Fundamenta Informaticae 73 (2006) 373–387
373
IOS Press
Multiple Images Embedding Scheme Based on Moment Preserving Block Truncation Coding Yu-Chen Hu Department of Information Engineering Providence University Taichung, Taiwan 433, R.O.C.
[email protected]
Abstract. A low-complexity grayscale image embedding scheme that can embed multiple secret images is proposed in this paper. In this scheme, different users can extract different secret images according to the secret keys they hold. To reduce the storage cost of the secret images, each of the secret images is first compressed using an improved version of the moment preserving block truncation coding scheme. The compressed message of each secret image is then encrypted by the DES cryptography system with different secret key and then embedded into the host image using the modulus least-significant-bit substitution technique. According to the experimental results, it is shown that the proposed scheme consumes a little computational cost. Besides, different users can extract different number of secret images. In other words, the proposed scheme indeed provides a good approach for the hiding of grayscale images with access control.
Keywords: image hiding, block truncation coding, DES
1. Introduction In recent years, the research towards data hiding [1, 2] becomes more and more popular. Typically, the data hiding schemes can securely transmit the secret data via the Internet with imperceptibility. In other words, the data hiding techniques embed certain secret data into multimedia data. Those multimedia data may be in the form of texts, images, audios, or videos. Based on the type of digital medium that was
Address for correspondence: Department of Computer Science and Information Engineering, Providence University, Taichung, Taiwan 433, R.O.C.
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used to embed secret data, the data hiding schemes can be categories into text hiding schemes, image hiding schemes, audio hiding scheme, and video hiding schemes. Basically, the design of the image hiding schemes is very important because digital images are popularly used medium among these digital media. Typically, the image hiding schemes can be classified into two main categories: spatial domain and frequency domain image hiding schemes. Among the spatial domain image hiding schemes, the least-significant-bit (LSB) substitution technique is the most intuitive method. In the LSB substitution technique, the secret data is embedded into the low-order LSB bits of the host pixels. The major disadvantage of the LSB substitution technique is that the image quality degradation may be occurred when the number of bits embedded in each pixel of the cover image is greater than or equal to 4. To solve the problem of image quality degradation, the optimal LSB substitution should be used instead of the simple LSB substitution. In the optimal LSB substitution technique, all the combinations of possible substitution are examined to find out the optimal one. The optimal substitution means the one incurs the least mean squared error (MSE) between the cover image and the embedded image. Although the optimal LSB substitution technique is guaranteed to achieve the best image quality of the embedded image, the high computational cost is its major drawback. In 2001, Wang et al. proposed the approximately optimal LSB substitution with genetic algorithm [3] to improve the performance of the optimal LSB substitution in terms of computational cost. In addition, Chang et al. introduced a greedy LSB substitution scheme [4] to further reduce the computational cost with a little image quality loss. In 2003, the LSB substitution method based on modulus function [5] was introduced to further improve the image quality of the stego-image. Furthermore, Lin et al. proposed a color image hiding scheme [6] that is able to embed both color and grayscale image based on the LSB substitution technique in 2002. For the image hiding schemes based on the LSB substitution, the hiding capacity is limited by the size of the host image and the number of bits used to embed the secret image. If the secret image is directly embedded into the host image without compression, the size of the secret image should be much smaller than that of the host image. To solve this problem, the secret image to be embedded into the host image can be compressed before performing the embedding operation. In 1998, Chen et al. proposed a virtual image cryptosystem based on the vector quantization (VQ) scheme [7]. In this scheme, the grayscale secret image is first compressed using the VQ scheme [8, 9]. The codebook is designed using the transformed host image. In addition, the DES encryption scheme is employed to encrypt the indices of the secret image and the system parameters such as the image size, the vector dimension, and so on. In 2003, Hu introduced an improved VQ hiding scheme [10] that can embed multiple grayscale secret images into another meaningful grayscale image. In addition to the spatial domain image hiding schemes, several frequency domain image hiding schemes had also been proposed. Chang et al. [11] designed the quantization tables of JPEG and employed the LSB substitution technique to hide secret data into the low-order bits of DCT coefficients. Spaulding et al. [12] proposed a bit-channel complexity segmentation steganography (BPCS) strategy to embed secret data into the compressed code of EZW. Noda et al. [13] use JPEG2000 lossy compression and BPCS steganography to embed secret data into JPEG200 compression code. Generally, the embedded secret data of the spatial domain image hiding schemes may be easily lost when some image processing operations such as smoothing, sharpening, and compressing have been performed on the embedded images. However, the hiding capacity of one spatial domain image hiding scheme is generally higher than that of a frequency domain image hiding scheme.
