International Conference on Intelligent Information Hiding and Multimedia Signal Processing
An Improved Adaptive QIM Watermark Iterative Algorithm Xinghua Sun1, Ju Liu1, Jiande Sun1, Niqing Yang1, Shilong Wu2 1 School of Information Science and Engineering, Shandong University, Jinan, 250100, China 2 Unit 61541 of PLA, Beijing 100094 E-mail:
[email protected],
[email protected],
[email protected] [3-5]. Cox et al proposed an Adaptive Quantization Index Modulation (AQIM) algorithm [5], which is based on adaptive modulation steps, and adopted the improved vision model to improve the robustness against magnitude changing of pixels. But in this algorithm, since the step is a function of the to-beembedded coefficients, and the modulation step in the blind detection is based on the watermarked coefficients, the quantization steps in watermark embedding are different from the ones in watermark detection. That results the AQIM algorithm can’t extract the exact watermark even in the case that the watermark isn’t attacked at all. According to this problem, we analyze the causes of it, and propose a feasible adaptive QIM watermark iterative algorithm to resolve this problem. In this algorithm, an iterative embedding method is adopted to change the to-be-embedded coefficients in order to make sure that when there is no attack, the original watermark can be extracted.
Abstract Quantization Index Modulation (QIM) algorithm is one of the most important blind detection watermarking algorithm. The Adaptive Quantization Index Modulation (AQIM), proposed by I. J. Cox, calculates the quantization step according to the Watson’s perceptual model, and makes the embedding steps vary according to the coefficients to be quantized adaptively. It has better reliability and robustness than the traditional Quantization Index Modulation (QIM) algorithm. But in the previous QIM series algorithms, the embedding step(s) during embedding is different from the one(s) in the detection. That results the watermark can’t be extracted exactly and integrally even without any attacks/processing. In this paper, an iterative AQIM scheme is proposed to resolve this problem. The simulations also show that the proposed algorithm has better performance than the AQIM algorithm proposed by I. J. Cox.
2. Adaptive quantization index modulation (AQIM)
1. Introduction With the distribution of the digital multimedia on Internet, the copyright protection of digital multimedia has been an urgent problem to be resolved. In such case, the techniques of watermarking are developed rapidly, and the researchers have proposed many kinds of watermarking algorithms, for which invisibility and robustness are the most two important properties. Among the existing algorithm, there are two most important kinds: Spread Spectrum (SS) algorithm [1] and Quantization Index Modulation (QIM) algorithm [2, 3]. As the most important blind watermarking algorithm, the QIM algorithm is proposed by Brain Chen et al[2], whose superiorities includes better robustness, large embedding quantity, less complexity, blind watermark detection, and so on. But the traditional QIM has worse invisibility locally because of the invariable modulation step, and is sensitive to the changing of magnitude of the pixels. Therefore, many adaptive watermark schemes have been proposed
978-0-7695-3278-3/08 $25.00 © 2008 IEEE DOI 10.1109/IIH-MSP.2008.160
The Adaptive Quantization Index Modulation (AQIM) proposed by I. J. Cox calculated the quantization step according to the Watson perceptual model, which improves the invisibility and robustness.
2.1. Watson perceptual model Watson perceptual model is a 8 × 8 block-based perceptual model in DCT domain. It consists of a sensitivity function, two mask models based on luminance and contrast respectively, and a combine component. Here we only consider the sensitivity function and the two mask models. 2.1.1. Sensitivity. In Watson model, a sensitivity table t ( i, j ) is defined, where i , j = 0,1, … ,7 , to reflect the sensitivity of human vision to different frequencies. The details of the sensitivity function can be found in literature [6].
