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Side-match Approach for Improving Histogram-Based Reversible Data Hiding

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Side-match Approach for Improving

Histogram-Based Reversible Data Hiding

Cheng-Hsing Yang Department of Computer Science, National Pingtung

University of Education Email:

chyang@mail.npue.edu.tw

Meng-Hsuan Tsai Department of Computer Science and Engineering, National Sun Yat-sen

University Email:

emma7337@gmail.com

Min-Hao Wu Department of Computer Science, National Pingtung

University of Education Email:

bm097116@mail.npue.edu.tw

Chiu-Chih Jen Department of Computer Science, National Pingtung

University of Education Email:

bm098108@mail.npue.edu.tw

Abstract― Reversible data hiding has drawn considerable attention in recent years. Being reversible, the decoder can extract the hidden data and recover the original image completely. In this paper we used the side-match prediction to achieve a histogram-based reversible data hiding. The histogram is created by exploiting all difference values between pixels and their predictive values. Experimental results show that our method is capable of providing a great embedding capacity without making noticeable distortion. In the one-level hiding, our method remains image qualities larger than 48 dB and has the best capacity. Moreover, in the multilevel case our method performs better than other existed methods. Our method can successfully increase the embedding capacity from histogram-based data hiding and remain the image quality well.

Index Terms ― reversible data hiding, side match, prediction, histogram

I. INTRODUCTION

With the rapid development of network technologies and the coming of the digital era, Internet has become indispensable for many people. By the development of Internet, a lot of new businesses are developed, such as e-commerce, e-learning, online game, and video-on-demand, etc. Many enterprises have expanded their traditional business activities in the Internet. On every day, thousands of multimedia data are transferred conveniently and efficiently over Internet. Because digital multimedia data, such as voices, videos, images, texts, etc., have the attributes of easy copy, modification, and distribution, the development of Internet has increased the problems of multimedia

securities. How to protect the authentication and the ownership of multimedia data has become an important topic. Many researchers have paid high attention to this topic. One of the most important approaches to this topic is the technique of information hiding.

Many approaches to information hiding have been proposed for different attributes, such as, capacity, imperceptibility, undetectability, robustness, and reversibility. These attributes are used for various applications, such as, secret communication, copyright protection, tampering detection, and other human-centered approaches. Besides, information hiding techniques can be categorized into two types: methods in the spatial domain and methods in the frequency domain. In the spatial domain, the secret messages are embedded by changing image pixels directly. On the other hand, in the frequency domain, the image is first transformed into its frequency domain, and then the secret messages are embedded in the transformed coefficients.

Recently, reversible data hiding has drawn many researchers’ attention. Reversibility allows original media to be completely recovered from stego-media after the embedded message is extracted. Many reversible data hiding approaches have been proposed [2-18]. According to where the data are embedded, these approaches can be classified into three categories: the spatial domain [2-13], the frequency domains [14,15], and other compression types, such as vector quantization

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(VQ) [16, 17]. In those developed reversible data

hiding methods, two main technologies have been widely applied: the difference-expansion-based technology [8-14] and the histogram-based technology [2-7]. In 2006, Ni et al. presented a reversible data hiding method based on the histogram [2]. Their method guarantees that the change of each pixel in the stego-image remains within ±1. Therefore, the PSNR value of the stego-image is at least 48 dB. But their method used the pixel values in the original image to create the histogram. The peak values of the histogram are not high enough. Some methods used the concept of prediction to increase the peak height [3-6].

In this paper, we propose a new reversible information hiding method based on the histogram for grayscale images. We used the side-match prediction to improve a histogram-based reversible data hiding. Our predictive difference values are as many as the pixel values, in our approach. All predictive difference values are transformed into histogram to create higher peak values and to improve the embedding capacity. Experimental results show that our histogram-based reversible hiding approach can raise a larger capacity and still remain a good image quality, compared to other histogram-based approaches. The remainder of this paper is as follows. In Section II, we introduce some related works of reversible information hiding technologies. Our proposed scheme is described in Section III and some experimental results are shown in Section IV. Finally, we bring some conclusions in Section V.

