A Tamper-Detection Scheme for BTC-Compressed Images with High-Quality Images

Abstract

This paper proposes a novel image authentication scheme, aiming at tampering detection for block truncation coding (BTC) compressed image. The authentication code is generated by using the random number generator with a seed, and the size of the authentication code is based on the user's requirement, with each BTC-compressed image block being used to carry the authentication code using the data hiding method. In the proposed scheme, to obtain a high-quality embedded image, a reference table is used when the authentication code is embedded. The experimental results demonstrate that the proposed scheme achieves high-quality embedded images and guarantees the capability of tamper detection.

1. Introduction

With the rapid development of multimedia and the Internet, a massive amount of digital information (i.e., images, video, and audio) is transmitted daily over the Internet which is a public channel. In fact, a huge amount of digital information is stored and transmitted each second. This means that transmitted data have many treats for being easily tampered or copied by malicious users. Therefore, the protection of transmitted data has become an issue of increasing concern. Many researchers have proposed data hiding and watermarking techniques to solve this security problem. Data hiding is a technique by which invisible secret data can be delivered securely by hiding the data in cover media, such as the ‘Hello Kitty’ image. Watermarking is another technique that is used to protect the copyright of digital data.

All current digital image compression techniques are based on exploiting the redundancy of information that is inherent in most digital images. This redundancy stems from the statistics of the image data, which are directly related to the probability distribution of the image data and can be treated by information theory techniques using image entropy concepts. Basically, image compression techniques can be divided into two types. The first type is called lossless compression, i.e., Huffman coding [1, 2] or arithmetic coding [3, 4]. The property of lossless compression is that the original image can be recovered after decompression. The second type of image compression technique, i.e., block truncation coding (BTC) [5-10,], wavelet coding and discrete cosine coding [11-13, 24], or vector quantization (VQ) [14, 15, 26], is lossy compression [5-16, 26], which is often used to compress digital images. This is because the latter has a better compression ratio than the former.

In the past five years, many watermarking schemes have been proposed in compression domain. In 2008, Lee and Lin [17] introduced a new watermark scheme that not only detects the tampered areas in the embedded image, but also enables to recover the areas where are tampered. In Lee and Lin’s scheme, each block in the image is used to carry watermark of other two blocks. Therefore, there are two copies of watermark for each block in the watermarked image. In 2010, Ahmed and Siyal [18] proposed a hash-based authentication scheme to verify the image by using a hash function. Ahmed and Siyal’s scheme obtained the good resilience against some attacks, i.e., JPEG compression, low-pass and high-pass filtering. In 2011, Chuang and Hu [19] introduced a new authentication scheme that is used to detect illegal modifications in the vector quantization compressed image. In their scheme, two sets of authentication data are needed to perform the tamper detection process and authenticate the given VQ compressed image. Their scheme achieved acceptable image quality of the embedded image and it provided accurate detection capability. From 2012 to 2013, Hu et al. proposed a three different tamper detection schemes [20, 23, 25] for the compressed images of BTC. In [23], the authentication codes of the image blocks are created from the quantization levels. Then, many copies of the authentication codes are embedded into the bit maps based on the permutation operation. In [25], a joint image compressed and image authentication technique had been proposed for the compressed images of BTC. In this scheme, pseudo random generator is used to generate the authentication code that is embedded into the bit maps of AMBTC-compressed image blocks. The embedded bit maps and these quantization levels are further compressed to reduce the storage cost. In [20], multiple sizes of authentication code are also embedded into the BTC-compressed image. Their scheme can obtain the clear tamper detection capability. However, the visual quality of the embedded image obtained by this scheme is still low, with the average quality of the embedded image being less than 39 dB. To obtain the higher visual quality while maintaining clear tamper detection capability for the BTC-compressed images, in this paper, we propose a new tamper detection scheme. In the proposed scheme, each quantization level of the BTC-compressed image block is used to carry the authentication code by referring to a reference table. Then, to detect any areas that have been tampered, the embedded authentication code is extracted and verified. The mathematical morphology operation can be used to improve the detection results [21]. Experimental results demonstrate that the proposed scheme achieves both high-quality of the embedded images and clear verification of any tampering that occurred.

The rest of this paper is organized as follows. Section 2 provides a review of related work, such as absolute moment block truncation coding [6] and Hu et al.’s scheme [20]. In Section 3, the details of our proposed scheme are discussed. The experimental results are provided in Section 4, and our conclusions are presented in Section 5.

 

2. Related Work

2.1 Absolute Moment Block Truncation Coding (AMBTC)

To compress images, Lema and Mitchell [6] introduced an AMBTC technique in 1984. In this scheme, the image is first partitioned into an image block with the size of n × n. Then, to encode the image block P, the mean value, mean, of the image block is computed and used to separate all of the pixels of P into two clusters. The first cluster L1 is used to contain all pixels that have value smaller than mean. The second cluster L2 is used to contain the rest pixels.This means that the corresponding bit value to be stored into the bit map, BM, is 0 or 1, when the pixel is in the cluster L1 or in the cluster L2, respectively.

