A public fragile watermarking scheme for 3D model authentication

A public fragile watermarking scheme for 3D model authentication

Chang-Min Chou, Din-Chang Tseng Computer-Aided Design

Vol. 38 (Nov. 2006) 1154–1165

Reporter: T. Y. Chen11 JUNE 2007

2

Information Hiding – Simple Classification for 3D Models

Information hiding

Steganography Watermarking

Spatial domain

Transform domain

Spatial domain

Transform domain

Robustwatermarking

Fragilewatermarking

Cayr2003aChen2006Tsai2006Wang2005aWang2005bWang2006WangP2006aWangP2006bWu2005b

Aspe2002aMare2004

Asho2004Bene1999aBene1999bBene1999cBors2006Kali2003

Cayr2003bCott2004Jin2004Kana1998Kim2000Ohbu2004

Bene2000Cayr2004Forn2000Lee2004Lin2005Wu2005a

Spatial domain

Transform domain

Yeo1999

Lin 2005Chou 2006

3

OutlineOutline• Introduction• The Proposed Scheme

– The watermark embedding scheme• The multi-function embedding method• The adjusting-vertex method

– The watermark extraction scheme and tamper detection

• Distortion Control• Experimental Results• Conclusions

4

Introduction~3D triangle meshesIntroduction~3D triangle meshes (1/4) Example : Sphere1

5

Introduction~3D triangle meshesIntroduction~3D triangle meshes (2/4) Sphere1.WRL

• #VRML V2.0 utf8

• # Produced by 3D Studio MAX VRML97 exporter, Version 8, Revision 0.92• # MAX File: sphere1.max, Date: Thu Dec 14 18:43:31 2006

• DEF Sphere01 Transform {• translation -0.3831 0 -1.533• children [• Shape {• appearance Appearance {• material Material {• diffuseColor 0.6 0.8941 0.6• }• }• geometry DEF Sphere01-FACES IndexedFaceSet {• ccw TRUE• solid TRUE• coord DEF Sphere01-COORD Coordinate { point [• 0 27.08 0, 0 23.45 -13.54, -6.77 23.45 -11.73, -11.73 23.45 -6.77, • -13.54 23.45 0, -11.73 23.45 6.77, -6.77 23.45 11.73, • 0 23.45 13.54, 6.77 23.45 11.73, 11.73 23.45 6.77, • 13.54 23.45 0, 11.73 23.45 -6.77, 6.77 23.45 -11.73, • 0 13.54 -23.45, -11.73 13.54 -20.31, -20.31 13.54 -11.73, • -23.45 13.54 0, -20.31 13.54 11.73, -11.73 13.54 20.31,

6

Introduction~3D triangle meshesIntroduction~3D triangle meshes (3/4) Sphere1.WRL

• 0 13.54 23.45, 11.73 13.54 20.31, 20.31 13.54 11.73, • 23.45 13.54 0, 20.31 13.54 -11.73, 11.73 13.54 -20.31, • 0 0 -27.08, -13.54 0 -23.45, -23.45 0 -13.54, -27.08 0 0, • -23.45 0 13.54, -13.54 0 23.45, 0 0 27.08, 13.54 0 23.45, • 23.45 0 13.54, 27.08 0 0, 23.45 0 -13.54, 13.54 0 -23.45, • 0 -13.54 -23.45, -11.73 -13.54 -20.31, -20.31 -13.54 -11.73, • -23.45 -13.54 0, -20.31 -13.54 11.73, -11.73 -13.54 20.31, • 0 -13.54 23.45, 11.73 -13.54 20.31, 20.31 -13.54 11.73, • 23.45 -13.54 0, 20.31 -13.54 -11.73, 11.73 -13.54 -20.31, • 0 -23.45 -13.54, -6.77 -23.45 -11.73, -11.73 -23.45 -6.77, • -13.54 -23.45 0, -11.73 -23.45 6.77, -6.77 -23.45 11.73, • 0 -23.45 13.54, 6.77 -23.45 11.73, 11.73 -23.45 6.77, • 13.54 -23.45 0, 11.73 -23.45 -6.77, 6.77 -23.45 -11.73, • 0 -27.08 0]• }• coordIndex [• 0, 1, 2, -1, 0, 2, 3, -1, 0, 3, 4, -1, 0, 4, 5, -1, 0, 5, 6, -1, • 0, 6, 7, -1, 0, 7, 8, -1, 0, 8, 9, -1, 0, 9, 10, -1, • 0, 10, 11, -1, 0, 11, 12, -1, 0, 12, 1, -1, 1, 13, 14, -1, • 1, 14, 2, -1, 2, 14, 15, -1, 2, 15, 3, -1, 3, 15, 16, -1, • 3, 16, 4, -1, 4, 16, 17, -1, 4, 17, 5, -1, 5, 17, 18, -1, • 5, 18, 6, -1, 6, 18, 19, -1, 6, 19, 7, -1, 7, 19, 20, -1, • 7, 20, 8, -1, 8, 20, 21, -1, 8, 21, 9, -1, 9, 21, 22, -1,

