Watermarking MPEG-4 2D Mesh Animation in the Transform

Domain

報告：梁晉坤報告：梁晉坤指導教授：楊士萱指導教授：楊士萱

2003/12/42003/12/4

Outline

MPEG-4 2D Mesh AnimationMPEG-4 2D Mesh Animation Digital WatermarkingDigital Watermarking Wavelet TransformWavelet Transform Discrete Cosine TransformDiscrete Cosine Transform Singular Value DecompositionSingular Value Decomposition Simulate ResultsSimulate Results ConclusionConclusion

MPEG-4 2D Mesh Animation

MPEG-4 synthetic visual coding allows 2D-MPEG-4 synthetic visual coding allows 2D-Mesh and 3D-Mesh represent generic Mesh and 3D-Mesh represent generic objects. objects.

MPEG-4 2D Mesh animation consists of a MPEG-4 2D Mesh animation consists of a sequence of polygon models, little sequence of polygon models, little watermarking techniques are proposed for watermarking techniques are proposed for it.it.

Mesh Object Plane, MOPMesh Object Plane, MOP

Mesh Object Plane

A Sequence of MOPs

Mesh Types

Uniform Mesh Delaunay Mesh

Digital Watermarking

It is the process of embedding extra data, It is the process of embedding extra data, the watermarking signal, to the digital data.the watermarking signal, to the digital data.

Watermark speciesWatermark species visible and invisiblevisible and invisible robust and fragilerobust and fragile public and privatepublic and private spatial and transform domainspatial and transform domain

ApplicationsApplications copyright protection, fingerprinting, copy copyright protection, fingerprinting, copy

control, data authentication, broadcast control, data authentication, broadcast monitoringmonitoring

Basic propertiesBasic properties transparency, robustness, securitytransparency, robustness, security

Modify on the Spatial Domain

Original Data

Watermark

WatermarkedData

Original Data Transform to the

Transform Domain

Modify on the Transform Domain

WatermarkInverse

Transformto the Spatial

Domain

WatermarkedData

FFT, DCT, Wavelet Transform, SVD, etc.

Wavelet Transform

Realizing discrete wavelet transform by Realizing discrete wavelet transform by “Filter Bank”“Filter Bank”

h0(t)

h1(t)

2

2y1

y0

X2

2

g0(t)

g1(t)

X’

Analysis Filter Synthesis Filter

Multi-resolution Representation

Original

L1 H1

L2 H2

……

Lp Hp

Embedding Procedure

Decomposing 2D mesh animation by multi-Decomposing 2D mesh animation by multi-resolution wavelet transformresolution wavelet transform p level decomposition generate (p+1) p level decomposition generate (p+1)

subbands, L-p, H-p, H-(p-1), … , H-1subbands, L-p, H-p, H-(p-1), … , H-1 Computing Euclid distance for L-p subbbandComputing Euclid distance for L-p subbband Choosing k largest coarse coefficients for Choosing k largest coarse coefficients for

watermarking in L-p subbandwatermarking in L-p subband

Embedding Procedure(Cont.)

Embedding component selection Embedding component selection Select larger component(X or Y)Select larger component(X or Y) The same, select X componentThe same, select X component

Perturbing selected component according to Perturbing selected component according to watermark Bitswatermark Bits Bit=1, add a positive value(Intensity)Bit=1, add a positive value(Intensity) Bit=0, sub a negative value(Intensity)Bit=0, sub a negative value(Intensity)

H-p,H-(p-1),…,H-1

Wavelet Decomposition

Compute EuclidDistance

L-p

SelectEmbedding Location

WatermarkEmbedding

I

-I

InverseWavelet Decomposition

Watermarked 2D MeshAnimation

Original 2D Mesh Animation

Extraction Procedure

Decomposing original and attacked 2D mesh Decomposing original and attacked 2D mesh animation by multi-resolution wavelet transformanimation by multi-resolution wavelet transform p level decomposition generate (p+1) p level decomposition generate (p+1)

subbands, L-p, H-p, H-(p-1), … , H-1subbands, L-p, H-p, H-(p-1), … , H-1 Computing Euclid distance from original mesh L-Computing Euclid distance from original mesh L-

p subbbandp subbband Find out suspected coarse vectorsFind out suspected coarse vectors Finally, watermark is extracted from these coarse Finally, watermark is extracted from these coarse

vectorsvectors

Original 2D Mesh Animation

Watermarked 2D MeshAnimation

Wavelet DecompositionWavelet Decomposition

L-p WatermarkExtraction

L’-p

Extracted Watermark

WV’: attacked coarse vectorsWV’: attacked coarse vectors WV: original coarse vectorsWV: original coarse vectors