After two clusters are determined, Equations (1) and (2) are used to compute two quantization levels, p and q, respectively:

where m denotes the number of pixels that have values that are equal to or larger than the mean.

In AMBTC technique, a compressed trio, also called as compressed block, (p, q, BM) is generated for each image block. Fig. 1 shows an example of the AMBTC technique. Assume that Fig. 1(a) is the original image block with the size of 4 × 4 pixels. The mean value, mean, of this block is 127.75. The bit map BM of this block, which is generated by using AMBTC, is presented in Fig. 1(b). According to Equations (1) and (2), the values of (p, q) is obtained as (103, 159). Then, the compressed trio, (103, 159, 0000110011001110), is sent to the receiver. Then receiver decodes the compressed trio to obtain the reconstructed image block, as shown in Fig. 1(c).

Fig. 1.Example of the AMBTC technique

2.2 Hu et al.'s Scheme

In this section, we introduce Hu et al.’s scheme [20]. The main purpose of their scheme is to protect the integrity of the BTC-compressed images from being tampered, where the BTC-compressed images are generated by using the AMBTC technique [6]. To achieve high accuracy in detecting tamper areas and less distortion of the BTC-compressed image, for each compressed trio (p, q, BM), a different value d between p and q are computed. Then, the different value d is used to embed the authentication code that is generated in advance using a pseudo random-number generator (PRNG). Then, to detect the tamper areas of the BTC-compressed image, the embedded authentication codes are extracted and verified. This scheme consisted of three procedures, i.e., authentication code generator, embedding, and detection procedures, each of which is described below.

Assume that the BTC-compressed image I with a size of W×H is processed by using Hu et al.’s scheme, and assume that the block size is set to n × n. Therefore, the entire number of k × l compressed image blocks is processed, meaning that k × l of compressed trios (p, q, BM) are generated, where k = W/n and l = H/n. Let b be the number of bits is embedded into each different value d.

For each compressed trio (p, q, BM), Hu et al. generates a random number r, meaning that k × l random values are generated for k × l compressed blocks of BTC-compressed image. Then, authentication code, w, is calculated by using Equation (3). According to Equation (3), the value of w is in the range of [0, 2b-1]. Then, to embed w into the compressed block, the value w is converted to the b-bit of binary form.

For example, random value r is generated as 26534, and b = 3. By using Equation (3), the authentication code, w, is 6, and its binary form is (110)2.

To embed w into the compressed trio (p, q, BM), the differenct value d is calculated as d=q-p and converted to binary form bd. Then, the last b-bit of db is compared with the binary form of w. If they are equal, the quantization levels are kept unchanged. Otherwise, the quantization levels are modulated to ensure that the last b-bit of db has the same value as the b-bit binary form of authentication code, w. When the binary form of w is not equal to db, the quantization levels are modulated. The first quantization level, p, is fixed, and two candidates, i.e., q1, q2, are computed by using Equations (4) and (5), respectively. These two candidates are used for replacing the second quantization level, q.

where ⎿ ⏌ is the floor function.

After the two candidates, q1 and q2, have been generated, which one that is closer to q is used for replacing q. The selected candidate is denoted as qs, and the quantization level, q, is replaced by qs.

After the replacement, to ensure that difference value between the new quantization level, qs, and the original quantization level, q, is small, the new quantization levels (p, qs) are adjusted. Then, the displacement of the adjustment of quantization levels is computed by Equation (6):

where dis is the displacement value, and ds is the absolute difference value between p and qs. Then, the quantization levels (p, qs) are adjusted to (p', q') by using Equations (7) and (8).

The above-mentioned steps are repeated until all of the quantization levels of the BTC-compressed image are processed completely. This means that each pair, i.e., (p, q), is used to carry b-bit of authentication code. To better explain the procedure used to embed the authentication code in Hu et al.'s scheme, the following example is provided. Assuming that b is 3, the BTC-compressed trio (82, 140, 1000110011101111) is used for embedding the 3-bit authentication code, w, and w = (101)2. To embed w into the BTC-compressed trio, the different value d = 58 is first obtained by subtracting 82 from 140. Since the last 3-bit of db being determined as (010)2, which is different from the authentication code w, (101)2. Therefore, according to Equations (4) and (5), two candidates, q1 and q2, are computed, where q1 is equal to (82+⎿58/23⏌×23+5)=143 , and q2 is equal to(143-23)=135. In this case, the first candidate q1 = 143 is chosen for replacing the quantization code q = 140 because it is closer to q than the second candidate, q2 = 135. Then, the new quantization levels are (82, 143). To adjust these new quantization levels, the absolute difference value, ds, and the displacement of the adjustment of the quantization levels, dis, are computed as 61 and 1, respectively. According to Equations (7) and (8), the adjusted quantization levels (p', q') are obtained as (81, 142).