II. RELATED WORKS

A. Ni et al.’s method

Ni et al. proposed a reversible data hiding method in 2006 [2]. Their method uses the histogram of an original image to embed secret messages. In the histogram, they find multiple pairs of peak and zero points, where a peak point corresponds to the pixel value which a maximal number of pixels in the cover image assume and a zero point corresponds to the pixel value which no pixel in the cover image assumes. To use a pair of peak and zero points to embed the secret messages, their algorithm is as follows:

1. Generate the histogram H(x) with x

0 ,255

of the original image.

2. In the histogram H(x), find a peak point p and a zero point z, wherep,z

0,255

.

3. Shift the values between the peak point and the zero point as follows:

(a) If p > z, move the whole part of the histogram H(x) with x

z1 ,p1

to the left by 1 unit.

(b) If p < z, move the whole part of the histogram H(x) with x

p1,z1

to the right by 1 unit.

4. Scan the image and embed one secret bit when a pixel with value p is met:

(a) If the to-be-embedded bit is 0, the pixel value remains p.

(b) If the to-be-embedded bit is 1, the pixel value is set to p1 and p1 when p is smaller than z and p is greater than z, respectively.

5. Output the stego-image, peak point p, and zero point z.

Fig. 1 shows an example of Ni et al’s method. The table in the left is an image with 5 × 5 pixels. The diagram in the right is the histogram, where a peak point p = 163 and a zero point z = 166 are found. Then, pixel values belonging to [164, 165] are moved to the right by 1 unit. The results are shown in Fig. 2. 162 165 163 161 161 164 162 165 161 161 162 163 164 164 161 163 163 161 162 165 163 163 163 163 162 0 2 4 6 8 10 161 162 163 164 165 166 pixels fr eque nc y

Figure 1. Ni et al.’s example.

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Pixels shown in Fig. 2 are scanned from left to

right and from top to down. All pixels with value equal to p = 163 can be used to embed one secret bit. The embedded results are shown in Fig. 3.

162 166 163 161 161 165 162 166 161 161 162 163 165 165 161 163 163 161 162 166 163 163 163 163 162 0 2 4 6 8 10 161 162 163 164 165 166 pixels fre q ue n cy

Figure 2. Results after shifting.

162 166 164 161 161 165 162 166 161 161 162 164 165 165 161 163 163 161 162 166 164 164 163 164 162 0 2 4 6 8 161 162 163 164 165 166 pixels fr eq u en cy

Figure 3. The embedded results.

B. Lin et al.’s method

In 2008, Lin et al. applied the histogram approach at a difference image to achieve the reversible data hiding [5]. Their method used the peak point of a histogram created from a difference image to create the free space for hiding messages. For an image H with P × Q pixels, a difference image with size P Q( 1) is generated. In order to avoid serious distortions, the original image was divided into 4 × 4 non-overlapping blocks in their experiments. Each block generates a difference image with size 4 × 3. Let Hi,j be a pixel value in image H at location (i, j) and Di,j be a difference value in difference image D at location (i, j). Their algorithm is as follows:

1. Generate the difference image D from the original image H. The formula is as follows:

1 , , ,ji jiji H H D .

2. Generate the histogram of the difference image and find the peak point p.

3. If the value Di,j is greater than p, change the value to Di,j+1.

4. Scan the difference image and embed a secret

bit when the value Di,j is equal to p as follows:

(a) If the to-be-embedded bit is 0, the value

j i

D, remains p.

(b) If the to-be-embedded bit is 1, the value

j i

D, is set to p1.

5. Use the original image and the embedded difference image to construct the stego-image S.

Let Si,j be a pixel value of the stego-image. The formula is as follows:

      , otherwise , if ,0 ,1 0 , 1 , 0 , 0 , i i i i i i H H D H H S       , otherwise , if ,0 ,1 1 , 0 , 0 , 1 , i i i i i i H H H D H S             . otherwise , if , 1 , 1 , 1 , 1 , 1 , , j i j i j i j i j i j i j i H H D S D S S

6. Output the marked image S and the peak point

p.

