Dual image-based reversible data hiding method using neighboring pixel-value differencing
Ki-Hyun Jung Department of Cyber Security, Kyungil University, 50 Gamasil-gil, Hayang-eup, Gyeongsan-si, Gyeongbuk 38428, Republic of Korea
[email protected]
Abstract: Dual image-based reversible data hidings are recently proposed where dual copies of a cover image are used to embed the secret data. In this paper, a novel reversible data hiding method based on neighboring pixel-value differencing is proposed. The mean value of neighboring pixels and differenced values are used to decide the size of embedding bits in the sub-block. The receiver can extract the secret data and recover the cover image from dual stego-images. The experimental results show that the proposed method has a higher capacity and still a good image quality. Keywords: steganography, data hiding, pixel-value differencing, reversible
data hiding.
1. Introduction
The multimedia data like as images, audio, and video are distributed much simpler and faster as the rapid growth of the computer and Internet technology. However, it also causes substantial financial damages and
becomes an imperative issue of copyright protection. To prevent digital contents from being intercepted by unauthorized parties is a critical demand in information security. Data hiding is related to concealing the existence of a secret message while cryptography is about protecting the content of secret data [1]. It is categorized as data hiding and reversible data hiding method as the original object can be restored from the stego-object together with the secret data. The well-known data hiding methods are least significant bit substitution and pixel-value differencing method. The least significant bit substitution is a simple embedding scheme to hide the secret data in the cover image that replaces the least significant bits pixel with the secret bit stream per a pixel [2]-[8]. The pixel-value differencing method is based on the difference of neighboring pixels where the secret data can be embedded in the edge area than the smooth area [9]-[14]. In the reversible data hiding, difference expansion, histogram shifting, and prediction-error expansion in the spatial domain are generally used [18]-[29]. Tian proposed a reversible watermarking scheme based on difference expansion [18]. Ni et al. proposed a new lossless data hiding based on a histogram modification, where the zero or minimum points of the image histogram are utilized [21]. The higher pixel values are increased by one for the zero or minimum point in the histogram. Li et al. proposed a reversible data hiding scheme using pixel-value-ordering and prediction-error expansion [29]. For non-overlapped equal-sized blocks, the second largest/smallest value was used to predict the max and min values.
Then prediction-error expansion was used to embed the secret data. As a result, half of image pixels are modified by one. Recently, dual image-based reversible data hiding methods were introduced where two similar images were produced from the cover image [30]-[32]. Lee et al.βs method is based on combinations of pixel orientation to increase the embedding capacity and a base-5 notational system [30]. The pixel value is changed at most plus or minus one that provides a good image quality.
Qin
et al. proposed a reversible data hiding based on exploiting modification direction for the first stego-image and a adaptive modification is used to refer to the first stego-image [31]. Lu et al. proposed a dual image-based reversible data hiding method based on LSB matching [32]. The LSB matching method is used to the non-reversible data hiding method, but it was demonstrated the LSB matching method and the dual stego-images are possible to recover the cover image with the secret data. Although there are many methods related to the dual image-based reversible data hiding, there is still a room to have a high embedding capacity with a low distortion to the human visual system. In this paper, a novel reversible data hiding method using neighboring pixel-value differencing method is proposed. The pixel-value differencing method for neighboring pixel-pairs on the sub-block is used to embed the secret bits and the dual stego-images are used to recover the cover image.
The rest of this paper is organized as follows. In section 2, the pixel-value differencing method in data hiding and the dual image-based reversible data hiding method using the least significant bits matching are explained. The proposed method is described in section 3 and the experimental results are presented and discussed in section 4. Finally, the conclusions are presented in section 5.
2. Related Works
There are many previous works that utilize the pixel-value differencing in data hiding, but it is difficult to utilize in the reversible data hiding since the cover image cannot be recovered. In the proposed method, we introduce a new combination of the pixel-value differencing with the dual image-based reversible data hiding method. In this section, we describe the pixel-value differencing and dual image-based reversible data hiding method using LSB matching. In the PVD method [9], different bits of the secret data could be embedded according to the degree of smoothness or contrast for two consecutive pixels. Lu et al. proposed the LSB matching method to design a dual image-based reversible data hiding [32].
