Dynamic energy enabled differentiation (DEED) image
watermarking based on human visual system and wavelet
tree classification
Min-Jen Tsai
Published online: 26 November 2009
# Springer Science + Business Media, LLC 2009
Abstract In this paper, we present a novel dynamic energy enabled differentiation (DEED) watermarking algorithm based on the wavelet tree classification and human visual system (HVS). The wavelet coefficients of the image are divided into disjoint trees and a wavelet tree consists of 21 coefficients which are divided into 6 blocks. One watermark bit is embedded into one wavelet tree using the energy differentiation of positive and negative modulation between coefficients of each block. In addition, the contrast sensitive function (CSF) of human visual system is also considered for better weighting in watermarking since the wavelet coefficients across the subbands perform different characteristics and importance. As DEED still requires extra storage of side information during the extraction and results non-blind watermarking approach, a random direction differentiation approach called DEEDRis then proposed which is a truly blind watermarking technique. This study has performed intensive comparison for the proposed scheme with other tree energy differentiation based techniques like WTQ, ABW-TMD and WTGM under various geometric and nongeometric attacks. From the experimental results, the advantage of DEED based algorithms is not only with low complexity, but also outperforms WTGM and WTQ in terms of robustness and imperceptibility of watermarking.
Keywords Digital image watermarking . Human visual system (HVS) . Tree energy differentiation . Wavelet
1 Introduction
As digital data are widely available online or elsewhere, and because they are easy to be modified, necessary works are required to protect the copyright and the verification of the DOI 10.1007/s11042-009-0422-5
M.-J. Tsai (*)
Institute of Information Management, National Chiao Tung University, 1001 Ta-Hsueh Road, Hsin-Chu 300 Taiwan, Republic of China
embedded genuine information. Digital watermarking has received significant attraction recently due to the popularity of the Internet and demand for the ownership protection [3]. Among the techniques for watermarking [3–5,9,18,19], the robustness of the digital watermarking is very crucial to counteract the various attacks of unauthorized modification.
Cox et al. [3] had proposed a global DCT-based spread spectrum approach to hide watermarks. Langelaar and Lagendijk [9] introduced the DEW (Differential Energy Watermarking) algorithm for JPEG/MPEG streams in the DCT domain. The DEW algorithm embeds label bits (the watermark) by selectively discarding high frequency DCT coefficients in certain image regions. Das, Maitra and Mitra had presented a successful cryptanalysis against the DEW scheme in [5] and proposed a more robust scheme.
On the other hand, Wang and Lin [18,19] introduced the technique of WTQ (Wavelet Tree Quantization) in the wavelet domain. The wavelet coefficients are grouped into so called super trees. The wavelet tree based watermarking algorithm embeds watermark bits by selectively quantizing the super trees. Even if the attacker has no knowledge of which two trees are used for embedding, he can still quantize those super trees that are not quantized earlier with respect to the estimated quantization indices. Das and Maitra had presented how that can be accomplished in [4] and such cryptanalysis attack is also confirmed in this study.
Al-Otum and Samara [1] later proposed an adaptive blind wavelet watermarking technique using tree mutual difference called ABW-TMD where the total embedding error is minimized by investigating which tree pairs will be allowed to embed the watermark bit and the embedding position will be saved as a sequential value in a private key. Even this design shows superior results to resist various image processing attacks than WTQ, the existence of the private key containing the watermark embedding location indicates such watermarking technique can not be categorized as “blind” watermarking approach. The authors [1] may not be aware of such subtle difference and named their scheme blind but it actually is not.
Instead of only using the tree structure in the wavelet domain for image watermarking, tree group energy differentiation approach with the adoption of human visual system has been first proposed in WTGM [16,17] algorithm. In WTGM, suppose that each watermark bit is embedded using one tree group, half of a tree group is used for positive modulation [10] and the other is used for negative modulation.
For suitable modulation, any two sub-tree groups should have close total energy (energy summation from wavelet tree coefficients) and the selection is essential the sum-of-subset problem in [5]. Even WTGM design is robust to the cryptanalysis of the watermarking attacks with high visual quality, the disadvantage for the WTGM is that the tree combination information must be kept secret which addresses extra storage space and the watermarking is not truly blind in essence. This is the similar situation from the analysis of ABW-TMD. Therefore, it is the motivation in this study to apply the dynamic energy enabled differentiation to investigate the differentiation approach with human visual system consideration for watermarking without the side information in this study. Under such conception, we proposed a human vision system based dynamic energy enabled differentiation (called DEED) watermarking algorithm which utilizes discrete wavelet transform (DWT) theory. DEED modifies the wavelet coefficient values of images dynamically and uses the differentiation of positive and negative modulation to embed the watermark. In the embedding process, we try to find the best coefficient energy differentiation direction of the embedded watermark
bit that make minimal change of coefficient’s energy within the tree. We then change the wavelet tree coefficient energy dynamically with differentiation direction, and embed the designated watermark bits into the energy differentiation between the coefficients. The purpose of the DEED design is robust to the cryptanalysis of the watermarking attacks with high visual quality. The weakness of DEED is that the differentiation direction information should be recorded and extra storage of side information is required as the WTGM or ABW-TMD does, they can not be categorized as the blind watermarking approach which will be unsuitable in practical applications. Therefore, a random direction differentiation approach called DEEDRis then proposed which is a truly blind watermarking technique with high robustness against attacks.
Under such motivation, DEED and DEEDR can construct a better wavelet tree watermarking algorithm for digital images and offer more credible technique to protect the digital intellectual property rights. This paper will be organized as follows. The details of the algorithms will be explained in Section2. Section3will show the experiments with discussion and conclusion is in Section4.
2 The DEED approach and the algorithms 2.1 The watermark embedding of DEED
We employ the same wavelet tree structure as depicted in the WTQ scheme in Fig. 1. Suppose that a 512×512 image is transformed, each wavelet treeΤ will be a collection of 21 wavelet coefficients, one coefficient from level 4, 4 coefficients from level 3, and 16 coefficients from level 2, and we can get 3072 wavelet trees. That is, a 512×512 image will be decompose into 3072 wavelet tree Τn where 0≤n≤3071. We then divide the 21 coefficients of one tree into 6 blocks as shown in Fig.2(a)and (b).
