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Multilevel Data Hiding for Embedding Reversibility upon Improving Histogram Shifting

Shiuh-Jeng Wang* Department of Information

Management Central Police University,Taoyuan,

Taiwan 333 *Whom correspondence sjwang@mail.cpu.edu.tw

Chi-Yao Weng Department of Computer Science National Tsing-Hua University,

Hsinchu, Taiwan 300

cyweng@is.cs.nthu.edu.tw

Dushyant Goyal Department of Electronics and Communication Engineering LNM Institute of Information

Technology, Jaipur, India Dushyant.lnmiit@gmail.com

Abstract—This paper presents a multilevel reversible data hiding method based on histogram shifting which can recover the original image in lossless way after the hidden data has been extracted from the stego image. The method generates a residual image using the prediction method to explore the similarity of neighboring and residual image, which comes from the difference between central pixel and its neighboring pixels, is used to hide the information. We also apply an improved histogram shifting method to select two peak points for achieving high embedding capacity. Our experimental results and analytical reasoning shows that the proposed scheme has higher peak signal-to-noise ratio (PSNR) and high data embedding capacity than that of other reversible data hiding methods presented in the literature. Even in the case of multiple levels embedding the PSNR remains in the perceptible range of human vision.

Keywords:; Reversible Data Hiding, Histogram Shifting, multiple level embedding

I. INTRODUCTION With the rapid development of multimedia technologies

and growing popularity of the internet, in the field of information security, image hiding technique [1, 2] plays a very crucial and important role to protect secret messages.

Many different data hiding approaches [3-7] have been proposed for the purpose of achieving high capacity, imperceptibility, robustness and reversibility. The well known method in the information hiding in images is the Least Significant Bit, LSB [5-7] substitution. This method directly replaces of the right most insignificant bit i.e. the LSB with the confidential information and thus can achieve the effect of information hiding (or steganography). Wide range of alternatives has also been presented to Least Significant Bit to improve upon the above mentioned attributes.

All of the above stated hiding methods are irreversible methods of data hiding. However, in case of some images like medical, military or artwork preserving images reversible information hiding techniques are applied as these images are required to be restored to the initial state to facilitate the identification. So, in order to accomplish the goal to recover the cover image losslessly reversible data hiding techniques are proposed [8-17]. Reversible hiding

algorithms allow extraction of intact hidden secret data from the stego carrier image and losslessly recover the original image as well.

Basically the data hiding methods developed till date can be classified into two main types based on the embedding domain. The first type applies data embedding in the spatial domain [10-14], with relatively low capacity, while the other type utilizes the coefficients in the transform domains, such as the integer DCT and the integer wavelet transform domains [8,11, 17] to hide the data.

In 2003, Tian [9] proposed a scheme called difference expansion (DE) to add embedded messages in the resulting high-pass band of the Haar wavelet decomposition. Later some modifications have also been proposed to improve the DE method [10-12]. In 2006, Ni et al. [14] presented a reversible data hiding method utilizing the zero and peak points of an image histogram to hide message and achieving reversibility to cause only slight distortion. But, the experimental results demonstrated that its largest hiding capacity to be only about 5 kb for test gray-level image of “Lena”. Later the method used the concept of prediction to increase the peak height for high capacity [16].

In this paper, we propose a modified reversible non overlapping block based multilevel residual image histogram shifting method and use the central block prediction method to generate the difference values. The confidential information is hidden in the peak point of the residual image. So, greater the value of the peak point more the number of bits can be embedded. The proposed scheme performs much better than the current image hiding methods. The experimental results show that PSNR values remains greater than 48dB for an embedding capacity of 0.7 bpp. The proposed reversible image hiding in order to restore image is bound to use some additional information hence the compression technique is used to compress the information and send as an overhead information as a secret key to make the scheme very secure. Hence the proposed algorithm outperforms other methods both in image quality and hiding capacity.

Rest of the paper is structured as follows. In the Section 2, Ni’s algorithm is briefly reviewed. Section 3 describes the framework of the proposed method of reversible data hiding, and the proposed scheme will be divided into two

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subsections which will illustrate the embedding and extracting procedures. In section 4 we present our experimental results and conclusions follow up in section 5 with some references at the end.

