An Overview of Reversible Data Hiding Schemes

2009 First International Conference on Software Engineering & Computer Systems, ICSECS09

An Overview of Reversible Data Hiding Schemes based on Difference Expansion Technique Osamah M. Al-Qershi, Khoo Bee Ee School of Electrical and Electronic Engineering, University Sains Malaysia Seri Ampanang, 14300 Nibong Tebal, Seberang Perai Selatan, Penang, Malaysia Abstract — Reversible data hiding is a type of data hiding techniques whereby the host image can be recovered exactly. Being lossless makes this technique suitable for medical and military applications. Difference expansion (DE) is one of the most important techniques which are used for reversible data hiding. This technique received more attention over the years because of its high efficiency and simplicity. The aim of this paper is to present a review of reversible DE-based data hiding techniques proposed so far in order to define the purpose of DE-based data hiding, reflecting recent progress, and provide some research issues for the future. Many researchers tried to improve its performance in terms of hiding capacity and visual perceptibility. However, some of the modified techniques need more improvements to be applicable. DE technique is still a promising technique and it is expected that more serious trials to improve it will be revealed during the next few years. INTRODUCTION Reversible data hiding scheme is the technique that allows embedding data inside an image and later the hidden data can be retrieved as required and the exact copy of the original host image is recovered. Some of the traditional reversible data hiding schemes are based on modulo-arithmetic additive and spread-spectrum techniques [1,2]. An example of these schemes is the one proposed by Honsinger et al., which based on addition of modulo 256 as an invertible operation [2]. Although some of these schemes are robust, the modulo-arithmetic-based reversible data-hiding algorithms have the disadvantage of salt-and-pepper visual artifacts and hinder watermark retrieval [3]. In order to enhance the robustness of the reversible watermarking and reduce the salt-and- pepper visual artifact of the above mentioned schemes, histogram shifting techniques were proposed. In this scheme, the embedding target is replaced by the histogram of a block of the image. A good example of the scheme is the circular interpretation scheme proposed by Vleeschouwer et al. [4, 5]. Although this type of data hiding schemes provides a higher quality of the embedded image, the embedding capacity is lower [6]. A different category of data hiding schemes involves methods that losslessly compress a set of selected features from an image and embed the payload in the space saved due to the compression. This type results in higher embedding capacity than the previously mentioned types [7]. Another scheme of this type is the generalized Least Significant Bit (g-LSB) embedding algorithm proposed by Celik et al. [8], which is based on grouping the pixels and embedding data bits into the state of each group. A very 741

different scheme was proposed by Tian based on modifying the difference between a pair of pixel values while keeping the average of them unchanged [9]. His method divides the image into pairs of pixels, then embeds one bit of information into each pair. Of course, not all pairs can be used for data hiding. The pairs that are only expandable and do not cause overflow or underflow errors are expanded. The location map indicates whether the pairs are expanded or not. The scheme displayed a remarkable performance in terms of high embedding capacity and low distortion in image quality [10]. However, the major drawback of Tian's scheme is the lack of capacity control [3]. Since Tian introduced the DE technique, the influence of his work can be easily found in many later works. The extensions of his method by other researchers have yielded many good and more sophisticated algorithms [10]. This definitely will inspire more researchers to improve it further. This paper presents a review of DE-based data hiding techniques proposed so far in the literature. Some efficient algorithms with their advantages and disadvantages with respect to the visible quality and capacity offered by them are explained. The paper is arranged as follows. The first section introduces the general principle of DE. The second reviews some recently proposed DE-based data hiding algorithms. Then discussion and the conclusions are presented. DIFFERENCE EXPANSION TECHNIQUE The DE embedding technique involves pairing the pixels of the host image and transforming them into a low-pass image containing the integer averages and a high-pass image containing the pixel differences. If x and y be the intensity values of a pixel-pair, then l and h are defined as  (x + y ) , l=  2 

h= x− y

(1)

This transformation is invertible, so that the gray levels x and y can be computed from l and h  h + 1 , and h y=l−  x=l+  2  2 

(2)