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Figure 1. Flowchart of image hiding using the simple LSB substitution technique
In this paper, we develop a novel spatial domain image hiding scheme that can hide multiple secret images, assure safety of secret images, and require shorter time of processing. The rest of this paper is organized as follows. Some related schemes are reviewed in Section 2. In Section 3, the newly proposed scheme is introduced. Then, experimental results are given in Section 4. Finally, a brief conclusion is given in Section 5.
2. Related Schemes In this section, some related schemes are reviewed. First, the simple LSB substitution technique is introduced. Next, the LSB substitution technique based on modulus function [5] is discussed. Finally, the moment preserving block truncation coding (MPBTC) scheme for image compression is described.
2.1. Simple LSB Substitution Technique Simple LSB substitution technique is the most simple and intuitive spatial domain image-hiding scheme. It can be used to embed secret data in digital form into the host image. The embedding process of the simple LSB substitution technique is depicted in Fig. 1. To embed the secret data S into the host image H using simple LSB substitution technique, we must determine first the number of rightmost bits of each pixel r in host image that is used to hide the secret message. Here, r can be calculated by dividing the total bits of secret data S by the size of the host image. For example, r equals 2 when 32-bit secret data is to be embedded into one grayscale image of 4 4 pixels.
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Then the secret data S is decomposed to form a grayscale image S’ at r-bits. The rightmost r bits of the host pixels in the host image H are replaced with those r-bits pixels of S’ to complete the embedding process. E is the embedded result that embeds the secret data S into the host image H. The extracting procedure of the simple LSB substitution technique is very simple. First, the rightmost r bits of each pixel in the embedded image are extracted sequentially. By collecting these r-bit units to form the secret data, S can be then reconstructed. This hiding technique is quite easy; therefore, the security level of the secret image is lower. The interceptors can use bit analysis to get some information about the secret image. Besides, the size of the secret message is limited by the size of the host image and the value of r used in the simple LSB substitution technique.
2.2. Modulus LSB Substitution Method In 2003, Thien et al. proposed the modulus LSB substitution method [5]. To embed the secret data S into the host image H, the secret data S is first decomposed into r-bit units to form an image S’ with the same size as the host image H. Each value in the decomposed image S’ is ranged from 0 to -1. In other words, there are possible values for each. In the embedding process, each r-bit secret value is embedded into the host pixel sequentially. To embed the ith r-bit secret value in S’ into the ith pixel of the grayscale host image H, we need to find the modified value so that mod = , where is the closest value to among all the possible values that satisfy the modulus function. To determine , the difference value can be calculated according to the following formula.
(1)
Here, is the first guess of the difference value that can be used to embed into . It may not be the minimal difference value for the embedding process. The minimal difference value can be computed as follows. if (2) if if The value of is the difference between the original value hi and modified value . In other words, we can get the modified value according to the following equation. (3) Note that may be out of the range of valid gray values. To solve this problem, needs adjustment by using to the following formula. if if
(4)
By sequentially calculating the modified value for each host pixel to embed r-bit secret data using the above-mentioned process, the stego-image is then generated.
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The extracting process of the modulus LSB substitution technique is very simple. By extracting each pixel in the stego-image, the r-bit secret unit can be recovered by using the modulus function. By performing the same operation on each pixel in the stego-image, the secret data S can thus reconstructed. An example that embeds 8-bit secret data into a host image of 2 2 pixels is given below. In this example, two bits of the secret data is embedded into each host pixel. In other words, r equals to 2.
The results of as shown in the array D can be calculated according to Eq. (1).
The results of minimal difference value can be calculated using Eq. (2) and are shown in D’.
After getting the value , we can get the modified values according to Eq. (3).
Continue the same example, we will illustrate how to extract the secret data S from the stego-image. We need to generate the decomposed secret image S’ from the stego-image using modulus function. The results are shown as follows:
Then, the secret data can be obtained.
