1. Feature Space Based Watermarking in Multi-Images
Xin Zhou

2. Outlines Introduction Feature Space Based Watermarking
Simulation Results
Conclusion

3. Introduction
Goal:
Implement the watermarking in a set of images or video based on eigen-decomposition or SVD (Singular Value Decomposition)

4. Introduction(2) Where to embed bits?
Spatial Domain: Directly process original values of the host image according to the watermark
Frequency Domain: Transfer the host image into another domain and change the corresponding coefficients according to the watermark
Is it possible to embed bits in the feature domain?

5. Introduction(3) Other’s Work What I want to do
Using SVD (Singular Value Decomposition) to embed bits in one image
Using ICA (Independent Component Analysis) to detect the watermark
What I want to do
Find a method to use eigen-decomposition or SVD to embed watermark in multi-images or video
It will be more robust to embed bits in each images
More difficult for others to estimate the watermark

6. Feature Based Watermarking
Eigen-Decomposition and SVD
Embed one bit
Detection
Embed watermark in a set of images

7. Eigen-Decomposition and SVD
mxn matrix A, of rank r, can be expressed as the product:
A = U * S * VT
U is mxr term matrix
S is rxr diagonal matrix
V is rxn document matrix
If A is nxn matrix, r=n, we have
A *U= U * S

8. Embedding One Bit (1) Assume the host image is a mxn matrix
Perform the SVD to get S matrix
Embed one bit in the S matrix according to
where {si}: original coefficients
{si’}: marked coefficients
{b}: the bit to be embedded which is 0 or 1
k : watermark strength, adjusted by the just-noticeable- difference (JND) standard

9. Embedding One Bit(2) After Embedding: A’ = U * S’ * VT
where S’ is the watermarked singular matrix
A’ is the corresponding watermarked image

10. Detection Assume we get the watermarked image A’.
Perform eigen-decomposition or SVD to get the S’
Compare S and S’, we can get the watermark

11. Embedding in Multi-Images
Method I:
Generate a pseudo random codebook
Decide which bit should be embedded to which image based on the codebook
For a specific image, use the previous method to embed bits
Method II:
Use QIM-like method to decide which bit should be embedded to which image.

12. Simulation Results (1)

13. Simulation Results (2)

14. Conclusion
Using eigen-decomposition or SVD to embed watermark into multi-images.
Implemented basic functions of the proposed method
Need to do more tests under various attacks