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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 2003/7/22. Outline. Singular Value Decomposition SSA My Method Main Problems Future Works 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 報告:梁晉坤 指導教授:楊士萱博士 2003/7/22
Outline • Singular Value Decomposition • SSA • My Method • Main Problems • Future Works • Reference
Singular Value Decomposition • X:mxn, U:mn, 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 • AU S VT • S+aW Uw Sw VwT • AwU Sw VT • Extract • Compute Uw and Vw as above • AaUa Sa VaT(SaSw) • D=Uw Sa VwT(DS+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, 1iK • 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 • AU S VT • S+aW Uw Sw VwT, where W{0,1} • AwU Sw VT • Extract • Compute Uw and Vw as above • AaUa Sa VaT(SaSw) • D=Uw Sa VwT(DS+aW) • W=(D-S)/a • if Wi>=0.5 m_bits==1, else m_bits==0
Main Problems • Singular Value always is positive; most of singular values are small • A=U S VT,U,V are not basis • Rounding to half-precision
Future Works • Construct another frequency domain watermarking methods(DCT,Eigenvector)
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