Sharing a Large Secret Image Using Meaningful Shadows Based on VQ and Inpainting

Abstract

This paper proposes a novel progressive secret image-hiding scheme based on the inpainting technique, the vector quantization technique (VQ) and the exploiting modification direction (EMD) technique. The proposed scheme first divides the secret image into non-overlapping blocks and categorizes the blocks into two groups: complex and smooth. The blocks in the complex group are compressed by VQ with PCA sorted codebook to obtain the VQ index table. Instead of embedding the original secret image, the proposed method progressively embeds the VQ index table into the cover images by using the EMD technique. After the receiver recovers the complex parts of the secret image by decoding the VQ index table from the shadow images, the smooth parts can be reconstructed by using the inpainting technique based on the content of the complex parts. The experimental results demonstrate that the proposed scheme not only has the advantage of progressive data hiding, which involves more shadow images joining to recover the secret image so as to produce a higher quality steganography image, but also can achieve high hiding capacity with acceptable recovered image quality.

1. Introduction

In contrast to traditional information transmission, such as mail by the post office and delivery services of a delivery company, the Internet provides fast and convenient data transfer for thousands of users via worldwide networks. However, the Internet environment is public, so how to provide secure data transfer via the Internet becomes an important research subject. To date, two techniques, cryptography [1-3] and steganography [4-6], have been widely employed. The main idea behind cryptography is to encrypt data with a secret key. The procedure of encryption is essentially the re-encoding of data into meaningless ciphertext. Attackers cannot decode the ciphertext into the original data without the secret key. However, the meaningless appearance of the ciphertext readily attracts the attention of the malicious attacker. Steganography focuses on how to embed data into cover objects, such as video, audio, and digital images. The intent is to embed data by making the smallest possible distortion to the cover object; thus, steganography may draw less attention from attackers than cryptography [23-27]. The most representative method of image-based steganography is least significant bit (LSB) substitution [7-9], which embeds the secret data by directly substituting the LSB of the cover pixels in the image with the secret bits. Since the change of the LSB of the pixel has the smallest influence on the value of the pixel, this method can achieve the goal of embedding secret data while keeping low distortion of the cover image.

In contrast to the cryptography and steganography one-sender-to-one-receiver data transfer structure, the secret data sharing technique [10] embeds data in multi-images and sends the shadows to multi-receivers. Thus, the secret data can be retrieved by some receivers instead of all of them. As a result, even though some receivers lose their shadows, the secret data still can be reconstructed through cooperation among the residue receivers. Due to the development of the digitalization of our society, there are more and more sensitive digital image files need to be protected. Therefore, a lot of researchers are working on how to protect image type of secrets in secret sharing. The proposed methods of the previous works could be classified into two categories [11]. The first category is the polynomial-based secret image sharing, which hides the information of the image into the coefficients of the polynomial so that the secret image could be reconstructed lossless if and only if the polynomial is rebuilt during the secret image recover procedure. The other category is visual secret sharing (also called visual cryptography). The first (t, n) visual secret sharing scheme was proposed by Naor and Shamir [12]. Noar and Shamir’s scheme generates n shadows for a secret image and prints them on n transparencies. Any t or more than t transparencies stacked together could decrypt the secret image visually and approximately. Different from the polynomial-based secret image sharing, visual secret image sharing does not need complex computation and cryptographic knowledge to decrypt the secret image. However, there is a common limitation for aforementioned two categories, which is the superposing result of the shadow is either decrypted secret image correctly or exposed nothing of the secret image. In order to break this limitation, some researchers have been studied to solve how to sharing secret image progressively in visual secret sharing, which means that the more the participants work together, the higher quality of secret image they can retrieve. Fang and Lin proposed a progressively secret image sharing scheme for binary images [13]. In this scheme, the participants are weighted, which means, the important participant could have more than one shadows while other ordinary participant could have only one shadow each. In order to extend the application of progressively secret image sharing, Jin et al. [14] proposed a new scheme that could support both grayscale and color images with the use of halftoning and a novel microblock encoding scheme. There is a short come of Fang and Lin’s scheme and Jin et al.’s scheme, which is the generated shadows are noise-like shadows. It will be very hard for users to identify and manage them. Accordingly, some schemes were designed to generate user friendly shadows, which are shrunken versions of the secret image [15-16]. Surly these schemes provide easier way for shadows identification and management. However, this kind of shadow reveals some information of the secret image, so it is not applicable in secret image protecting applications. In order to provide the user friendly shadows generated mechanism and secret image sharing function in a progressive way simultaneously, Fang proposed a novel user friendly progressively secret image sharing scheme[17]. Fang’s scheme expands a pixel in the halftone secret image to a 2×2 pixels block and generates new blocks for meaningful shadows from it according to another meaningful image. To fix the pixel expansion problem in Fang’s scheme, Chang et al. proposed a new 2×2 sized block-wise operation based user friendly progressive visual secret sharing scheme [11]. In Chang et al’s scheme, the size of the secret image equals the size of the shadow image and the recovered secret image, in other words, the hiding capacity of Chang et al’s scheme is better than Fang’s scheme. To further improve the hiding capacity in the user friendly progressive secret image sharing mechanism, this paper proposes a novel progressive grayscale secret image sharing scheme based on VQ, EMD and image inpainting techniques. On the one hand, totally different from previous works’ block mapping mechanism, our proposed scheme skillfully design a procedure of progressively embedding the VQ indices of the complex part of the secret image into the cover images, and then, get the high quality shadow images. On the other hand, since the smooth part can be reconstructed vary well by using the inpainting technique with valid surrounding information, the proposed scheme reduces the information of the secret image to the information of the complex part of the secret image. As a result, the constructed shadow image is much smaller than the shadow image constructed in the previous works.

