Local complexity based adaptive embedding ... - Springer Link

Multimed Tools Appl https://doi.org/10.1007/s11042-018-6031-4

Local complexity based adaptive embedding mechanism for reversible data hiding in digital images Fang Cao 1 & Bowen An 1 & Heng Yao 2 & Zhenjun Tang 3

Received: 20 March 2018 / Revised: 17 April 2018 / Accepted: 18 April 2018 # Springer Science+Business Media, LLC, part of Springer Nature 2018

Abstract In this paper, a reversible data hiding scheme for digital images with high hiding capacity is proposed. Original image is segmented into smooth and rough regions based on local complexity. In order to achieve higher hiding capacity, we embed three bits into each pixel belonging to smooth region with lower local complexity and one bit is embedded into each pixel of rough region, which can effectively exploit more redundancy during data embedding compared with conventional methods of prediction error expansion (PEE). Additionally, the pixel selection mechanism is applied to reduce the number of shifted pixels, which leads to high visual quality of stego image. Experimental results show that, our scheme can achieve better rate-distortion performance than some of state-of-the-art schemes. Keywords Reversible data hiding . Prediction error expansion . Local complexity . Adaptive embedding . Hiding capacity . Image quality

1 Introduction In recent years, reversible data hiding (RDH) has become the research focus in the community of data hiding. RDH scheme in digital images can not only embed additional data into cover image, but also can fully recover the image to its original version after additional data are

* Fang Cao [email protected] * Bowen An [email protected]

1

College of Information Engineering, Shanghai Maritime University, Shanghai 201306, China

2

School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China

3

Guangxi Key Lab of Multi-Source Information Mining & Security, Guangxi Normal University, Guilin 541004, China

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extracted, which can be widely applied in the fields of image labeling, authentication, and retrieval for the important images such as military and medical images [23–25]. Current RDH scheme in images can be categorized into three main types: RDH using lossless compression [1], RDH using difference expansion (DE) [6, 29], and RDH using histogram shifting (HS) [8, 9, 14, 19]. In the earlier work of RDH [1], the lossless compression technique was adopted to compress the least significant bits (LSB) of cover image, and the vacated space can be utilized to embed additional data, which can also realize reversible image recovery by lossless decompression. However, the rate-distortion performance of this type of scheme was not satisfactory. In the DE-based RDH scheme [29], original image was segmented into a number of pixel pairs, and the difference of each pair was doubled and added with the additional bit to be embedded. Then, the modified difference was re-assigned to the two pixels of each pair. The receiver can easily retrieve additional bits according to the parity of the recalculated differences of stego pixel pairs. Due to DE operation, some pixels may occur underflow and overflow problems, and location map was required to record the information of the non-used pixels for the reversibility. In the HS-based RDH scheme [14], the histogram bins of original image between the peak point and the zero point were shifted towards the direction of zero point by one, and one vacant histogram bin neighboring to the peak point was established. Then, in order to embed additional bits, the pixel values corresponding to the peak point were either kept unchanged or modified by one. However, the information of peak point and zero point should be transmitted to the receiver side. Additionally, the histograms of some images may not have zero points, thus, zero point should be created through the lowest bin in the histogram and extra information are also needed to be recorded. In order to further improve the performances of embedding rate and stego-image quality for DE-based and HS-based schemes, many studies investigated to introduce the prediction strategy into RDH [2, 4, 7, 12, 15, 26–28]. Rather than directly utilizing original image as cover data, the relative data of original image, i.e., prediction error (PE), was constructed as cover data for embedding, and PE was acquired through the difference between original image and predicted image. Through the operations of DE [7, 15, 28] or HS [4, 27], PE was manipulated to carry secret bits and added back to predicted image to generate the final stego image. The same predicted result must be produced on the receiver side, which guaranteed the correctness of data extraction and image recovery. Thodi and Rodriguez proposed an improvement of DE-based scheme in [28], which adopted prediction error expansion (PEE) for reversible data embedding. This scheme greatly increased the hiding capacity. After that, many researchers have investigated the PEE mechanism and a lot PEE-based schemes have been reported [7, 15]. The conventional PEE schemes can generally embed one secret bit in each available pixel. Obviously, different regions of cover image had different capabilities of data accommodation. Therefore, Li et al. proposed an adaptive PEE scheme based on the pixel selection strategy in [7], which can embed two secret bits per pixel in the smooth regions of cover image where the adjacent pixel values were similar with each other. This scheme can effectively improve the embedding rate. Besides the study of RDH for uncompressed image in plaintext form, some researchers also conducted studies on RDH based on two images [11, 21], RDH for compressed images [5, 17, 20] and RDH for encrypted images [3, 16, 18, 30]. In this work, we claim that there is still improvement room for the performance of Li et al.’s scheme [7]. During the design of our scheme, the adaptive embedding mechanism of [7] is further improved to achieve better ratedistortion performance. Detailedly, in our scheme, more secret bits are assigned to be embedded into the pixels belonging to smooth region, which can lead to greater embedding rate and also satisfactory stego-image quality.