An information bit b ∈ { 0,1} is embedded by appending it to the LSB of the h difference, thus creating a new LSB. The watermarked difference is (3) h ′ = 2h + b Figure 1 shows an example of embedding one bit in a pair of pixels. The resulting pixel gray-levels are calculated from the difference ( h′ ) and integer average l using

equation (2). For an image with n-bit pixel representation, the gray levels satisfy x, y ∈ 0,2n − 1 if and only if h and l satisfy the following condition: (4) h ∈ Rd (l ) = 0, min(2 (2 n − 1 − l ), 2l + 1)

[

[

]

]

where Rd is called the invertible region. Combining (3) and (4), we obtain the condition for a difference h to undergo DE 2h + i ∈ Rd (l ) for i = 0,1

(5)

respectively. A location map is formed to distinguish between the three different groups. The map is then compressed, concatenated with the payload, and then embedded into the image. The major drawback of Tian’s scheme is the lack of capacity control, which results from having to embed the compressed location map along with the payload. The locations selected for expansion embedding determine the location map, so the compressibility of the location map depends on the set of expandable differences. Since it is impossible to predict the size of the compressed location map while selecting the locations to embed, it is difficult to determine the capacity in advance. Besides, at low embedding rates, the compressibility of the resulting location map is low, resulting in a large fraction of the available capacity to be used to embed the compressed map. DE-BASED DATA HIDING TECHNIQUES In this section, some of DE-based data hiding schemes proposed so far are presented with investigating related advantages and disadvantages of each scheme. 1. DE of Generalized Integer Transform Alattar extended Tian’s work and proposed a DE scheme of triplets [11]. In his scheme, data bits are embedded in spatial and cross-spectral triplets, instead of pairs, to increase the hiding capacity as two bits are embedded in each triplet. A modified version of the scheme proposed by Alattar, in which quads are used for embedding in order to increase the hiding capacity as three bits are embedded in each quad [12]. Later, he generalized his scheme for an n-pixels vector to maximize the hiding capacity [13]. For vector of N pixels ( a0u0 , a1u1 ,....aN −1u N −1 ) ,

Fig 1. Embedding end extracting phases for a pair

This condition is called the expandability condition for DE. A difference that satisfies the expandability condition is called an expandable difference. Meanwhile, the LSB of a difference may be replaced with an information bit. This is a lossy embedding technique since the true LSB is overwritten in the embedding process. However, in Tian’s scheme, the true LSBs of the differences that are embedded by LSB-replacement are saved and embedded with the payload, to ensure lossless reconstruction. The LSB of a difference can be flipped without affecting its ability to invert back to the pixel domain if and only if 2 h / 2 + b ∈ Rd (l ) for i = 0,1

(6)

This is called the changeability condition. A difference satisfying the changeability condition is called a changeable difference. An expandable difference is also a changeable difference. An information bit b is embedded into a changeable difference as (7) h′ = 2 h / 2 + b During embedding, differences are classified into three groups: expandable, changeable, and non-changeable. Data bits are embedded only into expandable and changeable differences using equation (3) and (7)

the forward transform represented by equation (1) is changed to   N −1  ∑ ai u i  v0 =  i =N0−1   ai    ∑ i =0 v1 = u1 − u 0 : (8) vN −1 = u N −1 − u0 where v0 is equivalent to l, v1, v2 ,..., vN −1 are equivalent to h, and a is constant. In the same manner the inverse transform is given by   N −1  ∑ ai vi  u0 = v0 −  i =N0−1   ∑ ai   i = 0  u1 = v1 + u0

: u N −1 = vN −1 + u0

(9)

A threshold T is used to elect expandable vectors in order to control the embedding capacity and hence control the