The following is a brief description of the proposed scheme. First, the proposed scheme extracts the complex blocks of the secret image and compresses them by using the vector quantization (VQ) technique [18,19]. Second, the compression result of the last step is embedded into multiple cover images via the exploiting modification direction (EMD) technique [20] and LSB. The inpainting technique [21,22] is adopted at the last step to recover the secret image. The advantages of the proposed scheme include achieving progressive secret image recovery and sharing secret images by using relatively smaller cover images with a high-quality stego image.

The rest of this paper is organized as follows. The VQ technique, EMD technique and PDE based image inpainting technique are introduced as related works in Section 2. Section 3 illustrates the detailed procedures of the proposed method. The experimental results are provided in Section 4. Finally, the conclusion is presented in Section 5.

 

2. Related Work

The proposed scheme uses the VQ technique to compress the complex blocks of the secret image, adopts the EMD technique to embed the compression result in the cover images and utilizes the PDE based image inpainting technique to reconstruct the smooth part of the secret image; thus, VQ, EMD and PDE based image inpainting technique are introduced in this section.

2.1 VQ technique

Gray proposed the VQ compression technique in 1984 [18]. The procedures of VQ can be separated into three phases: codebook generation, image encoding, and image decoding. The Linde-Buzo-Gray (LBG) algorithm is the classic method for generating the codebook, which contains N k-dimensional codewords . The first step of image encoding is dividing the image into h×w non-overlapping blocks. Every block b contains k = h×w pixels, which can be treated as a k-dimensional vector bv. Then, the encoding method finds the most similar codeword cwj for bv in by computing the Euclidean distance, where 0 ≤ j ≤ N-1. The index j of cwj in the codebook is kept as the compression result of bv. After all blocks of the image find their corresponding cowords, the image can be compressed into a VQ index table. Fig. 1 shows the flow chart of the VQ encoding phase.

Fig. 1.VQ encoding phase

The VQ decoding phase of the receiver involves finding the corresponding codeword according to the index in the VQ index table. The image can be reconstructed by finding all corresponding codewords of the VQ index table. The flow chart of the VQ decoding phase is shown in Fig. 2.