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So we can see that the modulation step is changed with C0 (i, j , k ) , and it will cause the error in watermark detection. 2.2.2. Analysis of AQIM. In the following sections, index (i, j, k ) will be ignored to simplify the
2.1.2. Luminance mask model. For the pixel block k, luminance mask t L ( i, j , k ) is defined: t L ( i , j , k ) = t ( i, j ) ( C0 ( 0,0,k ) C0,0 )
αT
(1)
Where α T denotes a constant, which is usually 0.649, C 0 (0,0, k ) denotes the DC coefficient of the kth
expression. We let step E denote the quantization step,
block, C 0, 0 denotes the mean of all the DC coefficients of the host image. 2.1.3. Contrast mask model. The luminance mask model t L (i, j, k ) is affected by the contrast mask model, which results in a mask threshold s (i, j, k ) .
{
s (i, j, k ) = max t L (i, j , k ), C 0 (i, j, k )
w(i , j )
( )
t L (i, j , k )1− w i, j
C0
, m E = round (q E ) , δ = q E − m E , then step E 1 δ ≤ , and W is the binary watermark. Based on (7), 2
qE =
1
} (2)
C 0 = t L ⋅ q E1− w
Where w(i, j ) is a constant. In Watson perceptual
= t L ⋅ (m E + δ )
model, w(i, j ) is 0.7.
During watermark embedding: Case1: mod(m E ,2) == W
2.2. Watson-based AQIM
C w = m E ⋅ step E
In traditional QIM
y = q( x, m ) (3) Where x denotes the to-be-embedded host image, m denotes the to-be-embedded information, q ( ) denotes the quantization function, and y denotes the watermarked image. In order to balance the invisibility and robustness, Cox proposed to use s (i , j , k ) as C 0 (i, j, k ) . s (i, j, k )
w
= m E ⋅ C 0 t 1L− w Case2: mod(m E ,2) ≠ W a) if δ ≥ 0
= (m E + 1) ⋅ C 0 t 1L− w w
= (m E + 1) ⋅ (m E + δ ) b) if δ < 0
by C w (i, j, k ) , the error will appear obviously. 2.2.1. AQIM. The quantization step in AQIM is defined: stepE = s ( i, j , k ) (4) w( i , j ) 1− w( i , j ) = max tL ( i, j, k ) , C0 ( i, j,k ) tL ( i, j, k )
is t L (i, j, k ) ≥ C 0 (i, j, k ) ,
1− w(i , j )
t L (i, j, k )
step E = t L (i, j, k )
If t L (i, j, k ) < C 0 (i, j, k )
is t L (i, j, k ) < C 0 (i, j, k ) ,
step E = C 0 (i, j, k )
C0 (i, j, k ) = t L (i, j, k )
w(i , j )
w (i , j )
t L (i, j, k )
1− w(i , j )
t L (i, j , k )
( w(i , j )−1) w(i , j )
⋅ tL
C w = (m E − 1) ⋅ step E
= (m E − 1) ⋅ C 0 t 1L−w w
(11)
w 1− w
= (m E − 1) ⋅ (m E + δ )
⋅ tL
During watermark detection, we set q D =
}
m D = round (q D ) :
, that
Cw step D
,
Case1: mod(m E ,2) == W In order to detect the watermark correctly, 1 1 m E − < q D < m E + should be satisfied. That is, 2 2
(5) 1− w(i , j )
(10)
w 1− w
detection, C w (i, j, k ) ≈ C 0 (i, j, k ) .If s (i, j, k ) is estimated
If t L (i, j, k ) ≥ C 0 (i, j, k )
⋅ tL
C w = (m E + 1) ⋅ step E
get the watermarked coefficient C w (i, j, k ) during
w(i , j )
(9)
w 1− w
= m E ⋅ (m E + δ )
is also a function of C 0 (i, j, k ) , so although we can
{
(8)
1 1− w
, that
1
1
1 1− w 1 1− w < C w < t L ⋅ m E + , which means t L ⋅ mE − 2 2
(6)
1
1
w 1 1− w 1 1−w < m E ⋅ (m E + δ )1− w ⋅ t L < t L ⋅ m E + (12) t L ⋅ mE − 2 2
⋅ step1E w(i , j ) (7)
We can see in this case, there won’t be any error in detection.