To embed the watermark into wavelet trees where the watermark sequence is a binary PN (±1) sequence of watermark bits, the DEED algorithm tries to modify the coefficients in each block dynamically. Since there is only one coefficient for block one, the scalar quantization is applied for differentiation purpose. Therefore, one watermark bit is embedded in one tree by modifying the coefficient energy 6 times (one time for one block). We first quantize the coefficient of block 1 with a pre-defined modular value S, and the thresholds of differentiation T1 and T2and the differentiation operations are as follows:
T1¼S4; T2¼3S4 dnð1Þ ¼ Tnð1Þ mod S ð1Þ Tn0ð1Þ ¼ Tnð1Þ dnð1Þ þ T1; if Wn¼ 1 and Tnð1Þ 0 Tnð1Þ dnð1Þ þ T2; if Wn¼ þ1 and Tnð1Þ 0 Tnð1Þ þ dnð1Þ T1; if Wn¼ 1 and Tnð1Þ < 0 Tnð1Þ þ dnð1Þ T2; if Wn¼ þ1 and Tnð1Þ < 0 8 > > < > > : ð2Þ
For block 2–6 which contains 4 coefficients in each block, DEED will adjust those coefficients according to the energy differentiation by positive and negative modulation.
First, we must determine a suitable differentiation direction of the block. There are 3 kinds of differentiation direction: vertical, horizontal and diagonal direction. If we can modify the energy of one block with different differentiation direction and make minimal change of the coefficients, the direction is exactly the best direction. Under such consideration, the best differentiation direction selection algorithm of wavelet coefficient energy is as follows:
Some notations are defined here for each treeΤnof group g, 1≤g≤5, 0≤n≤3071 and the length of watermark is Nw:
σn,g( Ur): The average of upper 2 coefficients σn,g( Lr): The average of lower 2 coefficients σn,g( Lt): The average of left 2 coefficients σn,g( Rt): The average of right 2 coefficients σn,g(D1): The average of 2 left-diagonal coefficients σn,g(D2): The average of 2 right-diagonal coefficients for ( n=0 ; n<Nw; n++) f Vn;g¼ sn;gðUrÞ sn;gð ÞLr Hn;g¼ sn;gð Þ sLt n;gð ÞRt Dn;g¼ sn;gðD1Þ sn;gðD2Þ ð3Þ if ( wn= =−1)
directionn;g¼ find maximum V n;g; Hn;g; Dn;g HL4 LH4 LH3 LH2 LH1 HH2 HH1 HL1 HL2 HH3 HL3 HH4 3.55 3.55 5.30 5.30 4.74 4.74 3.75 7.20 3.48 Fig. 1 A four-level wavelet tree structure. The coefficients corresponding to the same spatial location are grouped together. Each tree consists of one coefficient from level 4, 4 coef-ficients from level 3, 16 coeffi-cients from level 2. For WTGM
(S2) tree grouping, 64 coefficients
from level 1 are adopted. The weighting values for each level k are indicated at the center of each band
else if ( wn= =1)
directionn;g¼ find minimum V n;g; Hn;g; Dn;gg
Where directionn,g=0,1,2 means the differentiation direction is vertical, horizontal or diagonal respectively for block g in treeΤn.
If we find the vertical direction is the best choice of the differentiation direction, we will first calculate the average value of upper and lower coefficients of block g of tree n:
sn;gðUrÞ ¼ T n;gð1Þ þ Tn;gð2Þ=2 sn;gð Þ ¼ TLr n;gð3Þ þ Tn;gð4Þ=2
ð4Þ
Then DEED will calculate the difference difvbetweenσn,g(Ur) andσn,g(Lr) as
difv¼ s n;gðUrÞ sn;gð ÞLr ð5Þ
After this step, DEED will adjust the coefficient values and the modified energy differentiation of σn,g(Ur) and σn,g(Lr) will become s
0
n;gðUrÞ and s 0
n;gð Þ which satisfyLr the following relationship:
s0n;gðUrÞ s 0 n;gð ÞLr ; if wn¼ 1 s0n;gðUrÞ < s 0 n;gð Þ; if wLr n¼ 1 " ð6Þ i =10 i =12 i =13 i =11 i =6 i =8 i =9 i =7 i =14 i =16 i =17 i =15 i =18 i =20 i =21 i =19 i =2 i =4 i =5 i =3 i =1 Tn,3(j) Tn,5(j) j=1 j=3 j=4 j=2 j=1 j=3 j=4 j=2 block 2 block 3-6 j=1 j=3 j=4 j=2 j=1 j=3 j=4 j=2 j=1 j=3 j=4 j=2 Tn,1(j) Tn,2(j) Tn,4(j)
a
b
block 3-6 block 2 block 1 Fig. 2 a There are 21coeffi-cients to form a tree which is divided into 6 blocks. b In block
2–6, 4 nearby coefficients in level
2 and 3 are grouped to form
blocks. The symbol Tn,g(j)
represents the coefficient in tree
Let E[.]s represent the process of differential operations for each block coefficient. DEED will modify the coefficient energy to satisfy the conditions mentioned above:
E T n;gðjÞ j¼ 1; 2 Wn¼ 1 ¼ Tn;gð jÞ þΔ2 ; if sn;gðUrÞ ¼ sn;gð ÞLr Tn;gð jÞ ; if sn;gðUrÞ> sn;gð Þ andLr difvΔ Tn;gð jÞ þΔdif2 v ; if sn;gðUrÞ> sn;gð Þ andLr difv < Δ Tn;gð jÞ þdifvþΔ 2 ; if sn;gðUrÞ < sn;gð ÞLr 8 > > < > > : E T n;gð jÞ j¼ 3; 4 Wn¼ 1 ¼ Tn;gð jÞ Δ2 ; if sn;gðUrÞ ¼ sn;gð ÞLr Tn;gð jÞ ; if sn;gðUrÞ> sn;gð Þ and difLr vΔ Tn;gð jÞ Δdif2 v ; if sn;gðUrÞ> sn;gð Þ and difLr v < Δ Tn;gð jÞ difv2þΔ ; if sn;gðUrÞ < sn;gð ÞLr 8 > > < > > : E T n;gð jÞ j¼ 1; 2 Wn¼ 1 ¼ Tn;gð jÞ Δ2 ; if sn;gðUrÞ ¼ sn;gð ÞLr Tn;gð jÞ ; if sn;gðUrÞ < sn;gð Þ and difLr vΔ Tn;gð jÞ Δdifv 2 ; if sn;gðUrÞ < sn;gð Þ and difLr v < Δ Tn;gð jÞ difv2þΔ ; if sn;gðUrÞ> sn;gð ÞLr 8 > > < > > : E T n;gð jÞ j¼ 3; 4 Wn¼ 1 ¼ Tn;gð jÞ þΔ2 ; if sn;gðUrÞ ¼ sn;gð ÞLr Tn;gð jÞ ; if sn;gðUrÞ < sn;gð Þ and difLr vΔ Tn;gð jÞ þΔdif2 v ; if sn;gðUrÞ < sn;gð Þ and difLr v < Δ Tn;gð jÞ þdifvþΔ 2 ; if sn;gðUrÞ> sn;gð ÞLr 8 > > < > > : 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 ð7Þ TheΔ represents the differentiation intensity among the equations. When Δ is larger, the robustness of watermarking will be improved. In the mean time, it will affect the image quality more. While we have done the dynamic energy differentiation process from block 1 to block 6, the watermarking of bit wn into tree Τn is completed. The differentiation direction of every tree must be recorded in a storage space.