II. RELATED WORK In this section, we briefly review the Ni et al method of

histogram shifting for reversible data hiding. This method utilizes the peak point of the image histogram to embed the secret information into the image. Firstly, peak and zero points are searched in the image histogram. The peak point is a pixel values having the most number of occurrences in the image, and hence having the highest peak in the histogram. A zero point is the one having the zero or least occurrences in the image. In the histogram shifting approach the pixel values lying between the range of peak and zero point are need to be modified while pixels outside the range are left unchanged. The capacity of embedding data depends on the maxima or the peak size. A histogram of the ‘Lena’ image can be seen in Fig. 1.

Note, in the above case, if there is no zero point, then, the minimum is taken as the zero point. Thus, the pixel values having the minima points are recorded before embedding. Accordingly this extra data, also called as location map, needs to be embedded with the secret data.

We will briefly describe the histogram-based approach. The embedding algorithm can be divided into two parts after histogram has been generated. In the first part, the pixel value xi, ]255,0[∈ix , which are in between the peak point and the zero point are shifted closer to the zero point or away from the peak point. This shifting creates an empty space in the image histogram at the peak location. In the second part the secret data bit-stream ]1,0[∈is is embedded in the peak location. For each pixel value equal to the peak value if the to be embedded bit is ‘0’, the value of pixel value remains unchanged, otherwise, the value is incremented by 1. In this way, the stego image is constructed.

The extracting or the recovery procedure requires the information of the stego-image, such as the pair information of peak point and zero point, or location map since zero point is free. During the recovery procedure the stego image is scanned in the same order. If the stego pixel is equal to the peak value of the pixel a secret bit ‘0’ is extracted and the recovered image pixel is remained unchanged. If the stego-pixel value is equal to one more than the peak value, then the bit extracted is 1, and the recovered image pixel is decremented by 1. Finally, the image is scanned again and the histogram i.e. the pixel values between the peak and the zero points are shifted back by 1 closer to the peak to their original location. Lastly, the zero points are replaced back into the recovered image.

Fig. 1 A Histogram of Lena Image

III. PROPOSED SCHEME In this paper, we propose to use a residual image to apply

the histogram shifting algorithm. The reasoning behind this is that the histogram shifting algorithm uses the peak point to embed the secret information into the algorithm. We observed the characteristics of an image carefully and found out that the pixel values are highly correlated among each other. In order to enhance the embedding capacity of the proposed scheme, we use a residual image whose histogram generally follows the Laplacian distribution with more number of pixels centered around the zero value. In this section we will describe the prediction method followed by the embedding and extracting algorithm in detail:

A. Generation Residual image The embedding process of our proposed scheme involves

calculating the prediction errors to generate a residual image from the correlation of the neighborhood pixels and then embedding the secret bits in the prediction errors. Here we cannot predict the complete image at one go as in traditional prediction technique because in that case the error propagation will be very large. For seeking less error propagation, we divide our image into blocks and then use the prediction technique to generate the prediction blocks. Therefore, we have to leave some pixels unused for successful reconstruction in the prediction. In our proposed scheme, we use the central pixel of a block to be a predictor and to predict the remaining pixels of the blocks. In this kind of prediction technique, we use the central pixel to predict the neighbouring pixels since the neighbouring pixels are highly correlated and similar to the central pixel. The residual block is constructed by taking the difference between the predicted and the original values. The Fig. 2 and Fig 3 are illustrated the concept.

A1 A2 A3

A4 C A5

A6 A7 A8

Fig. 2 Linear Prediction by using Central pixel In the above case, the pixels A1, A2, A3, A4, A5, A6,

A7, A8 are predicted as C and the difference or residual block is constructed as Fig. 3.

3

A1-C A2-C A3-C

A4-C C A5-C

A6-C A7-C A8-C

Fig. 3 The residual block from Fig. 2 In our proposed scheme, we also describe our improved

histogram shifting algorithm. The residual image histogram follows a Laplacian distribution and consists of peaks centered around zero and zero points near the extremes. So, in order to achieve high embedding capacity, we firstly find two peak points (M1 and M2) from the histogram, such that M1 M2, and their corresponding zero points (m1, m2), i.e. such that the first peak point (M1) is just greater than m1 and the second peak point (M2) is just smaller than m2. The strategy of this is to avoid overlapping in the shifting phase. Once the peak and zero pair are searched the histogram between (m1, M1) is shifted left by 1 unit and the histogram between (M2, m2) is shifted right by 1 unit. After the pixel shifting, we applied the histogram-based approach, which the secret is embedded into two peak points, the detail algorithm is shown as below.

