-560, 1998.

[4] X. Mao, M. Shiba, and A. Imamiya, Watermarking 3DGeometric Models Through Triangle Subdivision," Proc. ofSecurity and Watermarking of Multimedia Contents III,IS&TISPIES'sElectronicImaging, pp.253-260, Jan.2001.

[5] 0. Benedens, "Geometry-Based Watermarking of 3D Models,"IEEE CG&A, pp. 46-55, Jan. /Feb. 1999.

[6] Bong-Ju Jang, Ki-Ryong Kwon, Kwang-Seok Moon, and YoungHuh, "A New Digital Watermarking for Architectural DesignDrawing Using LINEs and ARCs Based on Vertex," IWDW2003,pp. 565-579, Oct. 2003.

5. ACKNOLWEDGEMENT

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