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 Singular Value Decomposition SSA SSA My Method My Method Main Problems Main Problems Future Works Future Works Reference Reference

Singular Value Decomposition X:mxn, U:m  n, S:n  n, V:n  n (Matrices) X:mxn, U:m  n, S:n  n, V:n  n (Matrices) X=U  S  V T where U,V are unitary matrices(UU T =U T U=I), S is a Singular matrix X=U  S  V T where U,V are unitary matrices(UU T =U T U=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 AA T and A T A The d singular values on the diagonal of S are the square roots of the nonzero eigenvalues of both AA T and A T A

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. 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 Embedding  A  U  S  V T  S+aW  Uw  Sw  Vw T  Aw  U  Sw  V T Extract Extract  Compute Uw and Vw as above  Aa  Ua  Sa  Va T (Sa  Sw)  D=Uw  Sa  Vw T (D  S+aW)  W=(D-S)/a

Basic SSA SSA(Singular Spectrum Analysis) is a novel technique for analyzing time series SSA(Singular Spectrum Analysis) is a novel technique for analyzing time series It’s based on Singular Value Decomposition It’s based on Singular Value Decomposition The basic SSA consists of two stages: the decomposition stage and the reconstruction stage. The basic SSA consists of two stages: the decomposition stage and the reconstruction stage.

Basic SSA(Cont.) Decomposition stage: Decomposition stage:  Time series F=(f 0,f 1,…,f N-1 ) of length N  L:Window Length  K:N-L  X i =(f i-1,…,f i+L-2 ) T, 1  i  K  X=[X 1 …X k ]:L  K, Hankel matrix

 Hankel matrix X  X=U  S  V T  X=X 1 +X 2 +…+X d where X i =s i  U i  V i T

Reconstruction stage Reconstruction stage  Y:L  K  Diagonal averaging transfers the matrix Y to the series (g 0,…,g N-1 )

Watermark Embedding W=[w 1,w 2,…,w n ]:watermarked sequences where w i  {0,1} W=[w 1,w 2,…,w n ]:watermarked sequences where w i  {0,1} Find candidate s i to embedding watermark as follows: Find candidate s i 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 This method is private watermarking, so we need original meshes and attacked meshes to construct X and Y

My Method

My Method(Cont.) Embedding Embedding  A  U  S  V T  S+aW  Uw  Sw  Vw T, where W  {0,1}  Aw  U  Sw  V T Extract Extract  Compute Uw and Vw as above  Aa  Ua  Sa  Va T (Sa  Sw)  D=Uw  Sa  Vw T (D  S+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 Singular Value always is positive; most of singular values are small A=U  S  V T,U,V are not basis A=U  S  V T,U,V are not basis Rounding to half-precision Rounding to half-precision

Future Works Construct another frequency domain watermarking methods(DCT,Eigenvector) Construct another frequency domain watermarking methods(DCT,Eigenvector)

Reference Watermarking 3D Polygonal Meshes Using the Singular Spectrum Analysis, MUROTANI Kohei and SUGIHARA Kokichi 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 An SVD-Based Watermarking Scheme for Protecting Rightful Ownership, Ruizhen Liu and Tieniu Tan, Senior Member, IEEE