7

Introduction~3D triangle meshesIntroduction~3D triangle meshes (4/4) Sphere1.WRL

• 9, 22, 10, -1, 10, 22, 23, -1, 10, 23, 11, -1, 11, 23, 24, -1, • 11, 24, 12, -1, 12, 24, 13, -1, 12, 13, 1, -1, 13, 25, 26, -1, • 13, 26, 14, -1, 14, 26, 27, -1, 14, 27, 15, -1, 15, 27, 28, -1, • 15, 28, 16, -1, 16, 28, 29, -1, 16, 29, 17, -1, 17, 29, 30, -1, • 17, 30, 18, -1, 18, 30, 31, -1, 18, 31, 19, -1, 19, 31, 32, -1, • 19, 32, 20, -1, 20, 32, 33, -1, 20, 33, 21, -1, 21, 33, 34, -1, • 21, 34, 22, -1, 22, 34, 35, -1, 22, 35, 23, -1, 23, 35, 36, -1, • 23, 36, 24, -1, 24, 36, 25, -1, 24, 25, 13, -1, 25, 37, 38, -1, • 25, 38, 26, -1, 26, 38, 39, -1, 26, 39, 27, -1, 27, 39, 40, -1, • 27, 40, 28, -1, 28, 40, 41, -1, 28, 41, 29, -1, 29, 41, 42, -1, • 29, 42, 30, -1, 30, 42, 43, -1, 30, 43, 31, -1, 31, 43, 44, -1, • 31, 44, 32, -1, 32, 44, 45, -1, 32, 45, 33, -1, 33, 45, 46, -1, • 33, 46, 34, -1, 34, 46, 47, -1, 34, 47, 35, -1, 35, 47, 48, -1, • 35, 48, 36, -1, 36, 48, 37, -1, 36, 37, 25, -1, 37, 49, 50, -1, • 37, 50, 38, -1, 38, 50, 51, -1, 38, 51, 39, -1, 39, 51, 52, -1, • 39, 52, 40, -1, 40, 52, 53, -1, 40, 53, 41, -1, 41, 53, 54, -1, • 41, 54, 42, -1, 42, 54, 55, -1, 42, 55, 43, -1, 43, 55, 56, -1, • 43, 56, 44, -1, 44, 56, 57, -1, 44, 57, 45, -1, 45, 57, 58, -1, • 45, 58, 46, -1, 46, 58, 59, -1, 46, 59, 47, -1, 47, 59, 60, -1, • 47, 60, 48, -1, 48, 60, 49, -1, 48, 49, 37, -1, 61, 50, 49, -1, • 61, 51, 50, -1, 61, 52, 51, -1, 61, 53, 52, -1, 61, 54, 53, -1, • 61, 55, 54, -1, 61, 56, 55, -1, 61, 57, 56, -1, 61, 58, 57, -1, • 61, 59, 58, -1, 61, 60, 59, -1, 61, 49, 60, -1]• }• }• ]• }

8

Introduction~ wmk. Introduction~ wmk. categorycategory• The application purpose

– Robust watermarking • To achieve intellectual property protection of digital contents.• To make the embedded watermarks remain detectable after being

attacked.

– Fragile watermarking• To authenticate the integrity of digital contents.• To detect the unauthorized modifications and locate the changed regions.