2.1 Pixel-Value Differencing Data Hiding Method Wu and Tsai proposed a high embedding capacity data hiding method using the pixel-value differencing where two consecutive pixels were used to decide the embedding bits on the sub-block. The difference value ππ = ππ+1 β ππ (β255 β€ ππ β€ 255) is calculated from two consecutive pixels ππ and ππ+1 respectively for the given 256 gray-valued cover image. The number of embedding bits n = log 2 (π’ β π + 1) can be obtained where the value of lower/upper bound in the range π
π+1 (i = 1, 2, ..., w) is given. Finally, the β² new difference (ππβ² , ππ+1 ) are calculated by Eq. (1) for m = ππβ² β ππ and ππβ²
= | π + π | where π is the integer value of the embedding bits.
π π (ππ β β β , ππ+1 + β β) if ππ is an odd number 2 2 β² (ππβ² , ππ+1 )={ π π (ππ β β β , ππ+1 + β β) if ππ is an even number 2 2
(1)
The example of the embedding secret bits is shown in Fig. 1. The gray values of two consecutive pixels are (60, 85). The difference value, ππ = 25 is located at from 23 to 54 in the range table ant the embedding bits n = 5 can be calculated. Assume that the leading embedding bits of the secret data are 100012 = 17. Finally, the new pixels (52, 92) of the sub-block are computed by Eq. (1) for the results of m = ππβ² β ππ = 40 β 25 = 15 and ππβ² = | π + π | = 23 + 17 = 40. In the extracting algorithm, the integer value of the embedded
β² secret bits, b = ππβ² β ππ = (ππ+1 β ππβ² ) β ππ = (92 β 52) β 23 = 17 is
calculated that could be derived from πiβ² = |ππ + π| during the embedding process.
2.2 Dual Image-based Reversible Data Hiding Method Lu et al. proposed a reversible data hiding method using LSB matching revisited technique which is used to non-reversible data hiding methods. The proposed method kept the modification rule table to enhance an image quality and reversibility. For the sub-block pixel pairs (pi, pi+1) and (pi+2, pi+3) of a cover image, the lowest bit of the first pixel is calculated and it is compared with the secret bit si by using the LSB matching method for each two pixel pairs. Next, the formula F(pi, pi+1 ) is used to determine the modified bit for two pixel pairs.
π
F(ππ , ππ+1 ) = πΏππ΅(β πβ + ππ+1 ) 2
(2)
Finally, the dual stego-images are generated as adjusting pixels through the modification rule table. For example, assume (pi, pi+1) = (44, 45), (pi+2, pi+3) = (37, 33) and secret bit stream s = 1011 00002 as shown in Fig. 2.
