A Digital Watermarking Scheme Based on Singular Value
A Digital Watermarking Scheme Based on Singular Value Decomposition Speaker: Prof. Chin-Chen Chang 2007/4/8
• • • Outline Digital Watermarking System Watermarking Category SVD (Singular Value Decomposition) Proposed Scheme Experimental Results Conclusions 2007/4/8 2
Digital Watermarking System 2007/4/8 3
Watermarking Category. Robustness • Three categories – Robust watermarking schemes – Fragile watermarking schemes – Semi-fragile watermarking schemes 2007/4/8 4
Watermarking Categoryembedding approach • Spatial domain-based scheme – Low computational complexity – Lower robustness • Frequency domain-based scheme – Need more computation – Provide better robustness 2007/4/8 5
• SVD-based schemes – Similar to frequency domain based scheme – SVD can be considered as a transformation 2007/4/8 6
SVD • Singular Value Decomposition • Assume that rank of A is r. • U and V are N x N orthogonal matrices, U x UT=I, V x VT=I • S is an N x N diagonal matrix, σ1 ≥σ2 ≥…≥σr ≥σr+1 =…=σN =0 2007/4/8 7
Proposed Scheme (1/3) 4 10011010 110001 011010 4 Binary watermarking image One bit needs to be embedded in three different blocks Original image Use a one way hash function based on Rabin’s scheme to decide the embedding block 2007/4/8 8
Proposed Scheme (2/3) • Embedding process Wi = 1, δ = 20 SVD Ux 23. 2527 x VT 3. 2527+δx. Wi 2007/4/8 9
Proposed Scheme (3/3) • Extracting process δ/2 = 10 SVD Ux 18. 6047 -5. 4539 =13. 1508 > 10 The same process W’ 1=1 W’ 2=0 2007/4/8 x VT W’ 2=1 W’ 1+W’ 2+W’ 3 > 2 W’=1 10
Experimental Results (1/7) • Seven 512 x 512 gray-scale test images and one 64 x 64 binary image 2007/4/8 11
Two measurements • PSNR – Peak Signal-to-Noise Ratio • BCR – Bit Correction Ratio 2007/4/8 12
Experimental Results (2/7) 2007/4/8 13
Original image 2007/4/8 Watermarked image (PSNR = 35. 37 d. B) Extracted watermark Bit Correction Ratio = 100% 14
Experimental Results (3/7) 2007/4/8 15
Watermarked image after JPEG compressing (PSNR = 35. 87 d. B) 2007/4/8 Extracted watermark (Bit Correction Ratio = 87. 92%) 16
Experimental Results (4/7) 2007/4/8 17
Watermarked image after sharpening process (PSNR = 29. 23 d. B) 2007/4/8 Extracted watermark (Bit Correction Ratio = 95. 73%) 18
Experimental Results (5/7) 2007/4/8 19
Watermarked image after blurring process (PSNR = 35. 60 d. B) 2007/4/8 Extracted watermark (Bit Correction Ratio = 92. 41%) 20
Experimental Results (6/7) 2007/4/8 21
Watermarked image after cropping process (PSNR = 35. 60 d. B) 2007/4/8 Extracted watermark (Bit Correction Ratio = 90. 19%) 22
Experimental Results (7/7) 2007/4/8 23
Watermarked image after adding noise (PSNR = 32. 54 d. B) 2007/4/8 Extracted watermark (Bit Correction Ratio = 89. 28%) 24
Comparisons with other schemes Scheme Items Chandra (Global -based) Chandra (Blockbased) Hwang et al. Liu and Tan Spatial SVD SVD No No No Yes No Storing some matrices to extract watermark No Yes No No Robustness Low High Embedding quality Very high High Processing domain Extracting watermarks with original image 2007/4/8 Proposed scheme 25
Conclusion • SVD-based watermarking scheme for binary logo • The proposed scheme has good efficiency • The PSNR values of the watermarked images are all greater than 31 d. B 2007/4/8 26
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