For the differentiation in the horizontal or diagonal direction, the differentiation process is similar. We can replace Eq.4–6by Eq.8–10if the direction is horizontal and Eq.11–13
if the direction is diagonal:
sn;gð Þ ¼ TLt n;gð1Þ þ Tn;gð3Þ=2 sn;gð Þ ¼ TRt n;gð2Þ þ Tn;gð4Þ=2 2 4 ð8Þ Difh¼ s n;gð Þ sLt n;gð ÞRt ð9Þ s0n;gð ÞLt > s 0 n;gð Þ;Rt if wn¼ 1 s0n;gð ÞLt < s 0 n;gð Þ;Rt if wn¼ 1 2 4 ð10Þ sn;gðD1Þ ¼ Tn;gð1Þ þ Tn;gð4Þ =2 sn;gðD2Þ ¼ Tn;gð2Þ þ Tn;gð3Þ =2 2 4 ð11Þ Difd¼ s n;gðD1Þ sn;gðD2Þ ð12Þ
s0n;gðD1Þ> s 0 n;gðD2Þ; if wn¼ 1 s0n;gðD1Þ < s 0 n;gðD2Þ; if wn¼ 1 2 4 ð13Þ
The Eq.7of energy differentiation calculation process could be replaced by Eq.14if the differentiation direction is horizontal and Eq.15if the direction is diagonal as follows:
E T n;gð jÞ j¼ 1; 3 Wn¼ 1 ¼ Tn;gð jÞ þΔ2 ; if sn;gð Þ ¼ sLt n;gð ÞRt Tn;gð jÞ ; if sn;gð ÞLt > sn;gð Þ and difRt hΔ Tn;gð jÞ þΔdifh 2 ; if sn;gð ÞLt > sn;gð Þ and difRt h < Δ Tn;gð jÞ þdifh2þΔ ; if sn;gð ÞLt < sn;gð ÞRt 8 > > < > > : E T n;gð jÞ j¼ 2; 4 Wn¼ 1 ¼ Tn;gð jÞ Δ2 ; if sn;gð Þ ¼ sLt n;gð ÞRt Tn;gð jÞ ; if sn;gð ÞLt > sn;gð Þ and difRt hΔ Tn;gð jÞ Δdifh 2 ; if sn;gð ÞLt > sn;gð Þ and difRt h < Δ Tn;gð jÞ difhþΔ 2 ; if sn;gð ÞLt < sn;gð ÞRt 8 > > < > > : E T n;gð jÞ j¼ 1; 3 Wn¼ 1 ¼ Tn;gð jÞ Δ2 ; if sn;gð Þ ¼ sLt n;gð ÞRt Tn;gð jÞ ; if sn;gð ÞLt < sn;gð Þ and difRt hΔ Tn;gð jÞ Δdif2 h ; if sn;gð ÞLt < sn;gð Þ and difRt h < Δ Tn;gð jÞ difh2þΔ ; if sn;gð ÞLt > sn;gð ÞRt 8 > > < > > : E T n;gð jÞ j¼ 2; 4 Wn¼ 1 ¼ Tn;gð jÞ þΔ2 ; if sn;gð Þ ¼ sLt n;gð ÞRt Tn;gð jÞ ; if sn;gð ÞLt < sn;gð Þ and difRt hΔ Tn;gð jÞ þΔdifh 2 ; if sn;gð ÞLt < sn;gð Þ and difRt h < Δ Tn;gð jÞ þdifh2þΔ ; if sn;gð ÞLt > sn;gð ÞRt 8 > > < > > : 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 ð14Þ E T n;gð jÞ j¼ 1; 4 Wn¼ 1 ¼ Tn;gð jÞ þΔ2 ; if sn;gðD1Þ ¼ sn;gðD2Þ Tn;gð jÞ ; if sn;gðD1Þ> sn;gðD2Þ and difdΔ Tn;gð jÞ þΔdif2 d ; if sn;gðD1Þ> sn;gðD2Þ and difd < Δ Tn;gð jÞ þdifd2þΔ ; if sn;gðD1Þ < sn;gðD2Þ 8 > > < > > : E T n;gð jÞ j¼ 2; 3 Wn¼ 1 ¼ Tn;gð jÞ Δ2 ; if sn;gðD1Þ ¼ sn;gðD2Þ Tn;gð jÞ ; if sn;gðD1Þ> sn;gðD2Þ and difdΔ Tn;gð jÞ Δdifd 2 ; if sn;gðD1Þ> sn;gðD2Þ and difd < Δ Tn;gð jÞ difd2þΔ ; if sn;gðD1Þ < sn;gðD2Þ 8 > > < > > : E T n;gð jÞ j¼ 1; 4 Wn¼ 1 ¼ Tn;gð jÞ Δ2 ; if sn;gðD1Þ ¼ sn;gðD2Þ Tn;gð jÞ ; if sn;gðD1Þ < sn;gðD2Þ and difdΔ Tn;gð jÞ Δdif2 d ; if sn;gðD1Þ < sn;gðD2Þ and difd < Δ Tn;gð jÞ difdþΔ 2 ; if sn;gðD1Þ> sn;gðD2Þ 8 > > < > > : E T n;gð jÞ j¼ 2; 3 Wn¼ 1 ¼ Tn;gð jÞ þΔ2 ; if sn;gðD1Þ ¼ sn;gðD2Þ Tn;gð jÞ ; if sn;gðD1Þ < sn;gðD2Þ and difdΔ Tn;gð jÞ þΔdifd 2 ; if sn;gðD1Þ < sn;gðD2Þ and difd < Δ Tn;gð jÞ þdifd2þΔ ; if sn;gðD1Þ> sn;gðD2Þ 8 > > < > > : 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 ð15Þ Even it is possible that an attacker can evaluate the difference between block coefficients to guess the watermarked bit if the tree decomposition structure is available through cryptanalysis approach of [4], DEED can resist such cryptanalysis attacks since the best differential direction among blocks are different. That is, the best differential directions among blocks are chosen based on the watermark bit and the
coefficient energy difference. Therefore, such dynamic selection provides the flexibility during the embedding. However, DEED will try to avoid the situation when all 6 blocks are decreased or increased in only one direction and the attackers might be able to compare with all other trees to extract the watermark bits and try to modify the tree coefficients to remove the watermark information.