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visual quality of the embedded image as v1 ≤ T , v2 ≤ T , ….. v N −1 ≤ T . The advantages: (i) Simple and general scheme that can be applied for any number of pixels per vector, (ii) very high embedding capacity, theoretically 0.75 bpp in case of using quads, in comparison to the original DE technique which cannot exceed 0.5 bpp. The disadvantage is the overhead costs due to the embedding map, despite the modification which was proposed to increase the compressibility of the location map. He compared his work with Tian’s, and the results showed that Alattar's scheme has better performance than Tian's in terms of PSNR in case of high embedding capacity, while they are almost the same with low embedding capacity. 2. DE with Sorting Kamstra et al. extended the original DE technique in order to avoid the overhead cost caused by embedding the location map, and to make it easier to deal with capacity control [14]. In their scheme, the image is transformed into a low-pass and high-pass image L and H, respectively. Embedding is done by expanding or changing H–values, while the low pass image L is used to predict which locations to be embedded. In order to achieve that, they defined a regularity measure µ : C → R+ which measures the smoothness of L in the neighborhood of (i, j ) as the smaller µ (i, j ) , the more regular the image L around (i, j ) . The regularity measure can be defined as 1 (10) µ (i, j ) = ∑ ( L(i′, j ′) − L (i, j )) 2 W (i, j ) ( i′, j′)∈W ( i , j ) where W (i, j ) is a window surrounding (i, j ) , and L (i, j ) is the average of L inside W (i, j ) . Using µ all changeable locations are sorted in a list Cµ with ascending µ -values. The locations at the beginning of the list are more likely to be expandable than locations that occur more towards the end. As a consequence of this, the location bitstream, which is equivalent to embedding map in Tina's scheme, contains mostly 0s, especially in the beginning, and only very few 1s. This allows strong lossless compression. The advantages: (i) better capacity control, (ii) better visual quality at low embedding capacities. The disadvantages: (i) the theoretical maximum embedding capacity is still 0.5 bpp, (ii) low visual quality when embedding capacity approaches 0.5 bpp as their results showed that the performance of their scheme is almost the same as Tian’s. 3. DE with Companding Technique Weng et al. adopted DE for quads proposed by Alattar [15]. Their scheme aimed at increase the compressibility of the embedding map which consumes all the available hiding capacity. They proposed using companding technique in order to overcome low hiding capacities at small thresholds T. The companding technique contains a compression function C and an expansion function E as

 x x 2∆ + 1 hs − ∆ − 1, (16) h= 1 2 2 + ∆ + < − ∆ − h if h s  s In their first scheme, a 2-D overflow map is formed, indicating the expandable locations. The overflow map is losslessly compressed and then combined with a header segment in order to form the auxiliary information. In their second scheme, identification (at the decoder) of the set to which each location belongs is done by flag bits, which are embedded during embedding phase. Every location is associated with an integer called the order of

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modifiability α (i, j, ∆) , which is a measure of the ability of the difference value at a location to undergo modification. The only difference between the schemes is in the logic for determining the expandable set of differences. The advantages: (i) the amount of auxiliary information embedded is significantly reduced (ii) the computational intensity required for histogram shifting is much less than that required for the compression/decompression operations. Disadvantage: performance decays with high embedding capacities due to multiple embedding. 5. Adaptive Centralized DE Lee et al. proposed an adaptive scheme with very high embedding capacity [16]. In their scheme, the payload for each pixel in an image is dynamic in order to reduce the distortion of embedded image. In the proposed scheme, the original cover image is partitioned into a series of non-overlapping blocks, and the payload of each block depends on its block size and the image characteristics. Image blocks are classified into 4 types according to a predefined threshold T, so that the numbed of bits to be embedded in a block is determined by the type of the block. Although there are four types of blocks in the embedding procedure, only 1 bit is required to record these four different types. Therefore, the size of additional record is the same as Alattar’s technique. For each block of k pixels, the pixels are sorted in ascending order, and then the median value vm is taken as a reference while calculating the difference values among all the pixels in the block. The k − 1 difference values between vm and the other pixel values can be calculated as (17) 0 ≤ i ≤ k − 1 and i ≠ m di = vi − vm , The base of each block is defined as l. Consequently, the real range of data for each block is b ∈ {0,1,..., l − 1} the data bits b is inserted into each difference value by using the following equation: l × d i + b, for vi > vm (18) d i′ =  l × d i − b, for vi < vm The new pixel value vi′ after hiding data can be computed by the following equation: (19) vi′ = vm + d i′ where 0 ≤ i ≤ k − 1 and i ≠ m The advantages: (i) simplicity, (ii) very high embedding capacity, and (iii) better visual quality in terms of PSNR. The disadvantage of the scheme is the block type bits which are equivalent to embedding map in Tian's scheme. Those bits are not embedded into the image although they are needed to start extracting phase. The scheme has a very high capacity, but it needs some improvement to be applicable. 6. DE Without A Location Map Lin et al. proposed a scheme that adopts the relation among pixels in a block to determine whether a pair of