Fig. 4 shows an example of Lin et al.’s method. Fig. 4(a) is a 4 × 4 block H. Fig. 4(b) is the difference image D create from H, and the peak point is p = 1. Fig. 4(c) is the shifted difference

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image D’ which is obtained by shifting all values

larger than p = 1 in D. Suppose, the to-be-embedded secret data are 0110. Fig. 4(d) is the embedded difference image D’’ which embeds one secret bit to each pixel with value equal to p = 1 in D’. Fig. 4(e) shows the embedded image S after Step 5 is executed.

H 162 156 163 160 161 159 158 159 160 161 159 155 158 158 156 157 D 6 7 3 2 1 1 1 2 4 0 2 1 (a) (b) D’ 7 8 4 3 1 1 1 3 5 0 3 1 D’’ 7 8 4 3 1 2 2 3 5 0 3 1 (c) (d) S 163 156 164 160 162 159 158 160 160 162 159 154 158 158 155 156 (e)

Figure 4. An example of Lin et al.’s method.

III. OUR PROPOSED METHOD

In this section, we describe our method in detail. We used the side-match prediction to achieve a histogram-based reversible data hiding. This method can increase the embedded capacity and the image quality remains as well. Fig. 5 shows the main concept of the side-match prediction. Our

predictive method is to employ the neighboring pixels Hi,j1,Hi1,j1,Hi1,j and Hi1,j1 to predict the pixel Hi,j. 1 , 1   j i H Hi1,j Hi j1, 1 1 ,ji H Hi,j

Figure. 5. The main concept of the side-match prediction.

A. Embedding algorithm

Input: Original image, secret message

Output: Stego-image, two pairs of peak and zero points

1. Input the original imageH

H0,0,H0,1,...,H0,511,

H1,0,... H511,511

.

2. Predict each pixel in the original image as follows. Assume Hi,j is the pixel value in the

original image, and Di,j is the predictive

difference value. (a) If i = j = 0, then 128 , ,ji ji H D . (1) (b) If i = 0 and j ≠ 0, then 1 , , ,jijiji H H D . (2) (c) If i ≠ 0 and j = 0, then             2 1 , 1 , 1 , , j i j i j i j i H H H D . (3) (d) If i ≠ 0 and j = 511, then               3 , 1 1 , 1 1 , , , j i j i j i j i j i H H H H D . (4) (e) Else,

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                 4 1 , 1 , 1 1 , 1 1 , , , j i j i j i j i j i j i H H H H H D . (5)

3. Create the histogram H(x) with x

255,255

from all predictive difference values.

4. Find two pairs of peak and zero point (P1, Z1)

and (P2, Z2).

5. Let ' j i,

D be the new value of Di,j after the

following shifting step and embedding step. Shift the histogram as follows:

(a) ' j i, D is set to Di,j1 if Di,j

P11,Z11

. (b) ' j i, D is set to Di,j1 if Di,j

Z21,P21

.

6. Embed the secret message as follows: (a) If the to-be-embedded bit is 0, '

j i, D is set to j i, D .

(b) If the to-be-embedded bit is 1, ' j i, D is set to 1  j i,

D and Di,j1 when Di,j is equal to

P1 and P2, respectively.

7. Convert the predictive difference values into pixel value. Assume '

, j

i

H is the embedded pixel value in the stego-image.