Under such consideration, a more sophisticated design of watermarking is deployed during the embedding. A random number generator will be applied to select which group will embed the watermark bit wnand the others will embed bit -wn. For example, if g=1,2,4 are selected for treeΤn to embed bit wn, group 3,5 will embed bit -wn. Such arrangement will confuse the attackers since they can not find consistent embedding direction and no way to extract or remove the watermarks.
2.2 The watermark extraction of DEED
To extract the watermark from wavelet trees, the DEED algorithm must get the 6 possible outcomes of watermark bit w0n from block 1 to block 6 for reconstructed wavelet tree T0n After the information is collected, DEED can determine the final value of w0n from the 6 outcomes. If D[.] means the process of watermark extraction, we extract the possible w0n from block 1 as follows:
qnð1Þ ¼ T 0 nð1Þ mod S ð16Þ D T0nð1Þ h i ¼ 1 ; if qj nð1Þj< T1þT2 2 þ1 ; if qj nð1Þj T1þT2 2 ð17Þ We then need to extract the embedding information from block 2–6 by comparison of differentiation direction and coefficient energy. If d(Τn,g)=0,1,2 means the differentiation direction is vertical, horizontal or diagonal of block g inΤn, the equations of watermark extraction as follows: D T0n;g h i ¼ 1 ; if s 0 n;gðUrÞ s 0 n;gð Þ and d TLr n;g¼ 0 1 ; if s0n;gðUrÞ < s0 n;gð Þ and d TLr n;g¼ 0 ( D T0n;g h i ¼ 1 ; if s 0 n;gð Þ sLt 0 n;gð Þ and d TRt n;g¼ 1 1 ; if s0n;gð ÞLt < s0n;gð Þ and d TRt n;g¼ 1 ( D T0n;g h i ¼ 1 ; if s 0 n;gðD1Þ s 0 n;gðD2Þ and d Tn;g ¼ 2 1 ; if s0n;gðD1Þ < s 0 n;gðD2Þ and d Tn;g ¼ 2: ( 2 6 6 6 6 6 6 6 6 6 4 ð18Þ
From multi-resolution transform point of view, the location of watermarked coefficients in different wavelet level will play different importance during the image reconstruction. Therefore, the watermarked bits extracted from 6 blocks in each tree can not be treated equally during the watermark bit verification. How to get the appropriate weighting is another issue needed to be addressed.
Since the sensitivity of human vision is different from various spatial frequencies (frequency subbands), the HVS (Human Visual System) study is the key factor to provide a better understanding of visual effect and the imperceptibility of the watermarked image. For that reason, the watermarked coefficients of different wavelet level will affect the contrast sensitivity. Therefore, DEED has adopted the contrast sensitivity function (CSF) of the HVS from [7] to determine the accurate weighing values for different wavelet levels.
For watermarked images, there has been a need for good metrics for image quality that incorporates properties of the HVS. The visibility thresholds of visual signals are studied by psychovisual measurements to determine the thresholds. These measurements were performed on sinusoidal gratings with various spatial frequencies and orientations by given viewing conditions. The purpose of such study was to determine the contrast thresholds of gratings by the given frequency and orientation. Contrast as a measure of relative variation of luminance for periodic pattern such as a sinusoidal grating is given by the equation
C¼ Lð max LminÞ= Lð maxþ LminÞ ð19Þ where Lmaxand Lminare maximal and minimal luminance of a grating. Reciprocal values of contrast thresholds express the contrast sensitivity (CS), and Mannos and Sakrison [11] originally presented a model of the contrast sensitive function (CSF) for luminance (or grayscale) images is given as follows:
Hð f Þ ¼ 2:6* 0:0192 þ 0:114*fð Þ*e 0:114ð *fÞ1:1 ð20Þ where f ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffif2
x þ fy2 q
is the spatial frequency in cycles/degree of visual angle ( fx and fy are the spatial frequencies in the horizontal and vertical directions, respectively). Figure 3
depicts the CSF curve which characterizes luminance sensitivity of the HVS as a function of normalized spatial frequency and the knowledge from CSF can be used to develop a HVS dependent model. Therefore, CSF masking [2,7,11,14,15,20] is one way to apply the CSF in the discrete wavelet domain. CSF masking refers to the method of weighting the wavelet coefficients according to their perceptual importance. To apply the CSF in the DWT domain, CSF masking is employed and refers to the method of weighting the wavelet coefficients relative to their perceptual importance [14,15]. The weights of wavelet coefficient under CSF perceptual importance are shown for each subband in Fig.1.
If the wavelet tree is constructed by coefficients in HL or LH subband, the judgment value w0nis determined as follows:
w0n¼ D Th 0nð1Þi 3:55 þ D Th n;10 i 5:3 þ D T h 0n;2iþ D Th 0n;3iþ D Th 0n;4iþ D Th n;50 i 4:74
ð21aÞ
If the wavelet tree is constructed by coefficients in HH subband, the judgment value wnis determined as follows: w0n¼ D Th 0nð1Þi 3:48 þ D T0 n;1 h i 7:2 þ D T0 n;2 h i þ D Th 0n;3iþ D Th 0n;4iþ D Th 0n;5i 3:75 ð21bÞ Finally we will get the extracted watermark bit w0 0n from w0n as follows:
Wn0 0¼ 1; w 0 n 0 1; w0n < 0: ð22Þ To quantify the existence of the watermark after all watermark bits are extracted from the decoder, the normalized correlation (NC) coefficient [3] will be examined in order to identify the existence of the watermark. The formula of normalized correlation coefficient is as follows:
r W ; Wð 00Þ ¼ PNw n¼1 wnw 0 0 n ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PNw n¼1 w2 n P n¼1 w0 02 n s ¼ PNw n¼1 wnw 0 0 n Nw ð23Þ
The coefficient value is within−1 and 1. The existence decision is “yes” if r W; Wð 00Þ rT and “no” if r W; Wð 00Þ< rT. The thresholdρTis chosen based on the probability of false positive error Pfpwhich is computed by [8]:
PfP¼ XNw n¼ Nd w rðTþ1Þ=2e Nw n PNwn E 1 Pð EÞn ð24Þ
The estimation of the probability of a false positive (i.e., false watermark detection) is analyzed as following [8]:
We define the probability of false watermark detection as Pfp¼ P r W ; eW
rTjno watermark
n o
ð25Þ where P{A|B}is the probability of event A given event B, W is the given watermark and eW is the extracted one. Since W(n) and eWðnÞ are either one or negative one, and subsequently W2ðnÞ ¼ eW2ðnÞ ¼ 1. Let PE be the probability of bit error during extraction. A bit error occurs when WeðnÞ 6¼ W ðnÞ or more specifically, when eWðnÞ ¼ W ðnÞ (since WðnÞ; eWðnÞ 2 1; 1f g). If we let kðnÞ ¼ W ðnÞ eWðnÞ, then k(n)=−1 indicates a bit error and k(n)=1 indicates no error. We may rewrite the expressions forρ and Pfpin terms of k(n) as
r W ; eW ¼ PNw n¼1 WðnÞ eWðnÞ Nw ¼ PNw n¼1 kðnÞ Nw ð26Þ and Pfp¼ P XNW n¼1 kðnÞ NwrTjno watermark ( ) ; ð27Þ
Since k(n)∈ {−1,1}, it can be shown thatPkðnÞ must take on discrete values from the set Nw; Nwþ 2; Nwþ 4; . . . ; Nw 4; Nw 2; Nw
f g, or PkðnÞ ¼ Nwþ 2m, where
m=0,1,..., Nw. Thus, we find that
Pfp¼ P PNW n¼1 kðnÞ NwrTjno watermark ¼ P NW m¼ Nd wðrTþ1Þ=2e PfPkðnÞ ¼ Nwþ 2m no watermarkj g; ð28Þ
Where PfPkðnÞ ¼ Nwþ 2m no watermarkj g is the probability that the series { k(n) } contains m ones and Nw-m negative ones. Since
P
kðnÞ ¼ Nwþ 2m NwrT and 2m NwrT þ Nw, m’s range is from Nd wðrT þ 1Þ=2e to Nw. Therefore,
P XkðnÞ ¼ Nwþ 2m no watermarkj n o ¼ Nw m PNwm E 1 Pð EÞm ð29Þ
Where PEis the probability that k(n)=−1 and Nw
m
¼ Nw!