For the
first pixel pair (p1, p2) = (44, 45), the lowest bit value LSB(p1) = LSB(44) = 0 is calculated and is compared with s1=1. Since LSB(p1) β s1, F(44β1, 45) =
43
F(β β + 45) = F(21 + 45) = F(66) = 0 is obtained and F(44-1, 45) is equal 2 to s2 = 0. As a result, a first pixel pair (π1β² , π2β² ) = (44β1, 45) = (43, 45) is deduced. F(44β1, 45) = F(66) = 0 is also calculated for the secret bits s3s4 = 11 since the lowest bit value is LSB(p1) β s3. A second pixel pair (π1β² , π2β² ) = (44+1, 45) = (45, 45) is obtained because of F(44-1, 45) β s4. For the second pixel pair (p3, p4) = (37, 33) and s1s2 = 00, the lowest bit value LSB(p3) = 36
LSB(37) = 1 is calculated and then F(37β1, 33) = F(β 2 β + 33) = F(18 + 33) = F(51) = 1 is obtained since LSB(p1) β s1. Next F(37-1, 33) β s2, a first pixel pair (π3β² , π4β² ) = (36 + 1, 33) = (37, 33) is calculated for the second pixel pair. Since the lowest bit value LSB(p3) β s3, F(37β1, 33) = F(51) =1 is also calculated for the secret bits s3s4 = 00. A second pixel pair (π3β² , π4β² ) = (36+1, 33) = (37, 33) is obtained because of F(37-1, 33) β s4. In the second pixel pair, a new sub-block has to be modified according to the result of the analysis of the LSB matching in two pixel pairs by referring the modification rule table. As a final result, two pixel pairs (π3β² , π4β² ) = (36 + 1, 33) are modified to (π3β² , π4β² ) = (37 β 1, 33 β 1) = (36, 32) and (π3β² , π4β² ) = (37 + 1, 33 + 2) = (38, 35). In the extracting process, LSB(p1) = LSB(43) = 1 and F(43, 45) = 43
F(β 2 β + 45) = F(21 + 45) = F(66) = 0 are obtained for (π1β² , π2β² ) = (43, 45). 45
LSB(p1) = LSB(45) = 1 and F(45, 45) = F(β 2 β + 45) = F(22 + 45) = F(67) =
1 are calculated for (π1β² , π2β² ) = (45, 45). As a result, the secret bits s = 10112 is extracted. For two pixel pairs (π3β² , π4β² ) = (36, 32) and (38, 35), LSB(36) = 0 36
and F(36, 32) = F(β 2 β + 32) = F(18 + 32) = F(50) = 0 are obtained and 38
LSB(38) = 0 and F(38, 35) = F(β 2 β + 35) = F(19 + 35) = F(54) = 0 are also extracted. Finally, the cover image (p1, p2) = (β (p3, p4) = (β
36+38 32+35 β,β 2 β) 2
43+45 45+45 β,β 2 β) 2
= (44, 45) and
= (37, 33) could be recovered.
3. Proposed Method
The embedding capacity and the image quality are important measurements in data hiding methods. The proposed method uses a mean value of neighboring pixel values as base criteria to decide the embedding bits. The proposed method is based on the sub-block embedding mechanism to avoid RS-diagram attack and it is used the difference of the neighboring pixels to provide a high capacity and a good image quality. In this section, we describe a novel reversible data hiding method using neighboring pixel-value differencing.
3.1 Embedding Algorithm The detailed embedding algorithm of the secret data is described as follows.
Difference values are calculated by selecting basis pixel of the sub-block and the number of secret bits is decided on three pixel pairs of the sub-block.
Algorithm 1. The embedding algorithm Input: A cover image of W Γ H and the secret data Output: The dual stego-images of W Γ H Step 1: Divide into π΅ Γ π΅ non-overlapping sub-blocks. Step 2: For the sub-block pixel pairs of a cover image, calculate a mean value of neighboring pixels ππ by Eq. (3)
βπβ1 j=0 πj ππ = | ππ β β β|, (π΅ x π΅) β 1
πππ π β π
(3)
Step 3: For each pixel of the π΅ Γ π΅ sub-block, obtain the size of embedding bits ππ by following Eq. (4).
ππ = βlog2 ππ β
(4)
Step 4: For each pixel ππ of the π΅ Γ π΅ sub-block, calculate the embedding integer values ππ and ππ+1 by Eq. (5) where ππ is a bit stream of the secret data. The size value of embedding bits ππ can be obtained from
Step 3.
ππ ππ (ππ , ππ+1 ) = (β β , β β) 2 2
(5)
Step 5: Obtain a new pixel-pair (ππ1 , ππ2 ) for each two pixel pairs of the π΅ Γ π΅ sub-block.
(ππ1 , ππ2 ) = (ππ + ππ , ππ β ππ+1 )
(6)
Step 6: Repeat the above steps for all sub-blocks to obtain dual stego-images.
