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MPEG-4 2D Mesh Animation Watermarking Based on SSA

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

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  1. 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

  2. Outline • Singular Value Decomposition • SSA • My Method • Main Problems • Simulate Result • Reference

  3. 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

  4. 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.

  5. 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

  6. 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.

  7. 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

  8. Hankel matrix X • X=U  S  VT • X=X1+X2+…+Xd where Xi=si Ui ViT

  9. Reconstruction stage • Y:L K • Diagonal averaging transfers the matrix Y to the series (g0,…,gN-1)

  10. Watermark Embedding • W=[w1,w2,…,wn]:watermarked sequences where wi{0,1} • Find candidate si to embedding watermark as follows:

  11. Watermark Extracting • This method is private watermarking, so we need original meshes and attacked meshes to construct X and Y

  12. My Method

  13. 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

  14. 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.

  15. Simulate Result • Window Length=32 • MMSE=0.005 • Attacks: • Random Noise • Affine • S3 • MV Random Noise • MV Affine

  16. Future Works • Construct another frequency domain watermarking methods(DCT, etc.)

  17. 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

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