2.3. Moment Preserving Block Truncation Coding In 1979, Delp et al. proposed the moment preserving block truncation coding (MPBTC) scheme [14, 15] for image compression. This scheme consists of two procedures: the encoding procedure and the decoding procedure. In the encoding procedure of MPBTC, each digital image to be compressed is first segmented into a set of non-overlapped image blocks of k pixels, and then each image block is then compressed separately. To compress each image block, the block mean is computed and utilized as the quantization threshold to partition all pixels within each image block into two groups. Pixels with the values greater than
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or equal to the quantization threshold are classified into the first group. Otherwise, they are classified into the second group. A binary bit plane sized k is then generated to record the grouping information of pixels in each image block. The block mean and the standard deviation for each image block x are calculated according to the following equations:
(5)
(6)
(7)
After performing the grouping operation for each image block, two quantization levels for the two groups are then calculated to represent all pixels in each group. Since MPBTC aims to preserve the mean and variance of the image block, these two quantization levels a and b of MPBTC are computed according to the following equations.
(8)
(9)
where q stands for the number of pixels with values greater than or equal to . In the MPBTC encoding procedure, each compressed block comes out a triple (a, b, B), where the two variables a and b are the two quantization levels for the block, and the variable B stands for the bit plane. In fact, each triple of (a, b, B) is equivalent to ( , , B) in MPBTC because these two quantization levels a, and b can be derived from the block mean and the block variance . The decoding procedure of MPBTC is described as follows. Upon receiving the triple consisting of (a, b, B) of each encoded image block, the bit plane B is extracted to determine the grouping information of all pixels in each image block. Then these two quantization levels a, b are extracted. By simply recovering all the pixels of each group by their corresponding quantization level, the encoded image block can be reconstructed. After recovering all image blocks, the encoded image is then available. General speaking, MPBTC requires little computational cost while achieving high reconstructed image quality. The encoding procedure of MPBTC only requires simple mathematical operations. However, the major drawback of MPBTC is that the required bit rate of MPBTC is high. In MPBTC, the bit rate equals 2.0 bpp (bit per pixel) if the image block is of 4 4 pixels. In other words, a total of 32 bits is needed to store the triple (a, b, B).
3. The Proposed Image Hiding Scheme A novel grayscale image hiding scheme that embeds multiple secret images into another meaningful host image is introduced. In this scheme, different users can extract different secret images according to the
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access control rule. To embed multiple secret images into one given host image, the secret images are first compressed using an improved version of moment preserving block truncation coding. The improved version of moment preserving block truncation coding is introduced in Section 3.1. In addition, the embedding procedure and the extracting procedure are described in Sections 3.2 and 3.3, respectively.
3.1. Improved Moment Preserving Block Truncation Coding Basically, the MPBTC scheme is an effective scheme because it consumes little computational cost and achieves good reconstructed image quality. However, the high bit rate requirement is its major drawback. To remedy this problem, an improved version of moment preserving block truncation coding, we called it IBTC, is developed. The goal of IBTC is to reduce the bit rate of MPBTC while keeping good image quality. Recall that the encoded message of each image block of MPBTC comes out a triple of (a, b, B). Each triple of (a, b, B) is equivalent to ( , , B) in MPBTC because these two quantization levels can be derived from the block mean and the block variance . To reduce the bit rate of MPBTC, two techniques are employed in IBTC. First, the block mean and variance of each encoded block is further processed. Second, the bit plane of each encoded block is further compressed. In MPBTC, a total of 16 bits are used to represent the block mean and variance. To low down the bit rate of BTC, IBTC employs the concept, which was introduced by Delp et al. [14], suggesting that 6 and 4 bits are used to encode block mean and variance, respectively. The encoding rules of the block mean and variance of IBTC are given in the following: (10)
(11)
By using the above encoding rules, only 10 bits are needed to store the block mean and the block variance . In other words, 6 bits are saved. Here, the block mean is processed using the concept of uniform sub-sampling; while the block variance is encoded using non-uniform sub-sampling. That is because the distribution of the block variance of image blocks tends to be non-uniform in nature. In MPBTC, a total of 16 bits is required to store the bit plane if the image to be compressed is segmented into a set of non-overlapped blocks of 4 4 pixels. To cut down the storage cost of the bit plane, the concept of the bit plane coding using frequent patterns technique [16] is employed. The motivation of this technique is that the probability of each possible bit plane is not equal. For example, if the image to be compressed is partitioned into a set of non-overlapped 4 4 image blocks, the size of each bit plane is 16 bits. There are combinations of bit planes totally. However, the majority of the patterns are rarely encountered in practice. The reduction of bit rate can be achieved by selecting only the frequent patterns. Whenever a rare pattern is encountered, it is approximated to the closest frequent pattern using the simple Hamming distance measurement. If we can find a set of representative bit planes, a great deal of storage cost can be saved. In this scheme, a set of 128 image-independent edge patterns is designed to represent the bit plane. In other words, only 7 bits instead of 16 bits are needed to represent the bit plane in this scheme. In IBTC, we employ 64 frequent patterns [17] of 4 4 bits to further cut down the storage cost of the bit plane. Using 64 patterns to encode the bit plane for each image block, only 6 bits are needed to
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Figure 2. Flowchart of the proposed embedding procedure
represent the bit plane. The reason why we use 64 patterns instead of 128 patterns is that we find that the performance of the IBTC using a representative set of 64 frequent patterns is quite good. Besides, when 64 patterns are used in IBTC, the resultant bit rate equals 1 bpp. The resultant bit rate is much suitable for the compression of secret images than that using 128 patterns.