(a) If i = j = 0, then 128 ' , ' ,jiji D H . (6) (b) If i = 0 and j ≠ 0, then 1 , ' , ' ,jijiji D H H . (7) (c) If i ≠ 0 and j = 0, then             2 1 , 1 , 1 ' , ' , j i j i j i j i H H D H . (8) (d) If i ≠ 0 and j = 511, then               3 , 1 1 , 1 1 , ' , ' , j i j i j i j i j i H H H D H . (9) (e) Else,                  4 1 , 1 , 1 1 , 1 1 , ' , ' , j i j i j i j i j i j i H H H H D H . (10)

8. Output stego-image, (P1, Z1) and (P2, Z2).

As shown in Fig. 6, a 5 × 5 grayscale original image H

H0,0,H0,1,...,H0,4,H1,0,...,H4,4

is given to

explain our embedding algorithm. We predict the

pixels first. For example, D0,0H0,01287128

121  , D0,1H0,1H0,0 671 , D1,0 H1,0 0 2 6 7 6 2 1 , 0 0 , 0              HH , 1 4 5 6 7 6 7 4 2 , 0 1 , 0 0 , 0 0 , 1 1 , 1 1 , 1                     H H H H H D

and so on. The results are shown in Fig. 6. The histogram created from all predictive difference values is also shown in Fig. 7. According to the histogram, we find two pairs of peak and zero points: (P1, Z1) = (0, 3) and (P2, Z2)

1,3

. The

results and the histogram after shifting are shown in Fig. 8. 7 6 5 6 6 6 7 6 6 5 8 7 6 7 5 6 5 6 7 6 7 6 5 4 5

Figure 6. The original image.

-121 –1 –1 1 0 0 2 4 6 8 10 -3 -2 -1 0 1 2 3 0 1 0 1 –1 2 1 0 2 –1 –1 –1 0 1 0 2 0 –1 –2 0

Figure 7. The predictive difference values and their histogram.

-121 –1 –1 2 0 0 2 4 6 8 10 -3 -2 -1 0 1 2 3 0 2 0 2 –1 3 2 0 3 –1 –1 –1 0 2 0 3 0 –1 –3 0

Figure 8. The predictive difference values and their histogram after shifting.

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Then, we embedded the secret messages. The

predictive difference values equivalent to P1 or P2

are used to embed secret messages. Assume the secret message Ⅰ= 101001101000110(2). After the

secret message I is embedded, the predictive difference values and their histogram are shown in Fig. 9. Finally, the predictive difference values are inverted into pixel values. For example,

7 128 121 128 ' 0 , 0 ' 0 , 0  D     H , 5 7 2 0 , 0 ' 1 , 0 ' 1 , 0 DH    H , 6 2 6 7 0 2 1 , 0 0 , 0 ' 0 , 1 ' 0 , 1                D H H H , 8 4 5 6 7 6 2 4 2 , 0 1 , 0 0 , 0 0 , 1 1 , 1 ' 1 , 1 '                    D H H H H H

and so on. The embedded results are shown in Fig. 10. That is also the stego-image.

-121 –2 –1 2 1 0 2 4 6 8 10 -3 -2 -1 0 1 2 3 0 2 0 2 –2 3 2 1 3 –1 –2 –1 0 2 0 3 1 –2 –3 0

Figure 9. The predictive difference values and their histogram after embedding.

7 5 5 7 7 6 8 6 7 4 9 8 7 8 5 5 5 6 8 6 8 7 4 3 5 Figure 10. The stego-image.

B. Extracting and reversing algorithm

In the extracting and reversing process, the secret message is extracted and the embedded pixel values are reversed. The extracting and reversing

algorithm is shown as follows.

Input: stego-imageH , two pairs of peak and zero ' points (p1,z1)and (p2,z2)

Output: original image, secret message 1. Input the stego-image H . '

2. Process each pixel of stego-image H from ' left to right first then from top to bottom by Step 3 to Step 5 repeatedly.

3. Create predictive difference value D'i,j

from H . '

4. Use (P1, Z1) and (P2, Z2) to extract the secret

message, and recover the predictive difference values as follows:

(1) If the ' , j

i

D is equal to P1 or P2 , secret bit 0

is extracted and recover the predictive

difference is recovered as Di,jDi',j. (2) If the '

, j

i

D is equal to P1 1 or P2 1,

secret bit 1 is extracted and the predictive

differences are recovered as Di,jDi',j 1

or Di,jDi',j 1, respectively.

(3) If Di',j

P1, Z1

, recover the predictive error as Di,jDi',j 1.