An example of the embedding algorithm is shown in Fig. 3. For a 2 x 2 sub-block, assume that (pi, pi+1) = (44, 45), (pi+2, pi+3) = (37, 33) and the bit steams of the secret data s = 101100002 are given. In first, mean values of neighboring | 45 β β
pixels
π1 = | 44 β β
(45+37+33) 3
β | = | 44 β 38 | = 6, π2 =
(44+37+33)
(44+45+33)
3
3
| 37 β 40 | = 3,
β | = | 45 β 38 | = 7, π3 = | 37 β β and
π4 = | 33 β β
(44+45+37) 3
β| =
β | = | 33 β 42 | = 9
are
calculated. Next, calculate the embedding size of the secret data, π1 = βlog2 6β = 2, π2 = βlog2 7β = 2, π3 = βlog2 3β = 1, and π4 = βlog2 9β = 3 are obtained. For each pixel ππ of the π΅ Γ π΅ sub-block, calculate the
10 10 embedding integer values ππ and ππ+1 . (ππ , ππ+1 ) = (β 22β , β 22β) = (1, 1) for 3 3 a pixel π1 = 44 , (ππ , ππ+1 ) = (β2β , β2β) = (1, 2) for π2 = 45 . (ππ , ππ+1 ) = 0
0
2
2
(β β , β β) = (0, 0)
and
0
0
2
2
(ππ , ππ+1 ) = ( β β , β β) = (0, 0) are
obtained
for
π2 and π2 respectively. For each two pixel pairs of the sub-block, a new pixel
(ππ1 , ππ2 ) is calculated. (π11 , π12 ) = (44 + 1, 44 β 1) = (45, 43),
(π21 , π22 ) = (45 + 1, 45 β 2) = (46, 43), (π31 , π32 ) = (37 + 0, 37 β 0) = (37, 37) and (π41 , π42 ) = (33 + 0, 33 β 0) = (33, 33) are calculated. Finally, new sub-blocks of dual stego-images (π11 , π21 , π31 , π41 ) = (45, 46, 37, 33 ) and (π12 , π22 , π32 , π42 ) = (43, 43, 37, 33 ) are obtained as a result.
3.2 Extracting & Recovering Algorithm The following steps are repeated to extract the secret data and recover the cover image together. It can be directly executed from the two stego-images.
Algorithm 2. The extracting and recovering algorithm Input: The dual stego-images of W Γ H and the sub-block size value B Output: The secret data and the cover image Step 1: Divide into π΅ Γ π΅ non-overlapping sub-blocks from dual stegoimages.
Step 2: For the sub-block pixel pairs of dual stego-images, calculate a mean value of neighboring pixels ππβ² from Eq. (7).
ππβ²
ββπβ1 j=0 (
(ππ1 + ππ2 ) = || β ββ 2
ππ1 + ππ2 2
)β
(π΅ x π΅) β 1 β
|, |
πππ π β π
(7)
β
Step 3: For each pixel of the sub-block, obtain the size of embedding bits ππβ² .
ππβ² = βlog2 ππβ² β
(8)
Step 4: For each two pixel pairs of the sub-block, extract the cover pixel value ππ from Eq. (9).
(ππ1 + ππ2 ) ππ = β β 2
(9)
Step 5: The integer value ππ of secret bit streams is extracted and it is changed to bit streams π π by referencing the length of embedding bits ππβ² and the cover pixel vlaue ππ .
ππ = | ππ1 β ππ | + | ππ2 β ππ |
(10)
Step 6: Repeat the above steps for all sub-blocks to obtain the secret data and the cover image.