3.2. The Proposed Embedding Procedure The goal of the proposed embedding procedure is to embed multiple secret images into the host image. The flowchart of the proposed embedding procedure is depicted in Fig. 2. To embed t secret images into one host image using the proposed embedding procedure, each secret image must be compressed by the IBTC encoding procedure. Then, the DES encryption process [18] is executed to encrypt the . Now, the DES encrypted compressed code is available. compressed code with secret key The reason why we use different secret keys to encrypt the compressed codes of secret images is to provide the function that different users can extract different secret images. If only one user is allowed to extract all these secret images, the secret keys to encrypt the compressed codes of secret images are the same. Otherwise, we should assign the secret keys according to the desired rule for control access. Since there are some access control schemes that can be directly used to provide this function, we omit the detailed descriptions here. By collecting all the DES encrypted compressed codes of secret images, the whole encrypted compressed data DC is then generated. In other words, DC can be generated by successively merge the content of all the . Finally, DC will be embedded into the host image by the modulus LSB substitution technique [5]. To embed DC into the LSB bits of the host pixels, DC is partitioned into units of
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Figure 3. Flowchart of the proposed extracting procedure
t-bits. Each t-bit unit is embedded into the low order t-bits of the host pixel using the modulus LSB substitution technique as described in Section 2.2. After DC is embedded into the host image, the embedded image E is now generated.
3.3. The Proposed Extracting Procedure The flowchart of the proposed extracting procedure is depicted in Fig. 3. To extract these t secret images from the embedded image E, the reverse modulus LSB substitution procedure is first performed. Each unit of t bits that was embedded into the host pixel is calculated. By merging all the units of t-bits, the encrypted message DC is now available. In other words, the encrypted compressed code of each is performed to secret image can be generated. Then the DES decryption process with secret key generate the IBTC compressed code of each secret image. Here, only the legal user who holds the can successfully decrypt the compressed code of each secret image. In other correct secret key words, illegal user cannot obtain the compressed code of the secret image. Finally, the IBTC decoding process is executed to reconstruct the compressed secret images. Note that the variable t used in Figs. 2 and 3 denotes the total number of secret images to be embedded into the host image.
4. Experimental Results To verify the performance of the proposed scheme, a variety of simulations have been performed on a personal computer (PC) Pentium III, 500MHz with 128 MB RAM under the operation system of Linux RedHat 7.0. Five host images and four secret images of 512 512 pixels are used in the simulations. The host images are ”Baboon”, ”Boat”, ”Family”, ”Goldhill”, and ”Sailboat”. The secret images are ”Airplane”, ”Lena”, ”Pepper”, and ”Toys”. These testing images are shown in Fig. 4.
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(a) Airplane
(b)Baboon
(c)Boat
(d)Family
(e)Goldhill
(f)Lena
(g)Pepper
(h)Sailboat
(i)Toys
Figure 4.