m! Nð wmÞ!. Since we are given that no
watermark is embedded, we can assume that extracted mark eW consists of a series of random independent equally probable values from the set {−1,1}. Thus, PE=0.5. Substituting into Eqs.28and29, Pfp¼ XNW m¼ Nd wðrTþ1Þ=2e Nw m 0:5Nw ð30Þ
Given the reasonable assumption, PE=0.5 and Nw=512 as the watermark length, Pfpwill be as low as 4.5×10−4, 3.86×10−6and 8.45×10−9whileρT=0.15, 0.20 and 0.25 respectively. That means the appropriate ρT will be selected to meet the requirement given a false positive probability.
2.3 The complete algorithms of DEED
The complete design of the proposed algorithm is summarized as following: 2.3.1 DEED watermark embedding
1) Generate a seed by mapping a signature/text through a one-way deterministic function. Obtain a PN sequence W of length Nwusing the seed k.
2) Compute wavelet coefficients of a host image. Group the coefficients to form trees. 3) Randomly arrange the trees using some pseudorandom generator and each tree is
divided into 6 blocks. The block 1 has 1 coefficient in level 4 and block 2–6 has 4 coefficients in level 2 or level 3. The coefficient of block 1 inΤnis represented asΤn(1) and the jth coefficient of block 2–6 is represented as Τn,g(j) for g = 1 to 5. 4) FOR EACH watermark bit wn(n=0 to Nw- 1) DO
a) Select the modular value S and calculate theΤn(1) with Eq.1,2.
b) Find the suitable differentiation direction of Τn,g for g=1 to 5 from Eq. 3 and modify the energy with Eq.4–7if direction is vertical, Eq.8–10,14if direction is
horizontal, and Eq.11–13,15if direction is diagonal. A random number generator using the seed k will be applied to select certain groups to embed watermark bit wn and the others to embed - wn. The information of differentiation direction list for each tree blocks will be kept as a secret key.
c) Record the differentiation direction ofΤn,g.
5) Arrange back the modulated trees to their original positions.
6) Pass the modified wavelet coefficients through the inverse DWT to obtain a watermarked image.
2.3.2 Note
1) The watermark W is a binary PN sequence of ±1.
2) The maximal length of watermark=the number of trees. If the test image is 512×512, the maximum length of the watermark=3072.
2.3.3 DEED watermark extraction
1) Generate a seed by mapping a signature/text through a one-way deterministic function. Obtain a PN sequence W of length Nwusing the seed k.
2) Compute wavelet coefficients of a host image. Group the coefficients to form trees and arrange the trees using the same generator and the private key for the information of differentiation direction list.
3) FOR EACH watermark bit wn(n=0 to Nw− 1) DO
a) Using modular value S and T0nð1Þ to calculate the D Th 0n;gð1Þiwith Eq.16,17
b) Get the differentiation directions of T0n;gand determine the D T 0 n;g
h i
with (18) for g=1 to 5. If -wnhas been embedding for certain group g, D T
0 n;g
h i
¼ D T0n;g
h i
c) Calculate the judgment value w0nby (21a) and (21b). IF w 0n 0THEN w0 0n =−1 ELSE w0 0n =1
4) Compute the normalized correlationρ.
5) Ifρ is above the threshold ρT, the watermark W exists; otherwise, it does not exist.
2.4 DEEDRwatermarking
Since the information of differentiation direction list must be kept secret which addresses extra storage space is needed, DEED may be categorized as a non-blind watermarking scheme. Therefore, DEED has the weakness that if the differentiation direction information is lost or damaged, we could not calculate the value of extracted watermark bit w0 0n.
In view of this, we propose a revised method to make DEED more flexible. Since we use some pseudorandom generator to randomly arrange the trees in step (3) of DEED watermark embedding procedure, we can obtain the order value of each tree. Then we can use the order value of each tree as a new pseudorandom generator to
enforce the random direction of this tree and it is called DEEDR (R means random direction differentiation).
The pseudo code procedures are as follows:
Where d(Τn,g) is the differentiation direction of the gth block in treeΤn.
In the mean time, the random number generator applied in step (4) of DEED watermark embedding procedure will be applied for DEEDR to select which group will embed the watermark bit wnand the others will embed -wnfor each treeΤnin order to counteract the cryptanalysis attack for DEEDR.
During the watermark extraction step, we can use the same way to determine the differentiation direction of each block in each tree from the order value of each tree that the trees are arranged using the same pseudorandom generator. Therefore, the DEEDR algorithm is then designed which doesn’t need the extra information for watermark extraction, and DEEDRis a truly blind watermarking scheme.
