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

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



  • 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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