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Case2: mod(m E ,2) ≠ W a) if δ ≥ 0 , In order to detect the watermark correctly, 1 3 m E + < q D < m E + , which means 2 2 1
So we proposed an iterative watermark embedding algorithm, in which the watermark will be embedded iteratively only into the coefficients C w , which cause the detection error, until they meet the requirement of correct detection. Embedding algorithm. When mod(m E ,2) ≠ W , a) if 0 ≤ δ < ε C nw = (m E + 1) ⋅ step E (21) w = (m E + 1) ⋅ C (n −1)w t 1L− w
1
w 1 1−w 3 1−w t L ⋅ mE + < (m E + 1) ⋅ (m E + δ )1−w ⋅ t L < t L ⋅ m E + (13) 2 2
When δ = 0 ,
(m E + 1)
w ⋅ m E1− w
1
1 1−w < mE + 2
(14)
Where C (n −1)w denotes the embedded coefficient after
1 When δ = , 2
n-1 times watermark embedding.
( mE + 1) ⋅ ( mE + δ )1−w = ( mE + 1) ⋅ mE + w
1 2
w 1− w
1 > mE + 2
1 1− w
1
after
1
1
1
w 3 1− w 1 1− w t L ⋅ mE − < (m E − 1) ⋅ (m E + δ )1− w ⋅ t L < t L ⋅ m E − 2 2
{C nw }
(17)
must
satisfy
1
1 1 1− w
> mE − 2
w
is a decreasing sequence, with the limit 1
1 1− w , which make must satisfy C w < t L ⋅ m E − 2 sure that the watermark can be detected correctly.
(18)
1 , 2
( mE − 1) ⋅ ( mE + δ )
Cw
t L ⋅ (m E − 1)1− w so after numbered iterations, C w
When δ = 0 ,
w 1− w
iterations,
1 1− w Cw > t L ⋅ m E + , which make sure that the 2 watermark can be detected correctly. b) if ε ′ < δ < 0 C nw = (m E − 1) ⋅ step E (22) w = (m E − 1) ⋅ C (n −1)w t 1L− w
(m E + 1) ⋅ (m E + ε ) == m E + 1 1−w (16) 2 When 0 ≤ δ < ε , there exists detection error. b) if δ < 0 , In order to detect the watermark correctly, 3 1 m E − < q D < m E − , which means 2 2
When δ = −
numbered
1
w 1+ w
(m E − 1)
is an
increasing sequence with the limit t L ⋅ (m E + 1)1− w , so
(15)
1 There must exist 0 < ε < , which satisfies 2
w ⋅ m E1−w
{C nw }
1
1 1− w 1 1− w = ( mE − 1) ⋅ mE − < mE − 2 2
4. Simulations (19)
In order to prove the feasibility of the proposed algorithm, 1000 images are used in the simulations. During the simulations, watermark is embedded under the condition that Document-to-Watermark Ratio (DWR) is below 25. σ 2 DWR = 10log10 x2 (23) σ∆
1 There must exist − < ε ′ < 0 , which satisfies 2 1
1 1− w (20) ( mE − 1) ⋅ ( mE + δ ) == mE − 2 When ε ′ < δ < 0 , there will be detection error. In a word, when mod(m E ,2) ≠ W and ε ′ < δ < ε , the watermark will be detected by error. w 1− w
Where the difference ∆ = y − x 。 In the simulation, NC is selected as the measurement of watermark detection:
3. Improved AQIM iterative algorithm
L
NC =
Based on the analysis in section 2, we can see that watermark won’t be detected correctly if the modulation can’t make C w exceed a specific threshold..
∑ ( 2 W ( i ) − 1) ⋅ ( 2 W′ ( i ) − 1)
i =1 L
2 L
∑ ( 2W ( j ) − 1) ∑ ( 2 W ′ ( j ) − 1) j =1
j =1
Where L is the length of watermark.