Fig. 2.VQ decoding phase

2.2 EMD Technique

Zhang and Wang proposed the EMD information hiding technique in 2006 [21]. The main concept is that the secret data are expressed in a (2n+1)-based counting system first, and then are embedded in n pixels in the cover image. The detailed procedure of data embedding is as follows. First, the pixels of the cover image are separated into several clusters, which contain n pixels and will be used to embed a (2n+1)-based secret digit d. Second, a function f() is designed to calculate a (2n+1)-based number f by using all pixels of a cluster:

Third, the EMD method compares the to-be-embedded secret digit d with the computed number f. If the result is d = f, d is embedded in the current pixel cluster automatically without changing any pixel’s value in the cluster. Otherwise, the EMD method calculates a new value s = (d - f) mod (2n + 1). If s ≤ n, then ps = ps + 1; otherwise, p2n+1-s = p2n+1-s - 1.

2.3 PDE Based Image Inpainting Technique

This subsection presents Qin et al.’s PDE based image inpainting method using anisotropic heat transfer model [22], which can propagate both the structure and texture information from surrounding region into damaged region simultaneously. Qin et al. analogize image inpainting with a heat transfer process, let u be a damaged image, Ω be the region to be inpainted in u, and ∂Ω be the boundary of Ω. The procedure of fixing an image is treated as propagating the information of valid pixels from the exterior to the interior of Ω. The authors use a heat transfer model for homogenous medium, and consider the image as a temperature field by regarding the pixel value u(x, y) as the temperature.

To avoid edge blurring effects, in Qin et al.’s model, they decompose the gray-level propagation into two orthogonal directions. As a result, a spatially variable and content-dependent coordinate system O-ξη is introduced to replace the fixed Cartesian system O-xy. Let the unit coordinate vectors in the O-xy system be i and j, then, any point in the space could be expressed by a vector r=xi+yj, which becomes r=ξp+ηq in the O-ξη system, where ξ and η are the two components in the isophote and gradient directions respectively, and p and q are the two orthogonal unit vectors:

Here is the anisotropic heat transfer model in the PDE form:

where c2 is the propagation strength alone q varies spatially, and c is defined as following:

where k is a predetermined threshold to differentiate smooth and fluctuating regions. Eq.(3) can only be used for structure inpainting, the texture term Δu(x,y;α,d,t) can be expressed as:

where a ∈ [0,π] is the angle between the texture direction and the horizontal line, and $d$ the scale of texture periodicity. And ξa and ηa correspond to the texture direction and its perpendicular direction respectively.

Let A and B are weights for structure and texture respectively, A + B ≡ 1 and A,B ∈ [0,1], we get the equation for simultaneous structure and texture inpainting:

where the structure term Δsu(x,y;t) denotes the right part of equal sign in Eq. (3).

 

3. The Proposed Scheme

This paper proposes an EMD technique and inpainting technique based progressive image-hiding scheme. The proposed method extracts the complex blocks of the secret image and compresses them using the VQ technique, where the codeword in the VQ codebook are sorted by PCA first. The compressed result is embedded in all cover images and delivered to all participants to achieve the goal of progressive recovery of the complex blocks of the secret image, while the residue of the secret image is recovered by the inpainting technique based on the reconstructed information. The more participants join the reconstruction phase, the higher the quality of the secret image they will obtain.

The detailed secret image-embedding procedure is as follows:

Step 1. Divide the secret image I into sized non-overlapping blocks, where k is the number of dimensions of the codeword, i.e., , in VQ codebook C.

Step 2. Extract the complex blocks according to the variance value d of each block. If the variance value d of the current block is greater than the predefined threshold t, then the current block is determined to be a complex block. While finding all complex blocks, a location map is used to indicate whether a block is complex or not, where l ∈ {0,1}, l = 1 and l = 0 indicate a complex block and a smooth block, respectively.

Step 3. Compress the r complex blocks into sized VQ index table by using the VQ technique, where I is the index value and the code words in the VQ codebook are sorted by PCA technique before the compression process.