The complete design of DEEDRembedding and extraction is summarized as following: 2.4.1 DEEDRwatermark embedding
1) Same procedures of steps (1)–(3) from DEED Watermark Embedding. 2) FOR EACH watermark bit wn(n=0 to Nw− 1) DO
a) Select the modular value S and calculate theΤn(1) with Eq.1,2.
b) Use the order value n as a seed to generate a random value and make this value divided by 3 to determine the forced differentiation direction ofΤn,gfor g=1 to 5 as shown in Eg. (25).
c) Modify the energy with Eq.4–7if direction is vertical, Eq.8–10,14if direction is horizontal, and Eq.11–13,15if direction is diagonal. A random number generator based on the seed k will be applied to select certain groups to embed watermark bit wn and the others to embed - wn.
3) Same procedures of steps (5)–(6) from DEED Watermark Embedding.
2.4.2 DEEDRwatermark extraction
1) Same procedures of steps (1) from DEED Watermark Extraction.
2) Compute wavelet coefficients of a host image. Group the coefficients to form trees and arrange the trees using the same generator.
3) FOR EACH watermark bit wn(n=0 to Nw− 1) DO
a) Using modular value S and T0nð1Þ to calculate the D T0nð1Þ
with Eq.16,17. b) Use the order value n as a seed to generate a random value and make this value
divided by 3 to get the forced differentiation direction of T0n;g.for g=1 to 5. c) Apply Eq. 18 to determine the D T0n;g
h i
. If -wn has been embedding for certain groups, D T0n;g
h i
¼ D Th 0n;gi.
d) Calculate the judgment value w0nby (21a) and (21b). IF w 0n 0THEN w0 0n =−1 ELSE w0 0n =1
4) Same procedures of steps (4)–(5) from DEED Watermark Extraction.
3 Experiments and discussion
To evaluate the performance of the proposed method, the 512 × 512 Lena, Goldhill and Peppers images with 8 bits/pixel resolution are used for watermarking. In order to make the fair comparison, all the watermarked images will be set at the same PSNR values shown as in [19] of WTQ algorithm since it is the typically representative wavelet tree based approach. The wavelet filters used in this study for the wavelet tree watermarking is the CDF 9/7 filters [6] which are also used in WTQ. We employ a four-level wavelet transform and a watermark sequence of length 512. In order to compare the performance with the WTQ and WTGM schemes, Lena, Goldhill and Peppers are set at the same PSNR values of 38.2, 38.7 and 39.8 dB from [19] respectively while S of Eq.1is set at 48 andΔ applied in Eq.7,14,15is equal to 10. With watermark length Nw=512, the threshold ρTis chosen to be 0.23 for a false positive probability of 1.03×10−7. All the results from common image processing attacks, geometric attacks and security measure are tabulated in Table1(a), (b)and(c)respectively for Lena, Goldhill and Peppers. Those attacks are selected based on the fact that WTQ has tabulated in [19] so we can make the fair comparison. In addition, WTGM considers the tree grouping information globally but ABW-TMD only locally and the listed results from ABW-TMD is not as good as WTGM [16,17]. Therefore, we will only compare DEED, DEEDRwith WTGM and WTQ in this study.
3.1 Common image processing attacks 1) JPEG Compression Attacks
In this experiment, we perform JPEG compression with different quality factors (QF) on the watermarked image. The extracted results and NC values are depicted in Table 1. Figure 4(a, b) illustrate the JPEG compressed Lena image for visual comparison. From these results, we can see that the proposed algorithm for DEED and DEEDRis robust to
JPEG compression. For all cases, the extracted watermarks are with relatively high-NC values and the results are also better than two settings of WTGM(S1) and WTGM(S2). Even for the case that QF is equal to 30, we can still detect the embedded watermark but WTQ is failed for Lena and Goldhill image.
2) SPIHT Compression Attacks
SPIHT (Set Partitioning in Hierarchical Trees) [12] is an image compression algorithm that exploits the inherent similarities across subbands in a wavelet decomposition of an image. It implies uniform quantization and bit allocation applied after wavelet decomposition. Table 1 shows the extracted NC values and corresponding PSNR values between original image and attacked image. From these results, we can see that the proposed algorithm can tolerate the incidental distortions induced by high-quality SPIHT compression. The performance of DEED and DEEDRis still better than WTGM for the testing images. 3) Spatial-Domain Image Processing Attacks
Several spatial-domain image processing techniques, including median filtering, Gaussian filtering and sharpening performed on the watermarked image and the results are also shown in Table 1. Figure 4(c) shows a medium filter attacked image for visual result. For all cases, DEED and DEEDRalgorithms outperform the WTQ scheme with high normalized correlation values in all cases and watermark information therein can be successfully recognized. In addition, DEED based methods are comparable with WTGM for all cases.
3.2 Geometric attacks
1) Pixel Shifting Attacks (Circular Shift)
This kind of attacks is done by shifting the pixels circularly. Here, we shift the pixels to the left. From Table1, DEED based algorithms can detect the watermark but WTGM(S1) is unable to resist such attack for Lena and Peppers images.
2) Rotation Attacks (Rotation and Scaling)
The attack is done by rotating the image by a small angle, scaling the rotated image, and cropping the scaled image to the original image size. StirMark [13] software is adopted here for this attack since it provides the described testing functions. This rotation and scaling is a geometrical attack in the spatial domain and an illustration of the operation is demonstrated in Fig.5. From Table1, WTGM has better performance than DEED based algorithms but they all outperform WTQ while the rotation degree is up to 0.75°.