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The remaining parts of the paper are arranged as follows. Section 2 describes the proposed scheme detailedly, including the procedures of data embedding, data extraction, and image recovery. Experimental results and comparisons are given to demonstrate the effectiveness and superiority of our scheme in Section 3. Section 4 concludes this paper.

2 Proposed scheme In our scheme, the complexity of the original cover image is first calculated according to the relationship between the pixels, and the image is divided into smooth region and rough region. Then, the optimal pixel-selection threshold can be acquired to select the embeddable pixels and the shiftable pixels, and the remaining pixels are not modified. The pixels in the smooth and rough regions are embedded and shifted, respectively. It is noteworthy that, different with Li et al.’s [7], our scheme can adaptively embed three bits per pixel in the smooth region. The flowchart of the embedding procedure for our scheme is given in Fig. 1.

2.1 Principle of prediction method As a PEE-based RDH scheme, prediction method that is used to construct PE as cover data for embedding should be considered. Compared with the predictor of median-edge-detector

Fig. 1 Flowchart of embedding procedure of the proposed scheme

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(MED), the predictor of gradient-adjusted predictor (GAP) is more accurate and efficient [2], which is adopted in the proposed scheme. In GAP prediction, by calculating and comparing the values of adjacent pixels, the changes in the horizontal, vertical, diagonal and anti-diagonal directions are obtained, respectively. Then, the current pixel can be predicted with a high accuracy through Eqs. (1)–(3). The current pixel Ii, j for prediction and its neighboring pixels are shown in Fig. 2. d v ¼ jI e −I se jþjI sw −bj þ jI s −cj;

ð1Þ

d h ¼ jI e −ajþjI sw −I s j þ jI s −I se j:

ð2Þ

We let Igi, j = (Ie + Is)/2 + (Isw − Ise)/4 and d = dv − dh. Thus, the predicted result I’i,j for the current pixel Ii, j can be calculated: 8 e I
; if d > 80; >  > > > I e þ I g i; j =2; if d ∈ ð32; 80; > >
 > > I e þ 3I g i; j =4; if d ∈ ð8; 32; < 0 ð3Þ if d ∈ ð−8; 8; I i; j ¼ I
g i; j ;  > s g > I þ 3I =4; if d ∈ ð −32; −8 ; > i; j >
s  > > > I þ I g i; j =2; if d ∈ ð−80; −32; > : s if d ∈ ð−8; 8: I ; Therefore, the PE for the current pixel Ii,j is: Pi,j = Ii,j − I’i,j.

2.2 Adaptive embedding mechanism Inspired by Li et al.’s scheme [7], we divide the original cover image into two types of regions according to the complexity, which are called as smooth region and rough region, respectively. In the scheme [7], Li et al. proposed to adaptively embed two bits in the smooth region, while embed one bit in the rough region. Compared with the traditional schemes, this scheme can greatly improve the hiding capacity and reduce the cumulative distortion. In our scheme, we manage to embed more bits in the smooth region compared with [7]. When the number of Fig. 2 Current pixel Ii, j for prediction and its neighborhood

