1. Image Adaptive Watermarking Using Wavelet Domain Singular Value Decomposition
Source: Circuits and Systems for Video Technology,
IEEE Transactions on, Volume: 15, Issue: 1,
Jan. 2005, Pages: 96 – 102.
Author: Paul Bao and Xiaohu Ma
Sperker: Wei-Liang Tai
Date: 2005/2/17

2. Outline Introduction to Watermarking Introduction to SVD
Introduction to Wavelet
The Proposed Method
Experimental Results
Conclusions

3. Introduction to Watermarking
Invisible Watermarking
Robust Watermarking
It can against image processing such as filtering, lossy compression, sharpening, and so on.
Fragile Watermarking
It can detect any tiny alteration to the pixel value.
Semi-fragile Watermarking
It is moderately robust to lossy compression such as JPEG.

4. Introduction SVD Singular Value Decomposition = X
m × n
m × m
n × n D U V A
U and V are both orthogonal, U*UT=I, V*VT=I
Energy:

5. Original image
SVD分解
U 矩陣
D 矩陣
VT 矩陣

6. Introduction to Wavelet
Haar Wavelet Transform
Phase 1) Horizontal : ㄅ ㄆ ㄇ ㄈ ㄉ ㄊ ㄋ ㄌ ㄍ ㄎ ㄏ ㄐ ㄑ ㄒ ㄓ ㄔ A B C D E F G H I J K L M N O P
A+B
C+D
A-B
C-D
E+F
G+H
E-F
G-H
I+J
K+L
I-J
K-L
M+N
O+P
M-N
O-P
Phase 2) Vertical : ㄅ ㄆ ㄇ ㄈ ㄉ ㄊ ㄋ ㄌ ㄍ ㄎ ㄏ ㄐ ㄑ ㄒ ㄓ ㄔ
ㄅ+ㄉ
ㄆ+ㄊ
ㄇ+ㄋ
ㄈ+ㄌ
ㄍ+ㄑ
ㄎ+ㄒ
ㄏ+ㄓ
ㄐ+ㄔ
ㄅ-ㄉ
ㄆ-ㄊ
ㄇ-ㄋ
ㄈ-ㄌ
ㄍ-ㄑ
ㄎ-ㄒ
ㄏ-ㄓ
ㄐ-ㄔ

7. The Proposed Method Wavelet coefficient V = (21, 7, 4, 2) D k = 2
326
-38 6 19 16
-32 2 -7 -3 4 1
-10 5 -2 -9
D k = 2
SVD (D matrix)
B=0, S=S+1=12 21 7 4 2

8. Experimental Results

9. Experimental Results (Cont.)

10. Conclusions
A semi-fragile watermarking for image authentication is proposed.
Possess an excellent robustness to JPEG compression and a fragility to various image manipulation.