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

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

• Singular Value Decomposition

• SSA

• My Method

• Main Problems

• Simulate Result

• Reference

• 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

• 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.

• 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

• 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.

• 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

• Reconstruction stage

• Y:L K

• Diagonal averaging transfers the matrix Y to the series (g0,…,gN-1)

• W=[w1,w2,…,wn]:watermarked sequences where wi{0,1}

• Find candidate si to embedding watermark as follows:

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

• 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

• 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.

• Window Length=32

• MMSE=0.005

• Attacks:

• Random Noise

• Affine

• S3

• MV Random Noise

• MV Affine

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

• 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