If(WV’i> WVi)then wi=1

If(WV’i< WVi)then wi=0

Discrete Cosine Transform

X ={XX ={X00,X,X11,…,X,…,XN-1N-1} of length N= 2} of length N= 2pp

Y ={YY ={Y00,Y,Y11,…,Y,…,YN-1N-1}, Y is the transformed }, Y is the transformed

sequence of X, sequence of X,

DCTDCT

IDCTIDCT

1,...,1,0

)*2/(*)12(*)(*/21

0

Nn

NnkCOSXneNYN

kkn

1,...,1,0

)*2/(*)12(**)(1

0

Nk

NnkCOSYneXN

nnk

otherwise

nifne

,1

)0(,2/1)(

Embedding Procedure

Dividing 2D Mesh to a lot of point Dividing 2D Mesh to a lot of point sequences(each sequence include X,Y sequences(each sequence include X,Y component, and its length N=2component, and its length N=2pp))

Doing DCT to each point sequences, select Doing DCT to each point sequences, select a maximum absolute value from X,Y a maximum absolute value from X,Y component(DC value), and push to DCTVcomponent(DC value), and push to DCTV

Choosing k largest DC values from DCTV Choosing k largest DC values from DCTV for watermarking embeddingfor watermarking embedding

SelectEmbedding Location

WatermarkEmbedding

I

-IWatermarked 2D MeshAnimation

Original 2D

Mesh Animation

P seq.1.

P seq.2.

P seq.n.

DCT Push toDCTV

P’ seq.1.

P’ seq.2.

P’ seq.n.

IDCT

Extraction Procedure

Dividing original mesh and attacked mesh Dividing original mesh and attacked mesh to a lot of point sequencesto a lot of point sequences

Doing DCT to each point sequences, find Doing DCT to each point sequences, find out suspected DC values from original out suspected DC values from original mesh point sequencesmesh point sequences

Watermarking is extracted from the DC Watermarking is extracted from the DC valuesvalues

DCT

DCTV

Original 2D Mesh Animation

Watermarked 2D MeshAnimation

WatermarkExtraction

DCTV’

Extracted Watermark

P seq.1.

P seq.2.

P seq.n.

P’ seq.1.

P’ seq.2.

P’ seq.n.

DCT

WDC’ value: attacked DC valueWDC’ value: attacked DC value WDC value: original DC valueWDC value: original DC value

If(WDC’i> WDCi)then wi=1

If(WDC’i< WDCi)then wi=0

Singular Value Decomposition

X:mxn, U:mX:mxn, U:mn, S:n n, S:n n, V:n n, V:n n (Matrices)n (Matrices) X=U X=U S S V VT T where U,V are unitary where U,V are unitary

matrices(UUmatrices(UUTT=U=UTTU=I), S is a Singular U=I), S is a Singular matrixmatrix

The d singular values on the diagonal of S The d singular values on the diagonal of S are the square roots of the nonzero are the square roots of the nonzero eigenvalues of both AAeigenvalues of both AAT T andand AATTAA

The main property of SVD is the singular The main property of SVD is the singular values(SVs) of an Matrix(or image) have values(SVs) of an Matrix(or image) have very good stability, that is, when a small very good stability, that is, when a small perturbation is added to an Matrix, its SVs perturbation is added to an Matrix, its SVs do not change significantly.do not change significantly.

seqLLLLseqLLseq

LseqseqLseqL

seqLseqseq

A

2)1(1)1(

221

21

SVD Window Length= L needs 2L-1 point sequences

Embedding Procedure Embedding Procedure AAU U S S V VT T

Sw=S+aW ,where WSw=S+aW ,where W{0,1}{0,1} AwAwU U Sw Sw V VTT

Extraction ProcedureExtraction Procedure Compute U, V and S as aboveCompute U, V and S as above AaAaU U Sa Sa V VTT

D=UD=UTT Aa Aa V V Sa, Sa Sa, Sa SwSw W=(D-S)/a W=(D-S)/a

SelectEmbedding Location

WatermarkEmbedding

I

-IWatermarked 2D MeshAnimation

Original 2D

Mesh Animation

Do_Matrix SVDPush toSVDV

Do_IMatrix ISVD

SVD=> A=U*S*Vt

Original 2D Mesh Animation

Watermarked 2D MeshAnimation

WatermarkExtraction

D

Extracted Watermark

do Matrix=A

D=Ut*B*V Sa, Sa Sa, Sa SwSw

do Matrix=B

AssumeB=U*Sa*Vt

S

Simulate Results Compute for robustnessCompute for robustness

BER, bit error rateBER, bit error rate

Compute for transparencyCompute for transparency MMSE , motion mean square errorMMSE , motion mean square error

lengthwatermark

bitserrorofnumberBER

1

1 1

2,,

2,, ])()[(

)1(

1 M

i

N

jjijijiji ymmyxmmx

NMMMSE

AttacksAttacks Random noiseRandom noise AffineAffine SmoothingSmoothing Enhancement and Attenuation Enhancement and Attenuation Time warpingTime warping SimplifyingSimplifying