pixels can be expanded [17]. They aimed at increasing the embedding capacity as all of the embedding capacities can be used to embed the payload. In order to achieve that, the status of expandable differences is not saved in the location map. In their scheme, the host image I is divided into 4-pixel × 3-pixel overlapping blocks. For each block i, one bit of the payload is embedded into the difference between the two center pixels xi , yi . For each block, the differences between the maximum and minimum pixel values, and between the two center pixels xi , yi are calculated as di = max i − min i for each block i (20) hi = xi − yi st During the 1 pass, if hi is not expandable, the corresponding value d i is saved in the list ND1 . The image is scanned again, and for each block i , if d i < ND min 1 and di ≤ T , then a bit of the payload is embedded into the block. During the 2nd pass, the first column of the image is left undivided, and the image is divided again in the same manner in the 1st pass. The whole process is repeated again and the second list ND2 is formed. The maximum embedding capacity of a single layer is no more than ( (W − 1) / 2 + (W − 2) / 2) × ( H − 2) / 2 bits for an image of size W × H pixels. The advantages: (i) simplicity, (ii) no map is stored, and (iii) high embedding capacity in case of multilayer embedding. The disadvantage: the minimum value, NDmin 1 and NDmin 2 , for each layer are not embedded into the image although they are needed to start extracting phase. 7. Spatial Quad-Based DE Chang et al. proposed two quad-based schemes that select the suitable expandable blocks according to a measure function [18]. The proposed schemes can embed more than 2-bit information to each expandable block on average. Both schemes use the same measure function to classify blocks. The measure function ρ (b, T ) is a Boolean function given as: ρ (b, T ) = ( a11 − a12 ≤ T ) ∧ ( a 21 − a 22 ≤ T ) ∧ (21) ( a11 − a 21 ≤ T ) ∧ ( a12− a 22 ≤ T ) Where b is a 2×2 block in the host image. T is a predefined threshold. a11 , a12 , a21 , a22 are pixel values in block b. If ρ (b, T ) is true, b is selected to be embedded. A location map is used to record the embedded blocks. The location map is compressed and concealed as a part of the payload. However, the authors did not present the extracting phase and how to extract the location map which is needed to initiate extracting the payload. The advantages: (i) quite simple scheme, and (ii) high embedding capacity. The disadvantage is the need to embed the location map. Although the location map is supposed to be embedded into the image, the authors did not mention where and how to embed it.

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8. Two-Level DE Chiang et al. proposed a two-level DE scheme for medical images [19]. In their scheme, 14 bits of the payload are embedded into each smooth block of 4×4 pixels. During embedding, the image is divided into blocks of 4×4 pixels, and then a two-level DE transform is applied to each block. A smooth block is transformed into all-zero block except the upper leftmost pixel as shown in Fig. 2.

determined adaptively in order to meet the size of payload to achieve more embedding capacity while keeping distortion almost as same as the original DE method. The advantages: (i) better visual quality at the same payload size in case of original DE, (ii) the simplified location map can be embedded without compression. The disadvantages: (i) low visual quality at low payload capacities, and (ii) the pairs in the image may be scanned several times to find the proper value of T. DISCUSSION