Regarding the geometric attacks, WTGM(S2) performs well and it is necessary to discuss its characteristics. WTGM(S1) uses coefficient number 1~21 corresponding to relatively low-frequency components (level 2, 3 and 4 of DWT in Fig.1) for watermarking, which is the same as the WTQ and DEED schemes. On the other hand, WTGM(S2) uses coefficient number 6~85 corresponding to relatively high-frequency components (level 1 and 2 of DWT in Fig.1). Therefore, WTGM(S1) can be more effective in resisting JPEG and SPIHT compression but WTGM(S2) with medium-high frequency setting is superior to resist geometric distortion. Even DEED still performs better than WTGM(S1), it is the future research for DEED to adopt S2settings and verify whether it can improve its capability for geometric attacks while more high frequency components are associated with watermark
T able 1 Perfo rmance summ ary of DEED, DEED R , WTGM (S1 ), WTG M( S2 ) and WTQ scheme s for (a) LENA (b) Goldhi ll and (c) Peppe rs imag es Oper ations DEED DEED R WTGM (S1 ) WTGM (S2 ) WTQ (a) [Signa l P rocessing A ttacks] JPEG (QF = 90% ) 1.00 1.00 1.00 1.00 1.00 JPEG (QF = 50% ) 1.00 1.00 0.98 0.94 0.26 JPEG (QF = 30% ) 1.00 1.00 0.94 0.77 0.15 SPIHT (bitr ate = 0.7) 1.00 1.00 1.00 1.00 0.85 SPIHT (bitr ate = 0.5) 1.00 1.00 0.99 0.99 0.85 SPIHT (bitr ate = 0.3) 1.00 0.93 0.96 0.77 0.21 Med ian Filtering (4 × 4) 0.94 0.86 0.56 0.57 0.23 Gaus sian Filte ring 0.72 0.59 0.46 0.68 0.64 Sharp enin g 0.98 0.98 0.63 1.00 0.46 [Geometric Attac ks] Pixel Shifting (6 pixe ls) 0.23 0.24 0.14 0.89 0.34 Ro tation (0.75° ) 0.36 0.27 0.33 0.90 0.26 [Sec urity Measur ement] Multip le W ate rmarking (4 wate rmarks) 1.00 (31. 3dB) 0.67 (31. 1dB) 0.62 (31. 52dB) 0.59 (26.81d B) 0.1 1 (28. 05 dB ) Multip le W ate rmarking (8 wate rmarks) 1.00 (29. 4dB) 0.56 (29. 2dB) 0.15 (24. 46dB) 0.73 (29.81d B) N/A Bitp lane Remov al (5 bitpla nes) 0.98 (33. 6dB) 0.88 (33. 2dB) 0.78 (32. 74dB) 0.88 (33.52d B) 0.1 1 (18. 47 dB ) (b) [Signa l P rocessing A ttacks] JPEG (QF = 90% ) 1.00 1.00 1.00 0 1.00 1.00 JPEG (QF = 50% ) 1.00 1.00 0.99 0.99 0.71 JPEG (QF = 30% ) 1.00 1.00 0.95 0.92 0.23 SPIHT (bitr ate = 0.7) 1.00 1.00 1.00 1.00 0.35 SPIHT (bitr ate = 0.5) 1.00 0.98 0.99 0.97 0.23
SPIHT (bitr ate = 0.3) 0.99 0.88 0.94 0.87 − 0.06 Med ian Filtering (4 × 4) 0.94 0.85 0.65 0.52 0.24 Gaus sian Filte ring 0.80 0.75 0.58 0.80 0.56 Sharp enin g 0.99 0.98 0.79 1.00 0.39 [Geometric Attac ks] Pixel Shifting (6 pixe ls) 0.27 0.26 0.28 0.90 0.35 Ro tation (0.75° ) 0.33 0.28 0.43 0.89 0.21 [Sec urity Measur ement] Multip le W ate rmarking (4 wate rmarks) 1.00 (31. 9dB) 0.71 (31. 5dB) 0.74 (31. 24dB) 0.71 (29.87d B) 0.18 (28.57d B) Multip le W ate rmarking (8 wate rmarks) 1.00 (30. 0dB) 0.58 (29. 7dB) 0.14 (24. 58dB) 0.20 (28.28d B) N/A Bitp lane Remov al (5 bitpla nes) 1.00 (32. 2dB) 0.84 (31. 9dB) 0.93 (31. 70dB) 0.88 (31.21d B) 0.14 (16.18d B) (c) [Signa l P rocessing A ttacks] JPEG (QF = 90% ) 1.00 1.00 1.00 1.00 1.00 JPEG (QF = 50% ) 1.00 1.00 0.94 0.63 0.70 JPEG (QF = 30% ) 1.00 0.99 0.83 0.49 0.34 SPIHT (bitr ate = 0.7) 1.00 1.00 0.98 1.00 0.85 SPIHT (bitr ate = 0.5) 1.00 1.00 0.99 0.98 0.65 SPIHT (bitr ate = 0.3) 0.99 0.92 0.93 0.64 0.36 Med ian Filtering (4 × 4) 0.96 0.91 0.56 0.40 0.25 Gaus sian Filte ring 0.71 0.67 0.36 0.42 0.74 Sharp enin g 1.00 0.98 0.55 0.99 0.62 [Geometric Attac ks] Pixel Shifting (6 pixe ls) 0.29 0.25 0.18 0.86 0.34 Ro tation (0.75° ) 0.28 0.23 0.27 0.81 0.26 [Sec urity Measur ement] Multip le W ate rmarking (4 wate rmarks) 1.00 (32. 8 d B ) 0.73 (32. 37 dB ) 0.75 (32. 45dB) 0.64 (29.96d B) 0.22 (28.81 dB) Multip le W ate rmarking (8 wate rmarks) 1.00 (30. 87 dB ) 0.57 (30. 52 dB ) 0.22 (24. 41dB) 0.40 (29.18d B) N/A Bitp lane Remov al (5 bitpla nes) 0.98 (33. 98 dB ) 0.49 (33. 66 dB ) 0.73 (33. 42dB) 0.59 (33.39d B) 0.14 (16.93 dB)
embedding. On the other hand, it is for sure that S2settings for DEED will dramatically increase its complexity.
3.3 Security measurement 1) Multiple Watermarking
For algorithms well-known to all, the attacker may apply one or more watermarks using the same wavelet tree group modulation technique in an attempt to disturb the detector or to destroy the embedded watermark. Figure6shows an illustration of Goldhill image which is inserted by 5 watermarks. More watermarks are in the image, more image quality will be affected. However, DEED based algorithms achieve high correlation values for multiple watermark attacks. From Table 1, DEED and DEEDR have superior performance than WTGM and WTQ for up to 8 multiple watermarks.
2) Bitplane Removal
Bitplane removal is one of the major strategies used to defeat the WTQ scheme. We perform this attack designated on the embedded subbands, which reduces the impact on watermarked images. Figure 4(d) shows an illustration of Lena image where 5 lowest
Fig. 4 a Original watermarked Lena image by DEEDRb JPEG compressed Lena image with QF=40%,
PSNR=33.49dB andρ=1 c 4×4 Median Filter attacked Lena image with ρ=0.86 d The attacked Lena image
bitplanes in the wavelet domain are removed. Table 1 shows that the DEED based algorithms and WTGM can resist 5 bitplanes removed but WTQ can not.
3.4 Complexity of DEED with human vision system
The computation complexity of DEED is low from the view of mathematical analysis. The whole complexity should be discussed for wavelet transform, CSF and decision calculation respectively. Suppose the synthesis filters are h (low-pass) and g (high-pass) for wavelet transform. Take |h|=2N, |g|=2M, and assume M≥N. The cost of the standard algorithm for CDF 9/7 filters is 4(N+M)+2 and could be speeded up by the lifting algorithm in [6] to 2(N+M+2). The computation of wavelet transform is linear time mathematics.