An example of the extracting the secret bits and recovering the cover pixel for a 2 x 2 sub-block is depicted in Fig. 4. For the sub-block of dual stegoimages
are
given
as
(π11 , π21 , π31 , π41 ) = (45, 46, 37, 33 )
and
(π12 , π22 , π32 , π42 ) = (43, 43, 37, 33 ) which is obtained as given to the embedding example. Firstly, mean values of neighboring pixels π1β² = |β
(45+ 43) 2
(46+ 43) (37+ 37) (33+ 33) β+β β+β β 2 2 2
β
ββ β
3
β | = | 44 β β
(45+37+33) 3
β| = | 44 β
38 | = 6, π2β² = | 45 β 38 | = 7, π3β² = | 37 β 40 | = 3, and π4β² = | 33 β 42 | = 9 are calculated. Next, the embedding size of secret bits ππβ² is calculated.
π1β² = βlog2 6β = 2,
π2β² = βlog2 7β = 2,
π3β² = βlog2 3β = 1,
π4β² =
and
βlog2 9β = 3 are obtained as results. The cover pixel values of the sub-block can be recovered by Eq. (9). π1 = β 45, π3 = β
(37+ 37) 2
β = 37, and π4 = β
(45+ 43)
(46+ 43)
2
2
β = 44, π2 = β
β=
(33+ 33) 2
β = 33 are obtained. The integer
value of secret bit streams is calculated as follows. π1 = | 45 β 44 | + | 43 β 44 | = 2,
π2 = | 46 β 45 | + | 43 β 45 | = 3,
π3 = | 37 β 37 | +
| 37 β 37 | = 0, and π4 = | 33 β 33 | + | 33 β 33 | = 0 are calculated. Finally, integer values of the secret bit streams are changed to binary values
by referencing the length of embedding bits, π1 = 102, π2 = 112, π3 = 02, and π4 = 0002 are extracted as a result. The secret bit stream is 101100002 .
4. Experimental Results
In our experiments, 512 x 512 gray images were used as cover images as shown in Fig. 5 and the secret data is generated by pseudo-random numbers. The peak signal-to-noise ratio (PSNR) and the universal Q index are used to measure an image quality and the embedding capacity of the secret data is experimented. The PSNR of the gray image is calculated by comparing the cover image and dual stego-images as follows.
ππππ
= 10log10
2552 πππΈ
(11)
The MSE is the mean square error that is defined in Eq. (12).
ππ₯π»
πππΈ = β π=1
(ππβ² β ππ )2 , πxπ»
ππβ² = ππ1 or ππ2
(12)
A universal image quality index is also tested to demonstrate the quality of stego-images. This quality index is based on statistical measurements, and its definition is as follows.
4 ΞΈxy MxMxβ² ( ΞΈx2 + ΞΈy2) [Mx2 + Mxβ² 2]
Q=
(13)
β² In here, each factor is given in Eq. (14) where πππ is replaced with
ππ1 or ππ2 in experimental results.
Mx = ΞΈx2 =
1 WΒ·H
W-1 H-1
1 WΒ·H
W-1 H-1
1 ΞΈxy = WΒ· H
β β pij
i=0 j=0
,
Mxβ² =
(pij - Mx )2
β β
i=0 j=0
,
1 W-1 β WΒ·H i=0 ΞΈy2 =
H-1
β
j=0
pβ²ij
1 WΒ·H
,
W-1 H-1
β β
i=0 j=0
(pβ²ij - Mxβ² )2
,
(14)
W-1 H-1
β β
i=0 j=0
(pij - Mx )(pβ²ij - Mxβ² )
Image quality Q index is ranged [-1, 1] where 1 represents that the two images are exactly the same, and -1 means that the two images are unrelated each other. In Table 1 and Fig. 6, the embedding capacity and the visual image quality are compared with Lu et al.βs method. The experimental results show that the embedding capacity of the proposed method is 767,922 bits and the PSNR are 45.58 dB and 45.33 dB on average. Our method satisfies a higher capacity and
a better image quality than Lu et al.βs method without the distortion of the human eyes. Our method could hide 243,634 bits more than Lu et al.βs method and the image quality of dual stego-images are 8.44 dB and 8.15 dB better in the PSNR. Consider Baboon image as an Example, the proposed method can hide 772,544 bits whereas Lu et al.βs method can embed 524,288 bits. In the image quality, the proposed method has 47.49 dB and 45.50 respectively in the dual stego-images where Lu et al.βs method keeps 38.00 dB and 37.90 dB. It is demonstrated that the proposed method has a higher embedding capacity and a better image quality. In other measurement of the image quality, we tested in Q index as shown in Table 2 and Fig. 7 where the proposed method has a less distortion. Our method keeps 0.9767 and 0.9736 on average in the two stego-images whereas the Q index is 0.9018 and 0.9019 in Lu et al.βs method. The proposed method is better 0.0749 and 0.0718 on average on dual stego-images. The proposed method is close to 1 in Q index, that means the cover image and stego-image are very similar each other as shown Fig. 7. The first stego-image with the secret data is shown in Fig. 8. Our method maintains 45.58 dB and 0.9767 in Q index, which the proposed method is better 8.44 dB and 0.0749 on average. In Fig. 9, the second stego-image is shown where the image quality is 45.33 dB and 0.9736. The proposed method is better 8.15 dB and 0.0718 than the
previous work on average.