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secret bits required for embedding is not too much, i.e., lower payload, the proposed scheme can achieve a greater embedding rate of each pixel and the number of pixels to be modified during the process of embedding is fewer, which leads to smaller visual distortion for stego image and a better performance of embedding efficiency. In order to more accurately determine the complexity of image pixels, the forward complexity Cf is calculated, which represents the standard deviation of adjacent pixels: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i uh u ðI e −I Þ2 þ ðI sw −I Þ2 þ ðI s −I Þ2 þ ðI se −I Þ2 f f f f t ; ð4Þ Cf ¼ 4 where If = (Ie + Isw + Is + Ise)/4. Since we extract the embedded bits and recover the stego image in the reverse order, hence, the value of Cf can be calculated with the pixels that have been recovered. Therefore, the value of Cf in both encoder and decoder are unchanged and used to determine the complexity. At the beginning of adaptive embedding, the value Cf of each image pixel is computed and an image-partition threshold τp is defined to divide all the pixels into two parts. If Cf is smaller than τp, the pixel is classified into smooth region, otherwise into rough region. Then, the pixels in both smooth region and rough region are conducted with prediction. Finally, we embed three bits into each pixel belonging smooth region and shift its value: 8 < I i; j þ 7Pi; j þ b; Pi; j ∈½−T 1 ; T 2 Þ Pi; j ≥T 1 ; ð5Þ I *i: j ¼ I i; j þ 7T 1 ; : Pi; j < −T 1 ; I i; j þ 7T 1 ; where b∈ {0, 1, 2, 3, 4, 5, 6, 7} denotes the three bits to be embedded currently. T is capacityparameter, and T1 = ⌊T/7⌋, which ensures that the value of each pixel was modified smaller than T. In order to improve the visual quality of stego image, T should be taken the minimum within the desired range. In rough region, we embed one bit into each pixel. If the prediction error Pi,j belongs to the inner region [−T, T), the expanded prediction-error Pki,j can be calculated by Pki,j = 2Pi,j + b, where b ∈ {0, 1} denotes 1 bit to be embedded currently. Thus, the embedded pixel can be obtained: 0

I *i; j ¼ I i; j þ Pki; j ¼ I i; j −Pi; j þ Pki; j ¼ I i; j þ Pi; j þ b:

ð6Þ

If the prediction error P belongs to the outer region (−∞, −T) ∪ [T, ∞), P is shifted to P' by T. Consequently, the shifted pixel can be obtained:  I i; j þ T ; if Pi; j ≥T ; ð7Þ I *i; j ¼ if Pi; j < −T : I i; j −T ; There are two main parameters, i.e., image-partition threshold τp and capacity parameter T, in the proposed scheme. The selection of image-partition threshold τp is concerned with the selection of smooth region and the efficiency of the adaptive embedding. In the special case, when the threshold τp is set as 0, it means there is no smooth region in the whole image, and the adaptive embedding in this case is no different with the traditional PEE. Therefore, we should find the optimal threshold τp to achieve the satisfactory rate-distortion performance. On the other hand, the capacity parameter T determines the number of the embedded and shifted pixels. The value of τp can be obtained through the iterations. Figure 3 shows the PSNR values of stego image with respect to different τp increasing from 1 to 8 for three standard images sized

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512 × 512, including Lena, Baboon and Sailboat. Since hiding capacity affects the stegoimage quality, thus, we also conducted experiments under different hiding capacities. The optimal threshold τp corresponding to the largest PSNR of stego image is marked with a red circle in Fig. 3. We can find that, the largest PSNR of stego image can be achieved when τp is set as 1 for most situations. As for the capacity-parameter T, it can also be exploited through several iterations to seek out the optimal value. Denote the original cover image as I = {(i, j): 1 ≤ i ≤ N1, 1 ≤ j ≤ N2}, and a sub-image J = {(i, j): 1 ≤ i ≤ N1 − 2, 1 ≤ j ≤ N2 − 2}. Since the pixels at the image border need be used as reference pixels for prediction, thus, the sub-image J is utilized for data embedding. We predict J by GAP predictor and compute the prediction error Pi,j = Ii,j − I’i,j for each pixel with the coordinate (i, j) ∈ J. Then, for T ∈{1,…, 255}, the following three sets are constructed:

&

Expandable pixels:      EðT Þ ¼ ði; jÞ∈J : −T ≤ Pi; j < T ; 0≤I i; j þ Pi; j ≤254

&

Shiftable pixels:   SðT Þ ¼ ði; jÞ∈J : Pi; j ≥T ; I ij ≤255−T ∪ ði; jÞ∈J : Pi; j < −T ; I ij ≥T

Fig. 3 PSNR of stego images with respect to τp under different hiding capacities. The first row to the last row corresponds to the results for Lena, Baboon and Sailboat, respectively. The first column to the last column corresponds to the results under the hiding capacity of 20,000, 40,000 and 60,000 bits, respectively

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&

Overflow pixels: OðT Þ ¼ J−EðT Þ−SðT Þ

In our scheme, the shiftable pixels and the overflow pixels are not modified and all secret data are embedded into the expandable pixels. Besides the secret data, the auxiliary information and the location map are also required for embedding. The bit numbers of the pure secret data, the auxiliary information and the location map are Ni, Nai and ⌈log2(N1 × N2) × O(T)⌉, respectively. On the other hand, the hiding capacity of our scheme is denoted as |E(T)|. Therefore, the optimal value T* for the capacity-parameter that achieves a good tradeoff between hiding capacity and stego-image quality can be obtained by: T * ¼ arg min fjEðT Þj ≥N i þ N ai þ dlog2 ðN 1  N 2 Þ  OðT Þeg:

ð8Þ

T

Based on the adaptive embedding strategy described above, the detailed steps of data embedding, data extraction and image recovery are given in the following.

2.3 Data embedding The detailed procedure for data embedding consists of image partition, capacity-parameter determination, pixel-selection determination, secret data embedding and auxiliary information and location map embedding.

2.3.1 Image partition The forward complexity Cf is first computed for each pixel by Eq. (4), and then the image J is partitioned into smooth region Js and rough region Jr according to Cf of each pixel, where Js = {(i, j) ∈ J : Cf < τp} and Jr = {(i, j) ∈ J : Cf ≥ τp}.

2.3.2 Capacity-parameter determination After computing the prediction error for each pixel Pi,j = Ii,j − I’i,j, we select the pixels from J for embedding and shifting, respectively. Note that the capacity parameter T∈ {1, 2, …, 255}, and we set T1 = ⌊T/7⌋ in our scheme.

&

Embeddable pixels in Js:    Es ðT Þ ¼ ði; jÞ∈Js : −T 1 ≤Pij < T 1 ; 0≤I ij þ 7 Pij ≤248 :

&

Shiftable pixels in Js:   Ss ðT Þ ¼ ði; jÞ∈Js : Pij ≥T 1 ; I ij ≤255−7T 1 ∪ ði; jÞ∈ Js : Pij < −T 1 ; I ij ≥7T 1 :

&

Embeddable pixels in Jr:    Er ðT Þ ¼ ði; jÞ∈Jr : −T ≤Pij < T ; 0≤I ij þ Pij ≤254 :

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&

Shiftable pixels in Jr:   S r ðT Þ ¼ ði; jÞ∈Jr : Pi; j ≥ T ; I i; j ≤255−T ∪ ði; jÞ∈Jr : Pi; j < −T ; I i; j ≥T :

&

Overflow pixels: OðT Þ ¼ ð Js −ES ðT Þ−Ss ðT ÞÞ∪ð Jr −Er ðT Þ−Sr ðT ÞÞ:

We can embed three bits into each pixel belonging to Es and one bit into each pixel belonging to Er. However, the shiftable pixels and overflow pixels cannot be used to carry secret data, thus, the total number of the bits that can be embedded is equal to 3|Es| + |Er|, which should include pure secret bits as well as the auxiliary information and the location map for recording overflow pixels. The number of pure secret bits is Ni and the auxiliary information occupies 60 bits. In addition, for the cover images sized 512 × 512, the location of each pixel requires log2(512 × 512) = 18 bits to record, thus, the total number of bits used to record location map is 18|O(T)|. As a result, the total number of the bits that should be embedded is Ni + 60 + 18|O(T)|. Therefore, corresponding to Eq. (8), we need to find an appropriate capacity-parameter threshold T to satisfy the following relationship: 3jEs j þ jEr j≥ N i þ 60 þ 18jOðT Þj:

ð9Þ

For all possible values of T belonging to {1, 2, …, 255}, we choose the minimum that can meet the relationship in Eq. (9) as the optimal value of capacity-parameter threshold T*.