On the other hand, CSF masking is employed to apply the CSF in the DWT domain and the associated perceptual weighting function can be pre-calculated for each subband as shown in Fig.1. Therefore, the complexity of CSF implementation in DEED becomes the coefficient multiplication from the look-up table. This can be efficiently done in linear-time. The watermark decision procedure for Eq.4–15 and Eq.16–21b is pure add, subtract and comparison which can be done in linear time. From our simulation, the whole loop of
a
b
Fig. 5 An illustration of rotation and scaling attack for the Goldhill image. a counter clockwise rotation and scaling b clockwise rotation and scaling
Fig. 6 a Original Goldhill image b 5 watermarks are inserted into Goldhill by DEED.
DEED and DEEDR embedding and extraction under Intel Pentium 3.2G Hz, 1G RAM desktop computer will need less than 1 s to complete for 512×512 testing images.
Unlike the group strategy of sum-of-subsets in WTGM, it is essentially a known NP-complete problem [5]. Therefore, its complexity is higher than DEED and DEEDR. In conclusion, the DEED and DEEDRcomplexity is low and suitable for practical applications based on the mathematical analysis and simulation results.
3.5 Summary
DEED, DEEDR and WTGM algorithms apply the positive and negative modulation to embed the watermark within the trees. Therefore, the cryptanalysis-like attack for WTQ is not useful to remove the watermark for DEED and WTGM. From the outcomes in Table1, the tabulated results also disclose DEED and DEEDRare superior to WTGM and WTQ in almost all categories with significant high PSNR values. Since high PSNR has positive correlation with better image quality, the CSF human visual system applied in DEED and DEEDRshows accurate weighting and visual characteristics.
In fact, DEED utilizes the best coefficient energy differentiation direction of the embedded watermark bit that makes minimal change of coefficient’s energy within the tree. However, the weakness of DEED is that the differentiation direction information should be recorded and extra storage of side information is required as the WTGM or ABW-TMD does, it can not be categorized as the blind watermarking approach which will be unsuitable in practical applications. In addition, non-blind watermarking can essentially perform better than non-blind schemes since extra information can be preserved in the side information. There are apparent results from Table 1 where non-blind schemes like DEED, WTGM perform better than WTQ. Since such kind of comparison is not fair, a random direction differentiation approach called DEEDRis then devised which is a truly blind watermarking technique with high robustness against attacks. In summary, DEED is better than DEEDR since random direction differentiation doesn’t guarantee the best choice among selections. Nevertheless, there are vulnerabilities for DEED and WTGM. For example, DEED needs to record the tree structure and the modulation direction information where WTGM must keep the tree combination information secret which addresses extra storage space. Even it is possible to design a random grouping approach for WTGM, the affected coefficients will be significant (whole tree instead of blocks in DEED) and results very low image quality. The extended study should working on the design to efficiently reduce this extra cost. At the present time, DEEDRis the best choice since it doesn’t need the side information during the watermark extraction which is the truly blind watermarking approach.
In this study, we focus on the same decomposition structure for different wavelet tree watermarking algorithms. On the other hand, it is also possible to consider different decomposition level for DEED. For most of the wavelet tree watermarking architecture, it is pretty common to adopt 4 levels of decomposition (the S1setting as shown in Fig.1) which results only one coefficient existing in the Level 4 as shown in Fig.1for 512×512 images. Therefore, four level wavelet decomposition is the maximum possible decomposition structure for 512×512 images and DEED with DEEDR can only apply quantization approach to embed the watermark bit since there is one component left for embedding. For coefficients located at other levels, there are enough components (at least 4 coefficients) to choose the differentiation direction for watermark embedding. In the manner of alternatives, fewer level of wavelet decomposition has been discussed in Section3.2where WTGM(S2) format (coefficients in level 1 and level 2) are investigated for watermark embedding. From experimental results of Table 1, it is clear such decomposition structure for WTGM can
have better robustness against pixel shifting, rotation of geometric attacks even it is less resistant to JPEG, SPIHT compression and multiple watermarking attacks. The reason is apparent since more medium-high frequency components in S2are adopted for watermark embedding compared with the setting of S1. Even it is the future study for DEED to adopt S2settings and verify whether it can improve its capability for geometric attacks while more high frequency components are associated with watermark embedding, the results can be predicted based on the previous studies of WTGM that S2 settings for DEED will dramatically increase its complexity.
In addition, the maximum length of the watermark for DEED based algorithm is 3072 for the 512×512 image but the maximum length of the watermark for WTGM and ABW-TMD is 1536. On the other hand, the maximum length of the watermark for WTQ is only 768. Therefore, we can find the DEED based algorithms can contain much longer watermark bit length which increases the security level in practical applications.
4 Conclusion
The human vision system based tree energy differentiation (DEED) watermarking algorithms have been presented in this study. Compared with other watermarking schemes like WTGM and WTQ, the proposed algorithm can tolerate more common signal processing and geometric attacks. In addition, the human visual characteristics are considered for better performance in watermark extraction. Regarding the cryptanalysis of the algorithm, the algorithm can be public with the keys remained private for DEED and totally blind detection for DEEDRalgorithm.
Compared with the WTGM, ABW-TMD and WTQ scheme, the advantages of the proposed DEED algorithms are as follows:
1) The proposed algorithm can tolerate more common signal processing and geometric attacks with superior performance.
2) The length of the image key is large, which renders a better confusion/diffusion for security.
3) The human visual characteristics are considered in the wavelet tree watermarking systems to provide the better visual quality.
Acknowledgments The author would like to thank the anonymous reviewers with their valuable comments to improve the quality of this manuscript and Bai-Jiun Chen at National Chiao Tung University who helps to write the programs for software experiments. This work is partially supported by the National Science Council in Taiwan, Republic of China, under Grant NSC96-2416-H009-015, NSC97-2410-H009-034 and 99-2918-1-009-008.
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Min-Jen Tsai received the B.S. degree in electrical engineering from National Taiwan University in 1987, the M.S. degree in industrial engineering and operations research from University of California at Berkeley in 1991, the engineer and Ph.D. degrees in Electrical Engineering from University of California at Los Angeles in 1993 and 1996, respectively. He served as a second lieutenant in Taiwan army from 1987 to 1989. From 1996 to 1997, he was a senior researcher at America Online Inc. In 1997, he joined the institute of information management at the National Chiao Tung University in Taiwan and is currently an associate professor. His research interests include multimedia system and applications, digital right management, digital watermarking and authentication, digital forensic, enterprise computing for electronic commerce applications. Dr. Tsai is a member of IEEE, ACM and Eta Kappa Nu.
![Fig. 3 Luminance CSF [ 7 ]](https://thumb-ap.123doks.com/thumbv2/9libinfo/7589874.127289/9.659.98.589.572.924/fig-luminance-csf.webp)