5. Conclusions
We have proposed a reversible data hiding method using neighboring pixelvalue differencing. Neighboring pixel values and mean values were used to decide how many embedding bits to hide into dual stego-images. The experimental results demonstrated that the proposed method had the higher capacity and the good image quality. The proposed method had 767,922 bits embedding capacity and the image qualities of dual stego-images were 45.58 dB and 45.33 dB on average respectively. In the future, we will extend the proposed method to authenticate for unauthorized attacks.
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7
two consecutive pixels 60
24
85 22
lk =23 25
25
uk = 54
d = 85 β 60 = 25
Fig. 1.
55
m = dβ - d = 40 β 25 = 15 (piβ, pi+1β) = (60 - βm/2 β, 85 + βm/2β) = (60-8, 85+7) = (42, 92) secret data 10001001... number of embedded bits n = log2 (uk β lk + 1) = log2 (54-23+1) = log2 32 = 5
An example of the PVD data hiding method
new pixels 52
92
40 dβ = lk + b = 23 + 17 = 40
p1
p2
44
45
p3
p4
37
33
LSB(p1)=LSB(44)=0 =/ s1=1 s1 s2 F(p1, p2)=F(44-1,45)=LSB(21+45)=0 = s2=0 10 s3 s4 11 LSB(p1)=LSB(44)=0 =/ s3=1 F(p1, p2)=F(44-1,45)=LSB(21+45)=0 =/ s4=1
s1 s2 00 s3 s4 00
LSB(p3)=LSB(37)=1 =/ s1=0 F(p3, p4)=F(37-1,33)=LSB(18+33)=1 =/ s2=0
LSB(p3)=LSB(37)=1 =/ s3=0 F(p3, p4)=F(37-1,33)=LSB(18+33)=1 =/ s4=0
pβ1
pβ2
44-1
45
pβ1
pβ2
44+1
45
pβ3
pβ4
36+1
33
pβ3
pβ4
36+1
33
modification rule table pβ3
pβ4
37-1
33-1
pβ3 37+1
Fig. 2.