Step 4. Choose x cover images , whose size is , to embed the VQ index table IT and the location map L. The location map L is embedded in the first two cover images, , where CI1Pu and CI2Pu are the pixels in cover images CI1 and CI2, respectively, and each pixel is expressed by 8 bits as CIP = {b1b2…b8}. The embedding space of L is the last bit plane of CI1 and CI2. The L is embedded by modifying the last bit plane of CI1 and CI2 to satisfy . IT is progressively embedded in every two overlapping cover images by the EMD technique. For the first two cover images, CI1 and CI2, first divide the codebook size N into 2n + 1 parts, which is expressed as . Second, find the corresponding part x for index Iq, and embed it in the first 7 bits of every pixel of CI1 and CI2 using the EMD technique, introduced in Section 2. For example, assume N = 256, n = 2, I1 = 160, and the corresponding cover pixels after embedding the location map are CI1P1 = 32 and CI2P1 = 147, then the divided five parts of the codebook are g10 = [0,50], g11 = [51,101], g12 = [102,152], g13 = [153,203], and g14 = [204,255], and I1 = 160 belongs to g13 = [153,203], which means x = 3. Since the decimal values of CI1P1 and CI2P1 ’s first seven bits are 16 and 73, according to the EMD technique and Fig. 3, the stego decimal values of CI1P1 and CI2P1 ’s first seven bits are 17 and 73 after embedding x = 3 in them. Finally, the stego pixel pair is calculated by connecting the last bit of CI1P1 and CI2P1 to the new first seven bits.

Fig. 3.The embedding example of cover images CI1 and CI2

For the second two cover images, , further divide the previous parts in g1 into 2n + 1 additional parts for each of them and find the new corresponding part y for Iq. y is embedded in and CI3 also using the EMD technique. In contrast to the embedding procedure of embedding x in the first two cover images, y is embedded by only modifying the pixel value in CI3 while keeping the pixel value in unchanged. As to the previous example, since I1 = 160 belongs to g13 = [153,203], further divide g13 = [153,203] into five parts, g20 = [153,162], g21 = [163,172], g22 = [173,182], g23 = [183,192], and g24 = [193,203], and determine that Iq = 160 belongs to g20, which means y = 0. Assume that the corresponding pixel values are 147 and 230 in cover images and CI3, respectively; the stego pixel values are 147 and 229 after embedding y = 0 while keeping 147 unchanged, as shown in Fig. 4. The embedding procedure for the rest of the cover images is the same as the embedding procedure for and CI3.

Fig. 4.The embedding example of cover images and CI3

At the receiver end, the participants provide their stego images, VQ codebook, n, and the size of the secret image H × W. The decoding procedure follows the order of the stego image and the more participants cooperate, the higher the quality of the secret image they can reconstruct. The details of the secret image reconstruction process are described below.

Step 1. Extract the location map L of the blocks by calculating with stego images . After this, the number of complex blocks r can be observed by L.

Step 2. Extract the first r pixels from in order from up to down and left to right. Calculate the secret pixel value belonging to the specified part of g1 by using the EMD technique with the decimal values of the first seven bits from the corresponding pixels in . The current reconstructed index value equals the average integer value of the part to which it belongs. Since all code words in the codebook were sorted by PCA in the secret-embedding procedure, the more closely the index values are, the more similar the blocks reconstructed from them are.

Step 3. For the rest, for every two overlapping stego images, calculate the secret index value belonging to the specified part by directly using the EMD technique with the decimal values of the corresponding pixels in them. This allows the secret pixel value to be reconstructed by the average value of the new corresponding part. For example, calculate the secret index value belonging to the specified part of g2 by using the EMD technique with the decimal values of the corresponding pixels in . The new more accurate secret index value equals to the average value of the part from g2 to which it belongs.

