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

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

3 Singular Value Decomposition = XX m × nm × mm × n n × n DUVA 0 0 U and V are both orthogonal, U*U T =I, V*V T =I Energy:

4 Singular Value Decomposition

5 Discrete Wavelet Transform

6 Introduction to Wavelet ABCD EFGH IJKL MNOP A+BC+DA-BC-D E+FG+HE-FG-H I+JK+LI-JK-L M+NO+PM-NO-P ㄅㄆㄇㄈ ㄉㄊㄋㄌ ㄍㄎㄏㄐ ㄑㄒㄓㄔ ㄅ+ㄉㄅ+ㄉㄆ+ㄊㄆ+ㄊㄇ+ㄋㄇ+ㄋㄈ+ㄌㄈ+ㄌ ㄍ+ㄑㄍ+ㄑㄎ+ㄒㄎ+ㄒㄏ+ㄓㄏ+ㄓㄐ+ㄔㄐ+ㄔ ㄅ-ㄉㄅ-ㄉㄆ-ㄊㄆ-ㄊㄇ-ㄋㄇ-ㄋㄈ-ㄌㄈ-ㄌ ㄍ-ㄑㄍ-ㄑㄎ-ㄒㄎ-ㄒㄏ-ㄓㄏ-ㄓㄐ-ㄔㄐ-ㄔ ㄅㄆㄇㄈ ㄉㄊㄋㄌ ㄍㄎㄏㄐ ㄑㄒㄓㄔ Haar Wavelet Transform Phase 1) Horizontal : Phase 2) Vertical :

7 The Proposed Scheme 1.Apply DWT 2.Separate to blocks sized w x w 3.SVD 4.Decide d k 5. Embed

8 Example S: even  1 embedded odd  0 embedded

9 Example If 1 is embedded

10 Quantization Variable w k : Weight of block k w k = c 1 x m k + c 2 x σ k w max w min wkwk d max d min dkdk meanvariation

11 Experimental Results

12

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

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