A chaos-based robust wavelet-domain watermarking algorithm

1. A chaos-based robust wavelet-domain watermarking algorithm Author: Zhao Dawei, Chen Guanrong, Liu Wenbo From: Chaos, Solitons and Fractals 22(2004) 47-54 Advisor: Chin-Chen Chang Speaker: Jui-Yi Chang Date: 2004/5/26

2. Outline • Introduction • Logistic map • A new watermarking algorithm • Watermark detection • Experimental results • Conclusions

3. introduction Chaotic Logistic map: Label sequence SubimageDWT coefficients Original image subimage DWT Logistic map: Watermark sequence Labelsequence Watermarked DWT coefficients Watermarkedoriginal image Watermarkedsubimage IDWT

4. Select 256 elements Logistic map • Xk+1=μXk(1-Xk) , 0<μ≦4 • Use Chaotic Logistic map to selection elements. Sequence (Length=1024)

5. A new watermarking algorithm Label Sequence (Length=256) Subimage(128x128 pixels=256 blocks) Original image(256x256 pixels=1024 blocks)

6. A new watermarking algorithm DWT Subimage (128x128 pixels)

8. A new watermarking algorithm Sequence (Length=64) Use Chaotic Logistic map iwm(i) >Tw  1 iwm(i) ≦Tw  -1 If Tw=40 Watermark signal w(i)

9. A new watermarking algorithm • C’band(i)=Cband(i)+αw(i) , i=1,2…,N • If α=2C’band(1)=0+2*(-1)=-2… Cband are the original wavelet coefficients C’band are the watermarked wavelet coefficientsα is global parameter Watermarked wavelet coefficients(in HH)

10. A new watermarking algorithm IDWT Watermarked wavelet coefficients Watermarked pixel value Label Sequence (Length=256) Original image

11. Watermark detection N • ρ=(1/3N) ΣΣC’band(i)w(i) • Pf is a false alarm. • If |ρnew -ρold|< Pf , then watermark can be detect. • Use α, Pf, Tρto determine watermark exist? • α≦1, cannot detect the watermark correctly. band i=1

12. Experimental results (a) Original image. (b) Watermarked image. (c) Extracted subimage. (d) Watermarked subimage.

13. Experimental results (Cont.) • Relations between α and PSNR ρ, Tρ(Pf =10-8)

14. Experimental results (Cont.) Half cropped watermarked image (ρ=3.6549, Tρ=1.6385). (a) Rotated watermarked image. (b) Recovered image.

15. Conclusion • This scheme applies the wavelet transform locally, based on (1) the chaotic logistic map, and (2) embeds the watermark into the DWT domain. • This new schem has high fidelity and is highly robust against geometric attacks .