As for the example of the secret image-embedding phase, the first seven bits’ decimal values 17 and 73 can be calculated by the corresponding pixel values from the first stego image and the second stego image , respectively. The serial number 3 of the part is found by using the EMD technique with 17 and 73, which means the current secret index value belongs to g13 = [153,203]. As a result, the secret index value is recovered as 178, which equals the average integer value of g13 = [153,203], by using . If three participants cooperate to recover the secret image, assume the corresponding pixels in , respectively. The new serial number of the part in g2 is calculated as f(147,229) = (147×1+229×2)mod 5 = 0, which means the current secret index value belongs to g20 = [153,162]. In addition, the more accurate value of the current secret index is recovered as 158 by computing the average integer value of g2, as shown in Fig. 5.

Fig. 5.The example of the secret pixel value recovered by using three stego images

After reconstructing all complex blocks’ VQ index table, the complex part of the secret image can be rebuilt by decompressing the VQ index table according to the location map L. Then, the smooth blocks are recovered by using Qin et al.’s image inpainting technique [22] based on the information of the reconstructed complex blocks. Finally, the secret image can be progressively extracted with high quality.

 

4. Experimental Results and Analysis

In this section, the experimental results are provided to evaluate the performance of the proposed scheme. The programs for the experiments were run on a personal computer with the Windows 7 operating system. The CPU was AMD Phenom(tm) II X4 945 3.0GHz, 2G RAM. We wrote the programs in Matlab 7.6.0.324.

In 2012, He et al. proposed a simple yet effective blind image quality assessment [28], which outperforms conventional image quality assessment algorithms. However, in order to compare the image quality with other progressive data hiding techniques, the peak signal-to-noise ratio (PSNR) was adopted here to evaluate the image quality in our experimental results, which are defined as:

where , in which G and F are the height and width of the image, and Xi and Xi’ are the cover image’s pixel value and stego image’s pixel value, respectively. The ratio r of the secret image size H × W to the shadow image size H' × W' is used to evaluate the hiding capacity of the proposed scheme, which is defined as Eq. (8).

The first part of our experiments was designed to highlight the differences based on the two different test secret image types, the complex image and the smooth image, when threshold t of the variance in every block to separate the complex blocks from the smooth blocks is a fixed value. In the experimental tests, the three cover images were 256 gray levels of 256×256 size, as shown in Fig. 6. The six secret images were 256 gray levels of 512×512 size, as shown in Fig. 7. The size of the VQ codebook was 1024 with 16 dimensions. The threshold t was set as t = 3.

Fig. 6.Cover images: (a) Couple, (b) Lena, and (c) F16

Fig. 7.Secret images: (a) Lake, (b) Bridge, (c) Baboon, (d) Man, (e) Goldhill, and (f) Barbara

The numbers of complex blocks and smooth blocks in the test secret images are shown in Table 1, which also presents the percentage of the smooth blocks among the total blocks. Table 1 clearly indicates that Lake, Bridge, and Baboon are more complex than Man, Goldhill, and Barbara.

Table 1.The numbers of complex blocks and smooth blocks in test secret images

Table 2 records the experimental results of test images. In Table 2, most of the smooth secret images can achieve a bit better stego images than the complex images, since the quantity of the data embedded in the stego images related to the number of VQ indices calculated from the complex blocks.

Table 2.The experimental results of all test images

The more complex blocks in the secret image, the more data should be embedded in the stego images. All stego images’ PSNRs are higher than 50 in Table 2, which guarantees high security performance of the proposed scheme because it is extremely difficult to distinguish the difference between the stego image and the cover image if the PSNR of the stego image is higher than 50. It can be observed that the hiding capacity (ration r) of the proposed scheme is 4, which means the shadow size is only 1/4 of the secret image size.

Fig. 8 and Fig. 9 show the experimental results of hiding two representative test secret images from two groups into three cover images. Each figure presents the secret image used in the experiment, the separation result of complex blocks and smooth blocks, which are indicated by black blocks in the figure, the image quality of the three stego images and their visual effect, and the recovered secret image quality by using two stego images and three stego images, respectively.

Fig. 8.The experimental results obtained by using Bridge as secret image and using Couple, Lena, and F16 as cover images

Fig. 9.The experimental results obtained by using Goldhill as secret image and using Couple, Lena, and F16 as cover images

Based on either Fig. 8 and Fig. 9 or Table 2, the improved image quality of the recovered secret image obtained by using three stego images demonstrates that the proposed scheme can successfully achieve progressively reconstructed secret images.