pβ4 33+2
An example of Lu et al.βs reversible data hiding method
dual stego-images 43
45
36
32
45
45
38
35
dual stego-images
m1 = | 44 - floor[(45+37+33)/3)] | = | 44 β 38 | = 6 e1 = floor[log2 m1] = 2 s1 = 102 k1 = floor[102/2] = floor[2/2] = 1 k2 = ceil[102/2] = ceil[2/2] = 1 44
45
37
33
m2 = 7, e2 = 2, s2 = 11, k1 = 1, k2 = 2 m3 = 3, e3 = 1, s3 = 0, k1 = 0, k2 = 0 m4 = 9, e4 = 3, s4 = 000, k1 = 0, k2 = 0
44+1
44 -1
45
46
45+1
45 -2
37
33
37+0
37-0
43
43
33+0
33 -0
37
33
Fig. 3. An example of embedding procedure
mβ1 = | ceil[(45+43)/2] β floor[(ceil[(46+43)/2] + ceil[(37+37)/2] + ceil[(33+33)/2])/3] | = 6 eβ1 = floor[6] = 2 45
37
46
s1 = 102
d1 = | 45 β 44 | + | 43 β 44 | = 2
s2 = 112 s3 = 02 s4 = 0002
33
43
43
37
33
p1 = ceil[(45+43)/2)] = 44 p2 = ceil[(46+43)/2)] = 45 p3 = ceil[(37+37)/2)] = 37 p4 = ceil[(33+33)/2)] = 33
Fig. 4. An example of extracting and recovering procedure
44
45
37
33
(a) Airplane
(b) Baboon
(e) City
(f) Gatbawi
(i) Lena
(j) Lotus
(c) Boat
(d) Children
(g) House
(h) Island
(k) Man
(l) Peppers
Fig. 5. Cover images
Table 1. Comparisons of the embedding capacity and the visual image quality Cover images
Lu et al.'s method Capacity (bits)
PSNR #1 (dB)
The proposed method PSNR #2 (dB)
Capacity (bits)
PSNR #1 (dB)
PSNR #2 (dB)
Airplane
524,288
38.31
38.31
781,964
47.44
45.46
Baboon
524,288
38.00
37.90
772,544
47.49
45.50
Boat
524,288
38.31
38.31
766,097
47.50
44.96
Children
524,288
34.57
34.62
759,934
47.49
44.05
City
524,288
38.31
38.31
769,079
47.45
45.47
Gatbawi
524,288
30.81
30.98
776,804
33.43
45.48
House
524,288
38.32
38.31
779,948
47.42
45.46
Island
524,288
38.32
38.31
748,493
47.55
45.55
Lena
524,288
38.31
38.31
773,666
47.43
45.46
Lotus
524,288
36.03
36.37
761,290
42.28
45.52
Man
524,288
37.99
38.10
762,933
43.92
45.50
Peppers
524,288
38.31
38.31
762,312
47.52
45.52
Average
524,288
37.13
37.18
767,922
45.58
45.33
Fig. 6. Comparison chart of PSNR
Table 2. Comparisons of the visual image quality Q index Cover images Airplane
Lu et al.'s method Q index #1
The proposed method
Q index #2
Q index #1
Q index #2
0.8167
0.8167
0.9769
0.9727
Baboon
0.9851
0.9851
0.9992
0.9990
Boat
0.9416
0.9417
0.9910
0.9893
Children
0.8509
0.8509
0.9633
0.9576
City
0.9299
0.9298
0.9739
0.9705
Gatbawi
0.8503
0.8505
0.9316
0.9226
House
0.8384
0.8382
0.9301
0.9248
Island
0.9278
0.9278
0.9934
0.9921
Lena
0.8997
0.8997
0.9863
0.9836
Lotus
0.9203
0.9209
0.9889
0.9880
Man
0.9434
0.9435
0.9953
0.9945
Peppers
0.9177
0.9175
0.9909
0.9889
Average
0.9018
0.9019
0.9767
0.9736
Fig. 7. Comparison chart of Q index
(a) 47.44dB
(b) 47.49dB
(c) 47.50dB
(e) 47.45dB
(f) 33.43dB
(g) 47.42dB
(h) 47.55dB
(j) 42.28dB
(k) 43.92dB
(l) 47.52dB
(i) 47.43dB
Fig. 8. First stego-images
(d) 47.49dB
(a) 47.46dB
(b) 45.50dB
(c) 44.96dB
(e) 45.47dB
(f) 45.48dB
(g) 45.46dB
(h) 45.55dB
(i) 45.46dB
(j) 45.52dB
(k) 453.50dB
(l) 45.52dB
Fig. 9. Second stego-images
(d) 44.05dB