Image Adaptive Watermarking Using Wavelet Domain Singular Value

Outline n n n Singular Value Decomposition Discrete Wavelet Transform The Proposed Scheme Experimental

Singular Value Decomposition A U D V 0 X = m×n m×m 0 X

The Proposed Scheme 1. Apply DWT 2. Separate to blocks sized wxw 3. SVD

Example S: even 1 embedded odd 0 embedded 8

Quantization Variable dmax wk: Weight of block k dk wk = c 1 xmk

Conclusions n n A semi-fragile watermarking for image authentication Automatically adapt for quantization Robustness

Two-thirds Theorem For an matrix and any orthonormal basis of , define and Then

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Image Adaptive Watermarking Using Wavelet Domain Singular Value Decomposition Source: IEEE Transactions on Circuits and Systems for Video Technology, Volume: 15, Issue: 1, Jan. 2005, Pages: 96 – 102. Author: Paul Bao and Xiaohu Ma Sperker: Jen-Bang Feng

Outline n n n Singular Value Decomposition Discrete Wavelet Transform The Proposed Scheme Experimental Results Conclusions 2

Singular Value Decomposition A U D V 0 X = m×n m×m 0 X m×n n×n U and V are both orthogonal, U*UT=I, V*VT=I Energy: 3

Singular Value Decomposition 4

Discrete Wavelet Transform 5

The Proposed Scheme 1. Apply DWT 2. Separate to blocks sized wxw 3. SVD 4. Decide dk 5. Embed 7

Example S: even 1 embedded odd 0 embedded 8

Example If 1 is embedded 9

Quantization Variable dmax wk: Weight of block k dk wk = c 1 xmk + c 2 xσk dmin mean wmin variation wmax wk 10

Experimental Results 11

Conclusions n n A semi-fragile watermarking for image authentication Automatically adapt for quantization Robustness to JPEG compression Fragility to various image manipulation 13

Two-thirds Theorem For an matrix and any orthonormal basis of , define and Then . 14