Test images of 512 512 pixels
For M N images, the mean square error (MSE) between the original image and the encoded image is defined as
MSE (12)
where and denote the original and the encoded pixel gray levels, respectively. The reconstructed quality of the image is measured by the peak signal to noise ratio (PSNR), which is defined as (13)
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Table 1. Results of the PSNR (unit: dB) of the embedded image using the proposed scheme that embeds one secret image into the host image
Table 2. Results of the PSNR (unit: dB) of the embedded image using the proposed scheme that embeds two secret images into the host image
Experimental results of the image quality of the embedded image using the proposed scheme that embeds one secret image into one host image are listed in Table 1. When one secret image is embedded into the host image using the proposed scheme, only one LSB bit of each cover pixel is changed to hide the IBTC compressed message of each secret image. Therefore, the image quality of the embedded image is high. In addition, experimental results of the image quality of the embedded image using the proposed scheme that embeds two, three, and four images into one host image are listed in Tables 2, 3, and 4, respectively. When multiple secret images are embedded into one host image of equal size, more LSB bits in each cover pixel are needed to hide the compressed secret message. To be specific, two, three, and four LSB bits of each cover pixel are required to hide the secret message of two, three, and four secret images, respectively. According to the results shown in Tables 1 to 4, we find that the image quality of the embedded image is the best when only one secret image is embedded into the host image. When more secret images are embedded into the host image, the image quality of the embedded image decreases. When four secret images are embedded into the host image using the proposed scheme, an average of 31.818 dB of the embedded image is achieved. These embedded images are shown in Fig. 5. It is obvious that the visual qualities of these five images are acceptable subject to the human vision system.
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Table 3. Results of the PSNR (unit: dB) of the embedded image using the proposed scheme that embeds three secret images into the host image
Table 4. Results of the PSNR (unit: dB) of the embedded image using the proposed scheme that embeds four secret images into the host image
Table 5.
Average results of the execution time (unit: second) of the proposed scheme
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(a) Embedded image ”Baboon” (b)Embedded image ”Boat” (c)Embedded image ”Family”
(d)Embedded image ”Goldhill” (e)Embedded image ”Sailboat” Figure 5. Embedded images of the proposed scheme with the embedding of four secret images
In the proposed scheme, instead of the original secret images, the IBTC-compressed and then DESencrypted secret message is embedded into the host image. That is because the proposed scheme intends to safely embed multiple secret images into one host image. However, the image qualities of the compressed secret images have great influence on the performance of the proposed scheme. To verify the performance of the proposed scheme, several simulations have been performed and the experimental results of the image quality of the compressed secret images are listed in Fig. 6. It is shown that an average of 31.304 dB image qualities of these secret images can be obtained. To verify the effectiveness of the proposed scheme in terms of computational cost, the average results of execution time of the proposed scheme are shown in Table 5. The proposed embedding procedure consists of three parts: the IBTC encoding process, the DES encryption process, and the secret embedding process. The execution time of the embedding procedure is the sum of the times of these three parts. The proposed extracting procedure also consists of three parts: the secret extracting process, the DES decryption process, and the IBTC decoding process. The execution time of the extraction procedure is the sum of the times for these three parts. From the results shown in Table 5, we find that the execution times of the embedding/extracting procedures increase when more secret images are embedded into the host image. Besides, the proposed extracting procedure consumes less computational cost than that of the proposed embedding procedure. Among the computational cost of the proposed scheme, the encryption and decryption process of the DES cryptosystem require the highest computational cost.
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(a) Compressed image ”Airplane” 31.193 dB (b) Compressed image ”Lena” 31.724 dB
(c) Compressed image ”Pepper” 32.038 dB (d) Compressed image ”Toys” 30.260 dB Figure 6. Embedded images of the proposed scheme with the embedding of four secret images
5. Conclusions A spatial domain grayscale image hiding scheme that can embed multiple secret images into another meaningful host image of the same size is proposed in this paper. In this scheme, different users can extract different secret images according to the secret keys that they hold. The proposed scheme is imperceptible because good image quality of the embedded image is achieved in this scheme. Illegal users cannot observe the visual difference between the host image and the embedded image. An average image quality of 31.304 dB of four secret images is accomplished. In addition, the proposed scheme consumes little computational cost. That is because both the IBTC scheme and the modulus LSB substitution technique require little time of computation. To embed more secret images into the host image, other compressed schemes such as JPEG or JPEG2000 can be employed to compress the secret images before they are embedded into the host image. However, a much higher computational cost and complex embedding/extraction procedures are needed in such scheme. In other words, the proposed scheme provides a low-complexity image hiding scheme for grayscale image hiding.
6. Acknowledgment This research was supported by the National Science Council, Taipei, R.O.C. under contract NSC 922213-E-126-010.
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