• The extraction strategies– Private (blind): Need the original model and watermark. – Public: In the absence of the original model and watermark.– Semi-public: Does not need the original model, but the original

watermark is necessary.

• The embedding strategies– Geometry: To modifying the vertex coordinates.– Topology: To modifying the vertex connectivity.

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• The causality problem– Arises when the neighboring relationship of a former

processed vertex is influenced by the perturbing of its later processed neighboring vertices.

• The convergence problem– The original model has been heavily distorted before

some vertices reach the predefined relationship.

IntroductionIntroduction (2/2)(2/2)

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The Proposed SchemeThe Proposed Scheme

• The watermark embedding scheme• The multi-function embedding method• The adjusting-vertex method

• The watermark extraction scheme and tamper detection

Watermarked mesh M ’

Watermark embedding Watermark extraction

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The Proposed Scheme (embedding)The Proposed Scheme (embedding)

• A mesh M(V,C)– V is the vertex set, a vertex v(x1,x2,x3)v’(x1’,x2’,x3’)

– C is the connectivity relationship

• A watermark W=(w1,w2, … ,wn)

• Keys: kw, kjq, kj

d, h( ), j =2,3

13

The Proposed Scheme (embedding)The Proposed Scheme (embedding)

• A vertex v(x1,x2,x3)v’(x1’,x2’,x3’)

– x1 is used to indicate if v is a mark vertex

– x2 is used for embedding watermark wi

– x3 is used for embedding h(wi)

• If v is a mark vertex, x1/ kw must be odd; otherwise x1’ = x1 + kw

• If v is a non-mark vertex, x1/ kw must be even; otherwise x1’ = x1 + kw

1

1'1

1

mod 2 ,

, ( 1 ) ( 0 )

,

w

x

k

w

m and

x if m and v is a mark vertex orx m and v is not a mark vertex

x k otherwise

14

The Proposed Scheme (embedding)The Proposed Scheme (embedding)For a mark vertex v(x1,x2,x3), • Calculate the barycenters x2

c and x3c

xjc (the barycenter of xj): the centroid of xj’s neighbors

1| ( )|

( )

, 2,3cj jN v

N v

x x j • xj is moved toward xj

c to xje, s.t. | xj

c - xje | is divisible by kj

q

- (| - | mod ),

(| - | mod ),

c q cj j j j j je

j c qj j j j

x x x k if x xx

x x x k otherwise

Xjq

dj

Xje

XjqXj

qXj

c Xj

Xj’

kjq kj

q kjq

15

The Proposed Scheme (embedding)The Proposed Scheme (embedding)

• Move xje to xj

’ for embedding wi and hi(=h(wi))

Xjq

dj

Xje

XjqXj

qXj

c Xj

Xj’

',

, 2,3- ,

j

j

e cj j j

j ej

x d if x xx j

x d otherwise

2 3

32

2

2 23 3 3

3

2

2

3

, , ( ) , ,

, ,

0

0 , , , , ) (

d d

qqd

i ik

kki i

d qi

ik

d d qi i

w w k

w

h

h k h k d k

d dwhere h h w

k N d k

kjq kj

q kjq

16

The Proposed Scheme The Proposed Scheme (The causality problem ～ The “adjusting vertex” method

))• The barycenters (x2 and x3) of a former processed vert

ex will be changed when any of its neighboring vertices was selected to be a mark vertex too and need to be perturbed.

• For each chosen mark vertex, we randomly assign an adjusting vertex from its neighboring vertices.

• The function of the adjusting vertex is to keep the barycenters of the mark vertex unchanged.

• To avoid the causality problem, the neighboring vertices of the previously selected mark vertices can’t be taken as adjusting vertices for later mark vertices.