750
2
(24)
The simulation results on the standard image, Lena.bmp, is showed here. Fig.1 shows the original image and the watermarked one. The PSNR of the watermarked image is 38.8387.
5. Conclusion. The simulations above show the feasibility and validity of the proposed improved AQIM iterative algorithm. From the comparison of AQIM and the proposed algorithm, we can see that the proposed algorithm improves the robustness of the AQIM algorithm by iterative embedding without any degradation in host image. The iterative algorithm proposed here makes the modulation step during embedding and that during detection be same. The iterative scheme improves the robustness against intensity changing and JPEG compression especially.
(a) (b) Fig. 1. (a) Host Image (b) Watermarked Image
Fig.2 shows the extracted watermark by different algorithms without any processing/attack. The original watermark is a 32×32 binary image. The NC resulted by AQIM is 0.5988, and the NC resulted by the proposed algorithm is 1.
6. Acknowledgement This work was supported by Program for New Century Excellent Talents in University (NCET-05-0582), Specialized Research Fund for the Doctoral Program of Higher Education (No. 20050422017), the Excellent Youth Scientist Award Foundation of Shandong Province (No. 2007BS01023, 2007BS01006) and Science Foundation of Shandong Province (No. Y2007G04).
(a) (b) Fig. 2. (a) Extracted watermark by AQIM (b) Extracted watermark by proposed algorithm
Fig.3 shows the detection curve after JPEG compression with quality factor varying from 20-100. The result shows that the proposed algorithm has better robustness than AQIM.
7. References [1] I. J. Cox, Joe Kilian, et al., “Secure Spread Spectrum Watermarking for Multimedia”, IEEE Trans. on Image Processing, 6(12), 1997, pp. 1673-1687. [2] Brian Chen and Gregory W. Wornell, “Quantization Index Modulation: A Class of Provably Good Methods for Digital Watermarking and Information Embedding”, IEEE Trans. on Information Theory, 47 (4), 2001, pp. 1423-1443. [3] J. S. Pan, Y. C. Hsin, et al., "Robust Image Watermarking Based on Multiple Description Vector Quantization", Electronics Letters, 40(22), pp. 1409-1410, 2004. [4] J. S. Pan, H. C. Huang, et al., “Intelligent Multimedia Data Hiding: New Directions”, Springer, 2007. [5] Q. Li, I. J. Cox, “Using Perceptual Models to Improve Fidelity and Provide Resistance to Valumetric Scaling for Quantization Index Modulation Watermarking”, IEEE Trans. on Information Forensics and Security, 2(2), 2007, pp. 127139. [6] A. B. Watson, “DCT Quantization Matrices Optimized for Individual Images”, Human Vision, Visual Processing, and Digital Display IV, SPIE(1913), 1993, pp. 202-216. [7] C. Lu, H. M. Liao, and M. Kutter, “Denoising and Copy Attacks Resilient Watermarking by Exploiting Prior Knowledge at Detector”, IEEE Trans. on Image Processing, 11. (3) 2002, pp. 280-292
Robustness against JPEG Compression 0.9 improved 0.8
AQIM
Normalized Correlation
0.7 0.6 0.5 0.4 0.3 0.2 0.1 20
30
40
50 60 70 Quality Factor of JPEG
80
90
100
Fig. 3. Detection NC after JPEG Compression
Table 1 shows the detection results after various attacks. In these simulations, we set the detection threshold be 0.1 to insure that the false detection ratio is under 6.9325e-004[7]. We can see that the improved scheme has better performance than the AQIM. Table 1 Detection results after various attacks Cropping median salt noise intensity attack 1/4 filter 3*3 0.005 changing Improved 0.7500 0.6753 0.6833 1.0000 AQIM 0.5860 0.5276 0.5467 0.7613
751