2.3.3 Pixel-selection determination For each pixel in the sub-image J, we calculate the forward complexity Cf by Eq. (4) and the backward-complexity Cb by Eq. (10), respectively: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðI nw −I b Þ2 þ ðI n −I b Þ2 þ ðI ne −I b Þ2 þ ðI w −I b Þ2 Cb ¼ ; 4

ð10Þ

where Ib = (Inw + In + Ine + Iw)/4. Then, the maximum of Cf, Cb and |If − Ib| is obtained:


ð11Þ M ¼ max C f ; C b ; I f −I b : Then, find the smallest pixel-selection threshold τm that satisfies the following relationship to set as the optimal pixel-selection threshold τm∗: 



τ *m ¼ arg min 3 Es T * ; τ m þ Er T * ; τ m ≥N i þ 60 þ 18jOðT Þj ; τm

where Es(T*, τm) Er(T*, τm)

{(i, j) ∈ Es(T*): M ≤ τm} and {(i, j) ∈ Er(T*): M ≤ τm}.

ð12Þ

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2.3.4 Embedding process During the embedding process, the sub-image J is traversed in the raster-scanning and conducted with the following steps until all bits are embedded. Step 1: Calculate the predicted result I″i,j for each pixel I*i,j in the stego image and obtain the prediction error P’i,j = I*i,j − I″i,j. Step 2: Calculate the values of Cf, Cb* and |If − Ib*| for each stego pixel. 8 < C f ≤τ *m ; C * ≤τ * þ T * ; :

b *m

* I f −I f ≤τ m þ T :

ð13Þ

Step 3: For all pixels satisfying Eq. (9) and (i, j) ∉ O(T*), all embedded bits can be extracted through: Step 4: Replace the LSB of the first 60 + 18|O(T*)| pixels in J with the binary bits for T*, τm∗, τp, |O(T*)| and a end-location flag. Step 5: In order to embed S and all secret bits, for all pixels satisfying Eq. (9), according to the locations of smooth region or rough region and the types of embeddable pixel or shiftable pixel, we embed one bit b1∈{0, 1} or three bits b2∈{0, 1, …, 7} into each pixel, or conduct the shifting operation (T1∗ = ⌊T∗/7⌋):

I *i; j

8   > I i; j þ Pi; j þ b1 ; > > > > * > ; > > I i; j þ T > * > < I i; j −T ; ¼ I i; j þ 7Pi; j  þ b2 ; > > > > > I i; j þ 7T *1 ; > > > * > > : I i; j −7T 1 ; I i; j ;

 if ði; jÞ∈ E r ðt Þ∩ Pi; j ∈ −T * ; T * ; if ði; jÞ∈ S r ðtÞ∩ Pi; j ≥T * ; if ði; jÞ∈ S r ðtÞ∩ Pi; j < −T * ;  if ði; jÞ∈ E s ðt Þ∩ Pi; j ∈ −T *1 ; T *1 ;

ð14Þ

if ði; jÞ∈ S s ðtÞ∩ Pi; j ≥T *1 ; if ði; jÞ∈ S s ðtÞ∩ Pi; j < −T *1 ; others:

After finishing the above process, the final stego image can be produced.

2.4 Data extraction and image recovery During the process of data extraction image recovery, the auxiliary information and location map are first retrieved through extracting the LSB of 60 + 18|O(T*)| pixels in the stego subimage J. Then, the extracted 60 + 18|O(T*)| bits can be transformed into the values of T*, τm∗, τp, |O(T*)| and the end-location flag, respectively. From the end-location flag, traverse the stego image in the reverse order of embedding process, and conduct the following steps until all embedded bits are extracted. Step 1: Calculate the predicted result I″i,j for each pixel I*i,j in the stego image and obtain the prediction error P’i,j = I*i,j − I″i,j. Step 2: Calculate the values of Cf, Cb* and |If − Ib*| for each stego pixel.