B. Embedding Algorithm The secret data is embedded in the two peak points. The pseudo embedding procedure for an 8-bit gray scale image I of size M × N can be described as: S be the secret message

]1,0[∈is , I’ be the stego image and ‘t’ be the hiding level. 1. Divide the original cover image into non-overlapping

blocks (B) with size K × K. 2. Use the prediction technique, which is described in

Section 3.1, to generate the residual block (RB) for each cover image block (B).

3. Generate the histogram H(x) of the residual block (RB). 4. Select the peak and zero points from the generated the

histogram of RB and apply the histogram shifting algorithm to perform the data hiding strategy.

5. Embed the secret data into the block at the peak points M1 and M2. If the pixel value is M1 and the secret bit si=1 then the value changes to M1 1. Otherwise, the value remains unchanged if the secret bit is 0. If the pixel value is M2 and the to be embedded secret bit si =1 then the value changes to M2+1. Otherwise, while if the secret bit is 0 the value remains unchanged.

6. We also apply our algorithm multiple times to embed secret information. For the case of multi-level data hiding the steps 4-6 are repeated, and after each iteration the value of the residual block is updated with the newly generated stego block (SB).

7. Finally perform the reverse, for example, inverse prediction transformation, to construct the final stego or marked image with the embedded secret data.

Consider an image block of sixe 3×3 as shown in Fig. 4 and

secret bits are given as “0000100”. Firstly, we chose the central pixel as predictor to predict

the other pixel of the block and calculate the residual block that is shown as Fig. 5. The histogram created from all the residual values is shown in Fig. 6. According to the histogram, we find the two pairs of peak and zero points as: (m1, M1) = (-2, 0) and (m1, m2) = (1, 2). Note, the embedding capacity equals the number of peak points (M1+M2), in this example it is 7 (3+4). Next, the histogram is shifted left by 1 unit in the range (-2, 0) and right by 1 unit in range (1, 2). Then the secret bits (0000100) are embedded in the image at the location of the peak points as shown in Fig. 7. After the secret message is embedded the residual values and histogram are shown in Fig. 7 and 8 respectively. Finally the residual values are converted into the stego pixels by adding the difference value to the central pixel of the block (Fig. 9).

Fig. 4 An example of cover block (B)

154 155 155

154 154 155

153 154 155

Fig. 5 The residual block (RB)

0 1 1 0 154 1 -1 0 1

Fig. 6 The histogram of residual

block

Fig. 7. Secret embedding

0 1 1 0 154 2 -2 0 1

Fig. 8. Histogram of original

image residual block

Fig. 9 The Stego block (SB)

154 155 155

154 154 156

152 154 155

C. Extraction Algorithm The extracting procedure is similar with the embedded

procedure exception the image is stego-image. The extracting procedure is described as follows. 1. Divide the 8-bit gray scale stego-image I’ with size M ×

N into non-overlapping blocks of size K × K. 2. Generate the residual stego-block (SB’) for each block

using the same prediction algorithm as used in the embedding phase in the same sequential order.

3. The residual stego-image block is scanned. If the residual pixel equals to the peak point M1 or M2, a secret bit 0 is extracted and the final pixel value

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remains unchanged. On the other hand, if the pixel value is equal to either M1 1 or M2 + 1, then, the secret bit 1 is extracted and the recovered pixel value is decremented for M2 1 and incremented for M1+ 1. The extracted bits are concatenated into the main bit stream S’ to form the secret data. Note that m1, m2, M1 and M2 are the received peak and zero points for each block whish are compressed using arithmetic coding and sent to the receiver as a secret key.