The second part of our experiments was designed to show the influence of threshold t on the performance of the proposed scheme and to compare the effectiveness of our proposed scheme with Chang et al.’s scheme [11]. In the experimental tests, the three cover images were 256 gray levels of 512×512 size Tiffany. The secret image was 256 gray levels of 512×512 size Barbara. The size of the VQ codebook was 1024 with 16 dimensions.

Table 3 shows the variation of PSNR values of stego images and recovered images when threshold t varies. It can be observed that as t increase the visual quality of stego images also increase while PSNR of recovered images decrease. It is due to that when t increase, more blocks can be judged ad smooth blocks leading to fewer complex blocks for VQ to encode.

Table 3.The PSNR values of stego images and recovered images (dB)

Table 4 shows the influence of threshold t on the execution time of the proposed scheme. It can be observed that as the threshold t increase, the execution time of recovering smooth blocks by inpainting technique increases. It happens because the number of the smooth blocks increases along with t increases. As a result, the inpainting time was spent on recovering the smooth blocks increases as well.

Table 4.Execution time of the proposed scheme (unit: second)

Fig. 10 show the experimental results of hiding secret image Barbara into three same cover images Tiffany. It presents the secret image used in the experiment, the separation result of complex blocks and smooth blocks, which are indicated by black blocks in the figure, the image quality of the three stego images and their visual effect, and the recovered secret image quality by using two stego images and three stego images with impaiting procedure, respectively. Here, the threshold t = 2.

Fig. 10.The experimental results obtained by using Barbara as secret image and using Tiffany as all cover images

In order to demenstrate the effectiveness of the proposed scheme, we compared our proposed scheme with Chang et al’s scheme [11] in visual quality of the stego image, visual quality of the recovered secret image, hiding capacity and computational complexity. Fig. 11 and Fig. 12 show the comparison results in visual quality of the stego images and visual quality of the recovered secret images. Here the threshold t = 2 in out proposed scheme and the quality factor Qf used in Chang et al.’s scheme is 1/3 [11].

Fig. 11.Comparison for the generated one shadow between the proposed scheme and Chang et al.’s scheme

Fig. 12.Comparison for the restored secret images between the proposed scheme and Chang et al.’s scheme

According to the two figures, Fig. 11 and Fig. 12, it is found that the proposed scheme degrades the image qualities of the shadows and the recovered secret image more slightly than Chang et al.’s scheme. The hiding capacity of the proposed scheme in the second part of the experiments is assigned as same as the hiding capacity in Chang et al’s scheme to observe differece of the out put images’ visual quality. However, it can be seen from Table 2, which is obtained from the first part of our experiments, since the shadow size equals the secret image size in Chang et al.’s scheme [11], the hiding capacity of our proposed scheme could achieve 4 times larger than that of Chang et al.’s scheme. This advantage makes the proposed scheme more suitable for the applications with the low bandwidth requirement. Chang et al’s scheme is capable of restoring secret images with different resolutions only by stacking different quantities of shadows together, while the proposed scheme has to recover the complex blocks of the secret image by decompressing the VQ indices and recover the smooth blocks by doing inpainting procedure to restore the secret image. In other words, the computation complexity of the proposed scheme is higher than Chang et al’s scheme. Table 4 shows that the execution time of the proposed scheme is about 1 minute on both sender and receiver side, respectively.

 

5. Conclusion

This paper proposes a new progressive secret image recovery scheme. The proposed scheme achieves not only high hiding capacity, which is proved by the secret image being four times larger than the cover image, but also by high stego image quality, which is higher than 50 dB, as shown in the experimental results. Observation of the visual effect provided in the experimental results―that the recovered secret image achieves higher quality by using three stego images than by using two stego images―demonstrates that the proposed scheme has the function of progressively recovering the secret image. In the future work, we will focus on improving the computation complexity of the proposed scheme.