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Step 3: For all pixels satisfying Eq. (9) and (i, j) ∉ O(T*), all embedded bits can be extracted through: $ 0 % 8 j 0 k Pi; j   > 0 > > ; if C f ≥τ p ∩ Pi; j ∈ −2T * ; 2T * ; > Pi; j −2 < 2 b¼ j k $ 0 % > Pi; j   0 0 > > > Pi; j −8 ; if C f ≥τ p ∩ Pi; j ∈ −8T *1 ; 8T *1 ; : 8

ð15Þ

and all original pixel values in J can be recovered through:

I i; j

j 0 k 8  0 > I *i; j − Pi; j =2 −b; if C f ≥τ p ∩ Pi; j ∈ −2T * ; 2T * ; > > > 0 > > > if C f ≥τ p ∩ Pi; j ≥2T * ; I * −T * ; > > i;* j 0 > * > > if C f ≥τ p ∩ Pi; j < −2T * ; < I i; j þ jT ; k  ¼ I * −7 P0 =8 −b; if C f < τ p ∩ P0 ∈ −8T * ; 8T * ; i; j 1 1 i; j i; j > > > 0 * > I * −7T * ; > if C f < τ p ∩ Pi; j ≥8T 1 ; > i; j 1 > > 0 > * * > I þ 7T ; if C f < τ p ∩ Pi; j < −8T *1 ; > 1 > : i;* j others: I i; j ;

ð16Þ

After all embedded bits are extracted, the first extracted 60 + 18|O(T*)| bits, i.e. S, are utilized to replace the LSB of the first 60 + 18|O(T*)| pixels in J to produce the final recovered image, and the remaining bits are the secret data.

3 Experimental results and comparisons In order to demonstrate the effectiveness and superiority of our scheme, experiments were carried out on a large number of standard images, and the environment of our experiments were based on a personal computer with a 3.30 GHz Intel i3 processor, 4.00 GB memory, Windows 7 operating system and Matlab R2010b. Figure 4 illustrates four standard test images, including Lena, Baboon, Goldhill and Barbara, with the size of 512 × 512 used in our experiments. The peak signal-to-noise ratio (PSNR) was used to measure the quality of the stego images compared with the original cover images: PSNR ¼ 10  log10

MSE ¼

2552 ; MSE

2 M N 1 ∑ ∑ I i; j −I *i; j ; M  N i¼1 j¼1

ð17Þ

ð18Þ

where MSE is the mean square error between the original cover image I and the stego image I*, Ii,j and Ii,j* denote the pixel values at the coordinate (i, j), and M and N are the height and the width of the images, respectively.

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Fig. 4 Original cover images. a Lena, b Baboon, c Goldhill, d Barbara

Fig. 5 Stego images embedded 1 × 105 bits. a Lena, b Baboon, c Goldhill, d Barbara

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Fig. 6 Hiding capacity with respect to the number of embedded pixels in smooth region

Figure 5 lists the stego images of the four original cover images in Fig. 4 that were all embedded with 1 × 105 secret bits. The PSNR values of the stego images in Fig. 5 are 27.52 dB, 25.73 dB, 29.25 dB and 26.85 dB, respectively. It can be found that, the visual quality of stego images for the proposed scheme is satisfactory. Also, all stego images can be reversibly recovered as the same with original images in Fig. 4. Because the proposed scheme is an improvement of Li et al.’s scheme [7] for hiding capacity, therefore, we compared our scheme with the scheme [7] with respect to the hiding capacity under the condition of the same number of the used, embedded pixels from the same smooth region, see Fig. 6. We can found from Fig. 6 that, the number of embedded secret bits for our scheme (i.e., hiding capacity) grows quickly with the increase of embedded pixels in the smooth region and is significantly greater than that of Li et al.’s scheme [7]. In order to demonstrate the superiority of the proposed scheme, we compared our scheme with the two state-of-the-art RDH schemes based on PEE, i.e., Thodi and Rodriguez’s scheme [28] and Li et al.’s scheme [7]. Figure 7 shows the ROC curves of PSNR values of stego images with respect to different embedding rates for Lena, Baboon, Goldhill and Barbara. It can be clearly observed from Fig. 7 that, the proposed scheme can achieve better visual quality of stego image than the schemes [7, 28] under the same embedding rate. In other words, our scheme has superior rate-distortion performance compared with [7, 28].