Transform methodsTransform methods SVDSVD DCTDCT D_4D_4 D_8D_8 Lift5_3Lift5_3 Conv9_7Conv9_7 Lazy Lazy HaarHaar

Test1 Mesh12

Mesh12Mesh12 128 MOPs, each MOP has 120 points and 128 MOPs, each MOP has 120 points and

187 triangles187 triangles Watermark, 127 bits PN codeWatermark, 127 bits PN code Quality=0.005 (MMSE)Quality=0.005 (MMSE) Simplifying and Scale Coefficient using Simplifying and Scale Coefficient using

Conv97 at LV =4Conv97 at LV =4

TypeType BERBER

P=2P=2 P=4P=4 P=6P=6

D_4D_4 00 00 00

D_8D_8 00 00 00

Lift5_3Lift5_3 00 00 00

Conv9_7Conv9_7 00 00 00

LazyLazy 0.3307090.330709 0.3149610.314961 0.1338580.133858

HaarHaar 00 00 00

DCTDCT 00

SVDSVD 00

Smoothing Attack({1/4,1/2,1/4})

Affine Attack-1( 1.3,0,(12,0) )TypeType BERBER

P=2P=2 P=4P=4 P=6P=6

D_4D_4 00 00 00

D_8D_8 00 00 00

Lift5_3Lift5_3 00 00 00

Conv9_7Conv9_7 00 00 00

LazyLazy 00 00 00

HaarHaar 00 00 00

DCTDCT 0.007874020.00787402

SVDSVD 00

Affine Attack-2( 1,25,(0,5) )TypeType BERBER

P=2P=2 P=4P=4 P=6P=6

D_4D_4 00 00 00

D_8D_8 00 00 00

Lift5_3Lift5_3 00 00 00

Conv9_7Conv9_7 00 00 00

LazyLazy 0.1653540.165354 0.1023620.102362 0.07086610.0708661

HaarHaar 00 00 00

DCTDCT 00

SVDSVD 00

Affine Attack-3( 0.7,65,(-11,-9) )TypeType BERBER

P=2P=2 P=4P=4 P=6P=6

D_4D_4 0.2125980.212598 0.1889760.188976 0.05511810.0551181

D_8D_8 0.2992130.299213 0.0236220.023622 0.007874020.00787402

Lift5_3Lift5_3 0.06299210.0629921 00 00

Conv9_7Conv9_7 0.1417320.141732 0.04724410.0472441 00

LazyLazy 0.4094490.409449 0.3464570.346457 0.2204720.220472

HaarHaar 0.3858270.385827 0.2677170.267717 0.007874020.00787402

DCTDCT 0.2677170.267717

SVDSVD 0.1732280.173228

SCAttack, all good Time warping Attack,all good

RN Attack-10%TYPETYPE BERBER

P=2P=2 P=4P=4 P=6P=6

N=1N=1 N=2N=2 N=1N=1 N=2N=2 N=1N=1 N=2N=2

D_4D_4 00 0.0708660.070866 00 00 00 00

D_8D_8 00 0.0393700.039370 00 00 00 00

Lift5_3Lift5_3 00 0.0157480.015748 00 00 00 00

Conv9_7Conv9_7 00 0.0157480.015748 00 00 00 00

LazyLazy 0.03149610.0314961 0.0472440.047244 0.03149610.0314961 0.0472440.047244 0.0629920.062992 0.0236220.023622

HaarHaar 00 0.0787400.078740 00 00 00 00

DCTDCT 00 0.0236220.023622

SVDSVD 00 0.007874020.00787402

RN Attack-20%TYPETYPE BERBER

P=2P=2 P=4P=4 P=6P=6

N=1N=1 N=2N=2 N=1N=1 N=2N=2 N=1N=1 N=2N=2

D_4D_4 00 0.0629920.062992 00 0.0236220.023622 00 00

D_8D_8 00 0.0629920.062992 00 0.007874020.00787402 00 00

Lift5_3Lift5_3 00 0.00787400.0078740 00 00 00 00

Conv9_7Conv9_7 0.0078740.007874 0.0157480.015748 00 00 00 00

LazyLazy 0.07086610.0708661 0.06299210.0629921 0.06299210.0629921 0.05511810.0551181 0.07874020.0787402 0.07086610.0708661