(4) If Di',j

Z2, P2

, recover the predictive difference as Di,jDi',j 1.

5. Convert predictive difference values Di,j into original pixel valueHi,j.

6. Output the original image and the secret message.

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Now, we perform extracting and reversing

operations on the embedded results shown in Fig. 10. Assume ' , j i H is an embedded pixel, ' , j i D is an embedded predictive difference value, Di,j is a

predictive difference value, and Hi,j is an original

pixel. For this example, (P1, Z1) = (0, 3) and (P2,

Z2)

1,3

. We process the first pixel value H0',0

first. ' 0 , 0 D ' 128 7 128 121 0 , 0      H . We can find that ' 0 , 0

D does not belong to any situation of Step 4, so D0,0  D0',0 121. Finally, calculate the

original pixel value 7 128 121 128 0 , 0 0 , 0  D     H . Next, the

second pixel value ' 1 , 0 H is processed. 2 7 5 0 , 0 ' 1 , 0 ' 1 , 0 HH   

D . We can find that

2

' 1 . 0 

D is equal toP21, so secret bit 1 is

extracted and the predictive difference value is recovered as ' 1 2 1 1 1 , 0 1 , 0  D     D . Finally,

calculate the original pixel value 6 7 1 0 , 0 1 , 0 1 , 0 DH    H . Similarly, other

pixel values H'i,j are processed in order to

generate their original pixel values Hi,j.

IV. EXPERIMENTAL RESULT AND DISCUSSION In this section, we show the experimental results of our proposed schemes and some discussions of the overflow and underflow problems. The detailed experimental comparison between our schemes and other scholar’s methods are shown in Section A. Section B shows some discussions.

A. Experimental results

In this subsection, we display the performance of our scheme. In our experiments, we used the random numbers as the secret messages. Five of 512 × 512 grayscale images, Airplane, Baboon, Boat, Lena and Peppers, are used as the cover images. As shown in Fig. 11, the side-match approaches of predicting pixel Hi,j can come

from different directions and have various methods. For example, from the left-up corner, { Hi,j1,

1 , 1   j i H , Hi1,j,Hi j1, 1}, {Hi,j1, Hi j1,1, Hi1,j} and {Hi,j1, Hi1,j} can be used to predict pixel

j i

H, . Similarly, from the right-up corner, {Hi,j1,

1 , 1   j i H , Hi1,j, Hi j1, 1}, { 1 ,j i H , Hi j1, 1, Hi1,j} and { 1 ,j i

H , Hi1,j } can be used to predict pixelHi,j. In the following experiment, we use {

1 ,j i

H , Hi1,j} to predict Hi,j from the right-up

corner. Table 1 shows a comparison among Ni et al.’s method [2], Lin et al.’s method [5], and our scheme when the embedding algorithm is applied once. Two peak points are the first highest point and the second highest point chosen from the histogram. The averaged capacity of our scheme is about 7 times of Ni et al.’s method and the image qualities of both their and our approaches are similar. Compared to the averaged capacity of Lin et al.’s method, our averaged capacity is 11% higher and the image quality is better. Besides, we performed the multilevel data hiding on our scheme. As shown in Fig. 12, we perform a 180o clockwise rotation on the test image after the hiding procedure is finished at each level. Table 2 and Table 3 show the embedding results of different levels and various images without and with the 180o rotation, respectively. The results show that the rotation operation can improve the image qualities such that more secret data can be embedded based on the same image quality. Table 4 shows a comparison among Lin et al.’s method [4], Lin et al.’s method [5], Hsiao et al.’s method [8], and our scheme with PSNR values close to 30 dB. Our method includes the rotation operation. The number of levels of our scheme is shown in the parentheses. Table 4 shows that our averaged capacity is 0.57% higher, 23.5% higher, and 6.7% higher than that of Lin’s et al.’s method [5], Hsiao’s et al.’s method [8], and Lin’s et al.’s method [4], respectively.

