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Wavelet-based digital image watermarking

Houng-Jyh Mike Wang, Po-Chyi Su, and C.-C. Jay Kuo

Open Access Open Access

Abstract

A wavelet-based watermark casting scheme and a blind watermark retrieval technique are investigated in this research. An adaptive watermark casting method is developed to first determine significant wavelet subbands and then select a couple of significant wavelet coefficients in these subbands to embed watermarks. A blind watermark retrieval technique that can detect the embedded watermark without the help from the original image is proposed. Experimental results show that the embedded watermark is robust against various signal processing and compression attacks.

©1998 Optical Society of America

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Figures (3)
Figure 1.
Figure 1. The blockdiagram of invisible watermark embedding and detection (a)embedding (b)detection.

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Figure 2.
Figure 2. Watermark retrieval from the watermarked 512 × 512 gray-level Lena image after (a) the 6 × 6 block mosaic attack, (b)the 50% uniform random noise attack, (c) the JPEG compression attack with 5% quality factor setting, and (d) the 512:1 compression attack with SPIHT.

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Figure 3.
Figure 3. Blind watermark retrieval for the gray-level Lena image of size 512×512 after (a) no attack, (b) soften filter attack, (c) JPEG compression attack and (d) 64:1 compression ratio attack by SPIHT.

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Equations (18)

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D = { T 2 12 σ 2 > T 2 12 , σ 2 , σ 2 > T 2 12 .
C s ( x , y ) = sign × ( a 0 T 2 0 + a 1 T 2 1 + … + a b T 2 b + … ) ,
T = C max , s 2 ,
C s , k ′ ( x , y ) = C s ( x , y ) + α s β s T s W k ,
E s , k ( x , y ) = α s β s T s W k ,
MSE ≤ Σ s = 1 N s Σ j = 1 N bit H s j ( α s β s T s ) 2 Height × Width ,
MSE ≤ N w Height × Width ( α max ) 2 ( T max ) 2 ( β max ) 2 ≤ 20.56 ,
α max ≤ 1 T max 20.56 × Height × Width N w .
E s , k * ( x , y ) = C s , k * ( x , y ) − C s ( x , y ) .
SIM ( I * , I ) = N w Σ k = 1 N w E s , k * ( x , y ) · E s , k ( x , y ) ∥ E s , k * ( x , y ) ∥ ∥ E s , k ( x , y ) ∥ ,
C s , b , k ′ ( x . y ) = sign × Δ p ( C s , b ( x , y ) ) × α s β s T s , b W k .
Δ p ( C s , b ( x , y ) ) = ( 1 + 2 p α s ) T s , b ,
DI S s , b , p ( x , y ) = ∣ Δ p ( C s , b ( x , y ) ) − ∣ C s , b ( x , y ) ∣ ∣ .
p = arg min p ′ DIS s , b , p ′ ( x , y ) .
DIS s , b , p ( x , y ) ≤ 2 α s T s , b .
E s , k * ( x , y ) = C s , b , k * ( x , y ) − sign × Δ p C s , b , k * ( x , y ) ,
MSE ≤ N w Height × Wight ( 2 α ) 2 ( T max ) 2 ( β ) 2 ≤ 20.56 .
α max ≤ 1 4 T max 20.56 × Height × Width N w .
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