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Fig. 7 Comparisons of ROC curves between the proposed method and the schemes [7, 28]

4 Conclusions In this paper, we propose a novel, adaptive reversible data hiding scheme with high hiding capacity based on PEE. The original cover image is first segmented into smooth region and rough region according to the local complexity, and one bit is embedded into each pixel of the rough region with high local complexity, and three bits are embedded into each pixel of smooth region with low local complexity. In this way, the redundancy can be exploited to a greater extent, which effectively improves the hiding capacity compared to the conventional PEE schemes. Also, pixel selection mechanism is utilized to reduce the number of the shifted pixels, which leads to high PSNR value of the stego image. Experimental results demonstrate that, the proposed scheme can achieve better rate-distortion performance, i.e., embedding rate with respect to stego-image quality, than some of state-of-the-art schemes, including Thodi and Rodriguez’s scheme [28] and Li et al.’s scheme [7]. In our future work, the robustness to content-preserving manipulations [22, 31] and the resistance to steganalysis [10, 13] will be further studied, and how to generalize the RDH scheme to the cover data of text, audio and video also deserves in-depth investigation. Acknowledgments This work was supported by the National Natural Science Foundation of China (61171126, 61272452, 61702332, U1636101, 61562007), Ministry of Transport and Applied Basic Research Projects (2014329810060), and Science & Technology Program of Shanghai Maritime University (20130479), Natural Science Foundation of Guangxi (2017GXNSFAA198222), and Research Fund of Guangxi Key Lab of Multisource Information Mining & Security (MIMS15-03).

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Multimed Tools Appl 29. Tian J (2003) Reversible data embedding using a difference expansion. IEEE Trans Circuits Syst Video Technol 13(8):890–896 30. Zhang XP (2012) Separable reversible data hiding in encrypted image. IEEE Trans Inf Forensics Secur 7(2): 526–532 31. Zhang Y, Qin C, Zhang WM, Liu FL, Luo XY (2018) On the fault-tolerant performance for a class of robust image steganography. Signal Process 146:99–111

Fang Cao received the B.S. degree in applied electronics from Shanghai Normal University, Shanghai, China, in 2002, the M.S. degree in signal and information processing from Shanghai Maritime University, Shanghai, China, in 2004, and the Ph.D. degree in communication and information system from Shanghai University, Shanghai, China, in 2013. Since 2005, she has been with the faculty of the College of Information Engineering, Shanghai Maritime University, where she is currently a Lecturer. Her research interests include image processing and computer vision.

Bowen An received the M.S. degree in signal and information processing from Wuhan University, Hubei, China, in 2004, and the Ph.D. degree in Electronic Science and Technology from Chinese Academy of Sciences, in 2006. Since 2006, he has been with the faculty of the College of Information Engineering, Shanghai Maritime University, where he is currently a Professor. His research interests include remote sensing image processing and signal detection.

Multimed Tools Appl

Heng Yao received the B.S. degree from Hefei University of Technology, China, in 2004, the M.S. degree from Shanghai Normal University, China, in 2008, and the Ph.D. degree from Shanghai University, China, in 2012. Currently, he is with School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, China. His research interests include digital forensics, data hiding. Image processing, and pattern recognition.

Zhenjun Tang received the B.S. and M.Eng. degrees from Guangxi Normal University, Guilin, P.R. China, in 2003 and 2006, respectively, and the Ph.D. degree from Shanghai University, Shanghai, P. R. China, in 2010. He is now a professor with the Department of Computer Science, Guangxi Normal University. His research interests include image processing and multimedia security.