Watermarked mesh M ’

Watermark embedding Watermark extraction

19

The Proposed Scheme (extraction)The Proposed Scheme (extraction)

• For each vertex, check its x1 to see if it is a mark vertex

• For each mark vertex,

– Extract w’ from x2

– Extract h’ from x3

– If h(w’) ≠h’, set the vertex and all its neighbors as suspicious vertices

• Report all the suspicious vertex

2

2

3

3

'2 2 2

'3 3 3

' (| - | mod )

' (| - | mod )

d

q

d

q

kc q

k

kc q

k

w x x k

h x x k

Detect and locate the modificationDetect and locate the modification

Distortion controlDistortion control1

1'1

1

mod 2 ,

, ( 1 ) ( 0 )

,

w

x

k

w

m and

x if m and v is a mark vertex orx m and v is not a mark vertex

x otherwk ise

Xjq

dj

Xje

XjqXj

qXj

c Xj

Xj’

',

, 2,3- ,

j

j

e cj j j

j ej

x d if x xx j

x d otherwise

32

2 3

2 3

2 3 2

3

, , ( ) , ,

, , ,,

0

0 ) ( ,

qq

d d

kki i i ik k

d d

di

di i i

qj j

w kwhere w h

w h k k Nh k

h wd

k

hd

d

- (| - | mod ),

(| - | mod ),

c q cj j j j j je

j c qj j j j

x x x k if x xx

x x x k otherwise

kjq kj

q kjq

22

Distortion controlDistortion control

The smaller the values of kw and kqs are, the smaller the distortion is.

d<10-3

Kw=10-3

Kq=10-3.5

(vs. PSNR)

23

The watermark digest method (invariant)

WD:

• wm: the indices of the mark vertices

• wp: the required perturbing displacements

24

Experimental ResultsExperimental Results

25

ConclusionsConclusions1. The traverse order is not needed in the watermark

extraction stage. 2. The adjusting vertex method can effectively limit the

distortion ratio caused by watermark embedding. 3. Different functions are defined for the three coordinates

of vertices.4. The average distortion of the marked models is under

user control.5. The proposed scheme can detect and locate all

unauthorized modifications.6. The proposed scheme is public and a relative small key

is needed for the watermark extraction.7. The watermark digest method is proposed.

26

• 1999, IEEE Computer Graphics and Applications, Watermarking 3D Objects for Verification, Boon-Lock Yeo and Minerva M. Yeung

• 2004, LNCS 2939, Authentication of 3-D Polygonal Meshes, Hsueh-Yi Lin, Hong-Yuan Mark Liao, Chun-Shien Lu and Ja-Chen Lin

• 2005, IEEE TRANSACTIONS ON MULTIMEDIA, Fragile Watermarking for Authenticating 3-D Polygonal Meshes, Hsueh-Yi Sean Lin, Hong-Yuan Mark Liao, Chun-Shien Lu, and Ja-Chen Lin

• 2005, International Multimedia Conference Proceedings of the 7th workshop on Multimedia and security, A fragile watermarking scheme for 3D meshes, Hao-Tian Wu , Yiu-Ming Cheung  

• 2006, Computer-Aided Design, A public fragile watermarking scheme for 3D model authentication, Chang-Min Chou, Din-Chang Tseng

• 2007, IJCSNS, Technologies for 3D Model Watermarking: A Survey, Chang-Min Chou and Din-Chang Tseng

27

Information Hiding – Simple Classification for 3D Models

Information hiding

Steganography Watermarking

Spatial domain

Transform domain

Spatial domain

Transform domain

Robustwatermarking

Fragilewatermarking

Cayr2003aChen2006Tsai2006Wang2005aWang2005bWang2006WangP2006aWangP2006bWu2005b

Aspe2002aMare2004

Asho2004Bene1999aBene1999bBene1999cBors2006Kali2003

Cayr2003bCott2004Jin2004Kana1998Kim2000Ohbu2004

Bene2000Cayr2004Forn2000Lee2004Lin2005Wu2005a

Spatial domain

Transform domain

Yeo1999

Lin 2005Chou 2006

Transform domain?

28

• The scheme is not suitable for those models with flat surfaces. Those models cannot tolerate a small distortion. – Improve it or the phenomenon cannot be avoided. (compare with

other schemes) – Perhaps, it raised by few adjusting vertices. Average them to all

vertices not qualified as mark vertices.• Combine some proposed schemes (proposed in this pap

er and that was reported last time) to develop an invertible fragile watermarking scheme.

• To develop a Semi-fragile watermarking scheme which is immune to affine transformation.

• …• Read some outstanding 2d wmk schemes, usage, constr

ains• Read more robust, transform domain, hiding schemes