Fig 2. Two level DE for a smooth block

The upper leftmost pixel is kept intact while a nonzero value is embedded into the lower rightmost pixel. The nonzero value is used to identify embedded blocks, while the other 14 locations in the block are used for embedding the payload. The advantages: (i) simplicity, (ii) no location map is needed, and (iii) high embedding capacity. The disadvantage of this scheme is limitation of number of smooth blocks. The scheme is suitable for certain images which have large number of smooth blocks. For natural images with less number of smooth blocks, the capacity may decay dramatically. 9. DE With Simplified Location Map Kim et al. proposed a novel scheme that exploits quasi-Laplace distribution of the difference values between pairs [20]. In their scheme, they defined a new set of equations based on a predefined threshold T to classify pairs of an image. Expandable pairs should satisfy the following conditions (22) h ≤T and (23) T ≤ l < 255 − T The expandable pair satisfying condition (23) and satisfying condition (24) h ≤ T / 2 is said to be unambiguously expandable (can be expanded at least twice). The expandable pair satisfying condition (25) T / 2 < h ≤ T  is said to be ambiguously expandable (can be expanded only once). Inexpandable pair satisfying condition (26) T < h ≤ 2T + 1 is said to be ambiguously inexpandable. Inexpandable pair satisfying (27) 2T + 1 < h is said to be unambiguously inexpandable. The purposes of this classification are to increase the embedding capacity, as some pairs can be expandable twice at least, and to simplify the location map, which yields to increase the compressibility of it. Moreover, the value of T is

The aims of improving the original DE proposed by researchers are two folds: first is to make the embedding capacity as high as possible, second is to make the visible distortion as low as possible. To achieve high embedding capacity, the reviewed schemes adopted three different approaches: (i) simplifying the location map in order to increase its compressibility, (ii) embedding payload without location map, and (iii) expanding differences more than once which allows more data to be embedded. Meanwhile, the visual quality may be enhanced by: (i) using predefined threshold T, (ii) selecting smooth areas to embed data, and (iii) using sophisticated classification functions. However, there is a trade off between distortions and embedding capacity. If distortion is minimized, only a few data can be embedded. On the other hand, if the embedding capacity is increased it results in low visible quality. In order to overcome the contrast between high embedding capacity and high visual quality, all the reviewed schemes, except (2)(8), employs thresholds in order to control the hiding capacity trying to minimize the distortion caused by expanding differences. The key of solving the capacity-quality issue is to use intelligent adaptive techniques to set the proper thresholds. Although the reviewed schemes can relatively achieve the two above mentioned aims, each scheme has its own drawbacks. The drawbacks can by summarized as 1- Some of the schemes, (1) (2) (3) (4) (5), did not display good visual quality for all frequencies of embedding capacity. 2- Some schemes need side information to initiate extracting phase, (5) (6) (7), while these data are not embedded into the host image. 3- Some of the schemes show good performance only with smooth images, which make them suitable for specific types of images (8). 4- Some of the schemes are complicated (3) (5) (9), and all of the schemes are time consuming as they scan the host image more than once. To overcome those drawbacks and improve the performance of DE-based schemes, a combination of two or more schemes may be used in order to get the advantages of them together. However, some of the schemes, (5) (6) (7), need more improvement to be applicable with a superior performance among the reviewed schemes. Only hiding capacity, in terms of bits per pixel (bpp), and visual quality, in terms of Peak Signal to Noise Ratio (PSNR), are used to evaluate the reviewed schemes. Visual

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quality is not that important for evaluating reversible data hiding technique as the original image can be retrieved exactly. It is suitable for non-reversible data hiding technique where the distortion caused by concealing data is permanent. Instead, it will be better if a different criterion based on complexity of the scheme and the time of processing is constructed to measure the performance. Such a criterion, combined with data hiding capacity, will be very effective to evaluate not only DE-based schemes, but all reversible schemes. Unfortunately, such a criterion will depend on the type of the code and the specifications of the machine used to simulate the scheme. More researches should be done to come up with a proper criterion to precisely reflect the performance of reversible data hiding techniques.

[7]

[8]

[9]

[10]

[11]

CONCLUSION This paper has presented some of the recent DE-based data hiding schemes together with their advantages and disadvantages. Comparing to the original DE technique, all the reviewed schemes displayed improved performance based on its hiding capacity or visual quality. However, each scheme has its own drawback which means that the optimal DE technique is still not achieved. All the schemes need more improvement to enhance its performance. Furthermore, it is expected that more serious trials to improve the original DE will be revealed during the next few years yielding to the optimal DE-based data hiding.

[12]

[13]

[14]

AKNOLEDGEMNT This work is supported by Ministry of Science, Technology and Innovation through eScienceFund grant 01-01-05-SF0114 and Ministry of Higher Education through Fundamental Research Grant Scheme (FRGS).

[15]

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