HaarHaar 0.04724410.0472441 0.03937010.0393701 00 0.03937010.0393701 00 00

DCTDCT 00 00

SVDSVD 00 0.0157480.015748

RN Attack-30%TYPETYPE BERBER

P=2P=2 P=4P=4 P=6P=6

N=1N=1 N=2N=2 N=1N=1 N=2N=2 N=1N=1 N=2N=2

D_4D_4 0.03937010.0393701 0.1259840.125984 00 00 00 00

D_8D_8 0.03937010.0393701 0.0629920.062992 00 00 00 00

Lift5_3Lift5_3 0.00787400.0078740 0.0551180.055118 00 00 00 00

Conv9_7Conv9_7 0.0157480.015748 00 00 0.0236220.023622 00 00

LazyLazy 0.08661420.0866142 0.1338580.133858 0.09448820.0944882 0.1023620.102362 0.157480.15748 0.118110.11811

HaarHaar 0.1102360.110236 0.2677170.267717 00 0.0157480.015748 00 00

DCTDCT 0.007862040.00786204 00

SVDSVD 00 00

RN Attack-40%TYPETYPE BERBER

P=2P=2 P=4P=4 P=6P=6

N=1N=1 N=2N=2 N=1N=1 N=2N=2 N=1N=1 N=2N=2

D_4D_4 0.03937010.0393701 0.0866140.086614 00 0.0236220.023622 00 00

D_8D_8 0.03937010.0393701 0.1023620.102362 00 00 00 00

Lift5_3Lift5_3 00 0.0393700.039370 00 00 00 00

Conv9_7Conv9_7 0.03149610.0314961 0.0157480.015748 00 00 00 00

LazyLazy 0.1259840.125984 0.1338580.133858 0.157480.15748 0.1417320.141732 0.157480.15748 0.118110.11811

HaarHaar 0.1338580.133858 0.2282460.228246 00 0.0236220.023622 00 00

DCTDCT 00 0.03149610.0314961

SVDSVD 00 0.007874020.00787402

RN Attack-50%TYPETYPE BERBER

P=2P=2 P=4P=4 P=6P=6

N=1N=1 N=2N=2 N=1N=1 N=2N=2 N=1N=1 N=2N=2

D_4D_4 0.0236220.023622 0.1338580.133858 00 0.05511810.0551181 00 0.007874020.00787402

D_8D_8 00 0.1259840.125984 00 0.007874020.00787402 00 00

Lift5_3Lift5_3 00 0.0472440.047244 00 00 00 00

Conv9_7Conv9_7 00 0.0629920.062992 00 00 00 00

LazyLazy 0.1732280.173228 0.5039370.503937 0.1889760.188976 0.5039370.503937 0.1496060.149606 0.1653540.165354

HaarHaar 00 0.2125980.212598 00 0.0708820.070882 00 00

DCTDCT 00 0.04724410.0472441

SVDSVD 0.007874020.00787402 0.03149610.0314961

Simplifying AttackTypeType BERBER

P=2P=2 P=4P=4 P=6P=6

D_4D_4 00 00 00

D_8D_8 00 00 00

Lift5_3Lift5_3 00 00 00

Conv9_7Conv9_7 00 00 00

LazyLazy 0.09448820.0944882 0.09448820.0944882 0.070866100.07086610

HaarHaar 00 00 00

DCTDCT 00

SVDSVD 00

Test2 Bream

BreamBream 32 MOPs, each MOP has 165 points and 32 MOPs, each MOP has 165 points and

270 triangles270 triangles Watermark, 31 bits PN codeWatermark, 31 bits PN code Quality=0.005 (MMSE)Quality=0.005 (MMSE) Simplifying and Scale Coefficient using Simplifying and Scale Coefficient using

Conv97 at LV =2Conv97 at LV =2

TYPETYPE Embedding time(sec)Embedding time(sec) Execution Time(sec)Execution Time(sec)

P=2P=2 P=4P=4 P=6P=6 P=2P=2 P=4P=4 P=6P=6

D_4D_4 0.0189050.018905 0.022320.02232 0.0234550.023455 0.0156350.015635 0.017240.01724 0.018780.01878

D_8D_8 0.0263250.026325 0.030760.03076 0.0329450.032945 0.021130.02113 0.025460.02546 0.0270750.027075

Lift5_3Lift5_3 0.0133450.013345 0.014070.01407 0.0160450.016045 0.015220.01522 0.0165850.016585 0.016880.01688

Conv9_7Conv9_7 0.0285250.028525 0.033910.03391 0.0366450.036645 0.024040.02404 0.0281250.028125 0.026120.02612

LazyLazy 0.011940.01194 0.0127250.012725 0.013110.01311 0.012120.01212 0.0142250.014225 0.013020.01302

HaarHaar 0.0172950.017295 0.019440.01944 0.020340.02034 0.016220.01622 0.0157550.015755 0.015230.01523

DCTDCT 0.1179650.117965 0.110580.11058

SVDSVD 1.143381.14338 1.205411.20541

Conclusion

SVD is robust, but consumes longer time SVD is robust, but consumes longer time Lazy is the worst wavelet filter for Lazy is the worst wavelet filter for

watermarkingwatermarking Acceptable quality and robust to attacksAcceptable quality and robust to attacks