1 , 1   j i H Hi1,j Hi j1, 1 1 ,ji H Hi,j Hi,j1 1 , 1  j i H Hi1,j Hi j1, 1

Figure. 11. The main concept of the side-match prediction.

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Figure. 12. The 180o clockwise rotation of Lena

Table 1. The comparison among Ni et al.’s, Lin et al.’s, and our proposed methods.

Images Ni et al.’s method [2]

Lin et al.’s

method [5] Our scheme

Airplane 17,415 69,941 94,524 Baboon 5,796 38,465 23,928 Boat 11,109 56,713 59,598 Lena 5,760 65,349 73,686 Peppers 5,737 64,632 68,853 Average 9,163 59,022 64,118 PSNR 48.30 48.67 48.70

Table 2. Without the 180o clockwise rotation.

Level Airplane Baboon Boat Lena Pepper 1 capacity 94,524 23,928 59,598 55,583 68,853 PSNR 49 48.34 48.66 48.62 48.75 2 capacity 148,907 45,375 100,462 98,857 118,595 PSNR 43.56 42.97 43.4 43.42 43.78 3 capacity 197,268 62,767 133,354 131,874 158,442 PSNR 40.16 39.78 40.43 40.42 40.6 6 capacity 287,945 109,830 207,783 208,771 247,900 PSNR 34.59 33.91 34.29 34.51 34.9 9 capacity 349,613 145,262 258,015 262,967 306,457 PSNR 31.08 30.46 31.33 31.18 31.21 12 capacity 396,062 175,019 297,053 303,317 351,457 PSNR 28.74 28.09 28.66 28.68 29.07

Table 3. With the 180o clockwise rotation. Level Airplane Baboon Boat Lena Pepper

1 capacity 94,524 23,928 59,598 73,686 68,853 PSNR 49 48.34 48.66 48.79 48.75 2 capacity 158,218 44,814 100,188 129,037 119,600 PSNR 44.96 44.53 44.24 45.06 44.81 3 capacity 199,636 63,972 132,407 173,169 159,889 PSNR 41.72 41.03 41.13 41.78 41.44 6 capacity 291,619 112,262 206,644 265,422 246,220 PSNR 36.24 35.7 36.02 36.52 36.16 9 capacity 353,363 149,460 256,635 330,350 303,720 PSNR 32.5 32.37 32.23 32.5 32.77 12 capacity 397,070 180,186 294,889 379,078 348,280 PSNR 30.2 29.87 29.86 30.27 30.12

Table 4. The comparison for multilevel data hiding.

Images Lin’s et al.’s method [5] Hsiao’s et al.’s method [8] Lin’s et al.’s method [4] Our scheme (Level) Airplane 362,847 286,488 367,392 409,755 (13) Baboon 230,079 138,398 162,544 170,628 (11) Boat 314,196 266,724 307,937 283,031 (11) Lena 346,568 303,700 309,166 393,246 (13) rotation clockwise  180

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Peppers 342,175 303,736 356,450 348,280 (12) Average 319,173 259,809 300,698 320,988 PSNR 30.19 30.00 30.26 30.10 B. Discussions

After secret messages are embedded in our method, the change of each pixel remains within ±1. Therefore, if pixel values are equal to 0 and 255 in the original image, they may become –1 and 256 in the stego-image and cause the underflow and the overflow problems. In order to avoid this problem, we used a pre-processing method [18]. When the pixel values are equal to 0 or 255 in the original image, they are changed into 1 or 254 in advance, respectively. For each pixel value 1, a flag bit is needed to record that its original pixel value is 0 or 1. Similarly, one flag bit is needed for each pixel value 254. So, for each pixel with values 1 or 254, if the pixel is changed from 0 or 255, the flag bit is set to 1; otherwise, the flag bit is set to 0. From the experimental results shown in Table 5, we know that the overflow and underflow probabilities are very few. Therefore, the overhead is low. Moreover, the overhead can be embedded together with secret data. For fourteen grayscale images, Table 4 shows the bits of overhead, the pure loads, and the PSNR values.

Table 5. The bits of overhead, the pure load and the PSNR values.

