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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

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
Outline
  • Singular Value Decomposition
  • SSA
  • My Method
  • Main Problems
  • Simulate Result
  • Reference
singular value decomposition
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
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 cont1
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
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
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
slide8
Hankel matrix X
  • X=U  S  VT
  • X=X1+X2+…+Xd where Xi=si Ui ViT
slide9
Reconstruction stage
    • Y:L K
    • Diagonal averaging transfers the matrix Y to the series (g0,…,gN-1)
watermark embedding
Watermark Embedding
  • W=[w1,w2,…,wn]:watermarked sequences where wi{0,1}
  • Find candidate si to embedding watermark as follows:
watermark extracting
Watermark Extracting
  • This method is private watermarking, so we need original meshes and attacked meshes to construct X and Y
my method cont
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
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
Simulate Result
  • Window Length=32
  • MMSE=0.005
  • Attacks:
      • Random Noise
      • Affine
      • S3
      • MV Random Noise
      • MV Affine
future works
Future Works
  • Construct another frequency domain watermarking methods(DCT, etc.)
reference
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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