4. If the embedding procedure was followed ‘t’ times i.e. multi-layer embedding was done then the steps 3 is repeated for ‘t’ times and with each iteration. The value of the new stego-residual block is updated as:

tt SBSB ''' = . 5. Once all the blocks are restored, the inverse prediction

rule is followed to recover the original image. Following the example of embedding procedure, we will

describe the complete extraction procedure. The stego-image generated after in example stated in embedding procedure shown in Fig. 9. Keeping the central pixel unchanged we calculate the predictive difference values. Now to perform extracting operation the decoder uses the overhead information of peak and zero pairs (-2, 0) and (1, 2) for the block. The pixels are processed sequentially and according to step 3 the secret bits 0 for the pixels equal to 0 and 1 and secret bits 1 for pixel values equal to -1 and 2 are extracted. After this the histogram is shifted back to its original shape. Finally the original image is recovered by inverse prediction algorithm.

IV. EXPERIMENTAL RESULTS To evaluate the performance of the proposed scheme, in our experiments we have used five gray-level images, and these images size are 512x512. The secret message in our algorithm was generated randomly. The Fig. 10 shows the stego-images produced by our proposed algorithm after first level of embedding. To evaluate the performance, we use the estimation function of peak-signal-to-noise-ratio (PSNR) and MSE, which is defined as Eq. (1) and Eq. (2).

)255(log10)(2

10 MSEdbPSNR ×= (1)

2

1 1

1MSE ( ( , ) ( , ))M N

x y

I x y I' x yM N = =

= −×

(2)

where, M and N denote the width and height of the cover image, respectively.

The performance of our method depends on the peak point in the residual image histogram in each block. Here we have found by experimentation that that best performance is given by the block size of 3×3. The reason behind this is that in a small size block the correlation among the pixels is large to have better embedding capacity. Here we have compared our results with Ni’s scheme [14] and the Lin’s multilevel scheme [15]. Fig. 10 shows the result of the test images for single layer embedding which demonstrates that the

proposed scheme makes the distortion of proposed scheme imperceptible. Table 1 and 2 are shown as the resultant with various levels by using our approach. From Table 1 and 2, tables show the superiority of the method from Ni’s method in terms of both hiding capacity and stego image quality since applied single layer embedding. Table 3 compares the results of embedding rate and average PSNR values of the proposed scheme with the with Ni’s scheme [14] and the Lin’s multilevel scheme [15].

(a) (f)

(b) (g)

(c) (h)

(d) (i)

(e) (j)

5

Fig. 10 The Cover images and Stego images by using our approach: (a-e) cover images; (f-j) stego image using first layer.

Table 1. The resultant of PSNRs using versus hiding level for five test images.

Images Level

Lena Baboon Jet Boat Peppers

1 53.55 55.03 52.39 52.71 52.70

2 47.96 50.38 47.49 50.27 47.93

3 45.13 47.50 44.62 45.07 45.08

5 41.38 43.65 40.95 41.33 41.30

9 36.63 38.89 36.37 36.67 36.52

12 34.25 36.38 34.26 34.26 34.10

Table 2. The resultant of hiding capacity (bits) using versus hiding level for five test images.

Lena Baboon Jet Boat Peppers

1 111,513 79,254 125,944 110,315 110,365

2 202,437 148,913 227,278 137,047 200,225

3 279,474 213,010 311,565 277,668 276,405

5 411,514 333,353 451,075 408,940 407,406

9 647,863 566,116 690,499 645,946 642,899

12 821,775 739,473 864,005 819,123 816,570

Table 3. Comparisons of Hiding capacities (bits) and average PSNRS with various approaches.

Ni et al. method [14]

Lin et al. method [15]

Our approach

Ave. PSNR 48.55 27.58 34.65Lena 5,460 416,882 821,775

Baboon 5,421 283,333 739,473Jet 59,979 436,168 864,005

Boat 7,301 379,624 819,123Pepper 57,150 421,341 816,570

V. CONCLUSION In this paper, we proposed a reversible data hiding

technique based on two peaks histogram shifting of the residual image for increasing the hiding capacity. The residual image is produced from central pixel and its neighboring pixels. The secret data is embedded at the peak points of the histogram. The proposed scheme outperforms some of the previous works like Ni et al.’s histogram-based and Lin et al.’s multilevel scheme both in terms of capacity

and PSNR. The results provided prove that the PSNR value of the scheme is greater than 48db with a capacity of greater than 0.7 bpp (bits per pixels) for all kinds of images. Besides, the computation complexity of the proposed scheme is also very small as it just deals with the shifting and searching operations.

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