Image overhead pure load PSNR

Airplane 0 94,524 49 Baboon 0 23,928 48.34 Barb 0 41,885 48.5 Boat 0 59,598 48.66 Girl 0 68,044 48.74 Goldhill 0 50,250 48.58 Jet 0 94,524 49 Lena 0 73,686 48.79 Pepper 17 68,853 48.75 Sailboat 0 39,679 48.48 Ship 16 35,042 48.44 Tiffany 0 74,456 48.81 Toys 3 60,997 48.68 Zelda 23 54,938 48.62 ACKNOWLEDGEMENTS

This research was supported by the National Science Council of the Republic of China under the Grants NCS 98-2221-E-153-001.

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[5] C.C. Lin, W.L. Tai, and C.C. Chang, “Multilevel reversible data hiding based on histogram modification of difference images,” Pattern Recognition, Vol. 41, No. 12, pp. 3582-3591, 2008.

[6] E. Chrysochos, V. Fotopoulos, A.N. Skodras, and M. Xenos, “Reversible image watermarking based on histogram modification”, 11th Panhellenic Conference

on Informatics with international participation, Vol. B, pp. 93-104, 2007.

[7] S. Yousefi, H. Rabiee, E. Yousefi, and M. Ghanbari, "Reversible date hiding using histogram sorting and integer wavelet transform," In Proceedings of IEEE DEST, pp. 487-490, 2007.

[8] J.Y. Hsiao, K.F. Chan, and J.M. Chang, “Block-based reversible data embedding,”

Signal Processing, Vol. 89, No. 4, pp.

556-569, 2009.

[9] D.M. Thodi and J.J. Rodriguez, “Expansion embedding techniques for reversible watermarking,” IEEE Transactions on Image

Processing, Vol. 16, No. 3, pp. 723-730,

2007.

[10] H.J. Kim, V. Sachnev, Y.Q. Shi, J. Nam, and H.G. Choo, “A novel difference expansion transform for reversible data embedding,”

IEEE Transactions on Information Forensics and Security, Vol. 3, No. 3, pp. 456-465,

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[11] H.L. Jin, M. Fujiyoshi, and H. Kiya, “Lossless data hiding in the spatial domain for high quality image,” IEICE Transactions

on Fundamentals, Vol. E90-A, No. 4, pp.

771-777, 2007.

[12] J. Tian, “Reversible data embedding using a difference expansion,” IEEE Transactions on

Circuits and System for Video Technology,

Vol. 13, No. 8, pp. 831-841, 2003.

[13] A.M. Alattar, “Reversible watermark using the difference expansion of generalized integer transform,” IEEE Transactions on

Image Processing, Vol. 13, No. 8, pp.

1147-1156, 2004.

[14] C.C. Chang, C.C. Lin, C.S. Tseng, and W.L. Tai, “Reversible hiding in DCT-based compressed images,” Information Sciences, Vol. 177, No. 13, pp. 2768-2786, 2007.

[15] S. Lee, C.D. Yoo, and T. Kalker, “Reversible image watermarking based on integer-to-integer wavelet transform,” IEEE

Transactions on Information Forensics Security, Vol. 2, No. 3, pp. 321-330, 2007.

[16] C.C. Chang and C.Y. Lin, “Reversible steganography for VQ-compressed images using side matching and relocation,” IEEE

Transactions on Information Forensics and Security, vol. 1, no. 4, pp. 493-501, Dec.

2006.

[17] C.H. Yang and Y.C. Lin, “Reversible data hiding of a VQ index table based on referred counts”, Journal of Visual Communication

and Image Representation, Vol. 20, No. 6, pp.

399-407, August 2009.

[18] H.W. Tseng and C.P. Hsieh, “Prediction-based reversible data hiding,”

Information Sciences, Vol. 179, No. 14, pp.

數據

Figure 4. An example of Lin et al.’s method.
Figure 6. The original image.
Figure 9. The predictive difference values  and their histogram after embedding.
Table 4. The comparison for multilevel data hiding.
+2

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