MPEG-4 2D Mesh Animation Watermarking Based on SSA

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MPEG-4 2D Mesh Animation Watermarking Based on SSA. 報告：梁晉坤 指導教授：楊士萱博士 2003/9/9. Outline. Singular Value Decomposition SSA My Method Main Problems Simulate Result Reference. Singular Value Decomposition. X:mxn, U:m  n, S:n  n, V:n  n (Matrices)

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### MPEG-4 2D Mesh Animation Watermarking Based on SSA

2003/9/9

Outline
• Singular Value Decomposition
• SSA
• My Method
• Main Problems
• Simulate Result
• Reference
Singular Value Decomposition
• X:mxn, U:mn, S:n n, V:n n (Matrices)
• X=U  S  VT where U,V are unitary matrices(UUT=UTU=I), S is a Singular matrix
• The d singular values on the diagonal of S are the square roots of the nonzero eigenvalues of both AAT andATA
SVD (Cont.)
• The main property of SVD is the singular values(SVs) of an Matrix(or image) have very good stability, that is, when a small perturbation is added to an Matrix, its SVs do not change significantly.
SVD (Cont.)
• Embedding
• AU  S  VT
• S+aW Uw  Sw  VwT
• AwU  Sw  VT
• Extract
• Compute Uw and Vw as above
• AaUa  Sa  VaT(SaSw)
• D=Uw  Sa  VwT(DS+aW)
• W=(D-S)/a
Basic SSA
• SSA(Singular Spectrum Analysis) is a novel technique for analyzing time series
• It’s based on Singular Value Decomposition
• The basic SSA consists of two stages: the decomposition stage and the reconstruction stage.
Basic SSA(Cont.)
• Decomposition stage:
• Time series F=(f0,f1,…,fN-1) of length N
• L:Window Length
• K:N-L
• Xi=(fi-1,…,fi+L-2)T, 1iK
• X=[X1…Xk]:L  K , Hankel matrix
Hankel matrix X
• X=U  S  VT
• X=X1+X2+…+Xd where Xi=si Ui ViT
Reconstruction stage
• Y:L K
• Diagonal averaging transfers the matrix Y to the series (g0,…,gN-1)
Watermark Embedding
• W=[w1,w2,…,wn]:watermarked sequences where wi{0,1}
• Find candidate si to embedding watermark as follows:
Watermark Extracting
• This method is private watermarking, so we need original meshes and attacked meshes to construct X and Y
My Method(Cont.)
• Embedding
• AU  S  VT
• Sw=S+aW ,where W{0,1}
• AwU  Sw  VT
• Extract
• Compute U, V and S as above
• AaU  Sa  VT
• D=UT Aa V Sa
• W=(D-S)/a
Main Problems
• Singular Value always is positive; most of singular values are small
• Rounding to half-precision
• Large perturbation to the matrix, its SV change significantly. It can not resist MV attacks.
Simulate Result
• Window Length=32
• MMSE=0.005
• Attacks:
• Random Noise
• Affine
• S3
• MV Random Noise
• MV Affine
Future Works
• Construct another frequency domain watermarking methods(DCT, etc.)
Reference
• Watermarking 3D Polygonal Meshes Using the Singular Spectrum Analysis, MUROTANI Kohei and SUGIHARA Kokichi
• An SVD-Based Watermarking Scheme for Protecting Rightful Ownership, Ruizhen Liu and Tieniu Tan, Senior Member, IEEE