Once the owner of the BTC-compressed image suspects that her/his image has been illegally tampered by others, he/she will use the tamper detection procedure to detect this image. Specifically, in this procedure, the embedded authentication code is extracted and compared with the original authentication code generated by PRNG with seed. By doing that, tamper locations are determined.

 

3. Proposed Scheme

After carefully considering Hu et al.’s scheme [20], we discovered that it embeds the authentication code into each BTC-compressed block (p, q, BM) by modifying the different value d between p and q. In their scheme, to minimize the distortion of the embedded BTC-compressed image, the two candidates, q1 and q2, are used to determine whether q1 < q < q2 = q1 +2b (if q1 < q) or whether q1 - 2b < q < q1 (if q1 > q), where b is the number of bits of authentication code. Then, the closer one is chosen to replace the second quantization level, q, and the new quantization levels are adjusted to generate the embedded quantization levels (p′, q′). Therefore, the original quantization levels (p, q) must be changed to the embedded quantization levels (p’, q’), which must be from 0 to 2b / 2. In other words, for each block, the mean square error (MSE) must be increased from 0 to (2b / 2)2. This means that, when b increases, the visual quality of the embedded image decreases. In this paper, to further improve the quality of the embedded image while maintaining the clear tamper detection capability, we propose a new tamper detection scheme for BTC-compressed images. In the proposed scheme, first, a reference table and the authentication code are generated. Then, the authentication code is hidden into the BTC-compressed block (p, q, BM) by referring to the reference table. The proposed scheme consists of two phases, i.e., embedding the authentication code and tamper detection.

3.1 Authentication Code Embedding Phase

In this section, the main idea of the authentication code embedding phase is presented. In the proposed scheme, the authentication code for each component of the compressed trio is generated by using PRNG, which is the same as was done in Hu et al.’s scheme, and the secret key, K, is used as the seed. Let AC be the authentication code, which is defined as AC = {ac1, ac2,..., ack×l }. Assume that image I with a size of W × H is compressed by using the AMBTC technique, with block size of n × n. Therefore, the entire number, k × l, of the BTC-compressed image block (p, q, BM) is obtained, where k = W/n and l = H/n. Fig. 2 shows the flowchart of the main processes in the authentication code embedding phase of our proposed scheme.

Fig. 2.Flowchart of the main processes in the authentication code embedding phase

To generate reference table R, which is based on the number of bits b of the authentication code, ac, and the extraction function h [22], the extraction function h is defined by Equation (9)

where gi is gray pixel values, which are integers from [0, 255], and b is the number of bits of the authentication code. Figs. 3(a) and (b) show the simplest cases of b = 2 and b= 3, respectively. Here, each square in reference table R is represented by an h value. The h values of any square and its 2b neighbors that are integers from 0 to 2b - 1, are mutually different.

Fig. 3.Reference table R with different values of b: (a) b = 2; (b) b = 3

Our proposed authentication code embedding phase can be broken into five steps. The corresponding algorithm is described in detail below:

Embedding authentication code algorithm

Input: BTC-compressed image I, the number of bits b of the authentication code, and the secret key K

Output: Embedded BTC-compressed image I'

Step 1: Generate the reference table R and the authentication code AC.

Step 2: For each of the quantization levels (p, q) that is located on the reference matrix R at row p and column q, read the authentication code, aci, from AC.

Step 3: From the value of b, a set, CS, of candidate elements within the reference table R is constructed, as shown in Fig. 4. Note that the 2b elements in the candidate set CS are exactly composed of non-repeating integers between 0 and 2b-1. Fig.s 4(a), (b), and (c) show the candidate sets when the number of bits b are 2, 3, and 4, respectively.

Fig. 4.Candidate set with different values of b

Step 4: To embed the authentication code, aci, into quantization levels (p, q), find a position (p', q') in the candidate set CS that satisfies R(p', q') = aci.

Step 5: Repeat Steps 2 through 4 until all quantization levels of the BTC-compressed image I have been processed completely.

After all of the steps have been completed, the authentication code AC is embedded into the entire image I. To better explain the authentication code embedding phase, an example is provided in Fig. 5. Assume that the quantization levels (p, q) of the BTC-compressed image block are (3, 2), the authentication code, aci, is 4, b is 3, and the reference table R is constructed as shown in Fig. 3(b). According to Step 2, the quantization levels (3, 2) are located on the reference table R, and the candidate set CS is determined as shown in Fig. 5. Then, to embed the authentication code, aci, into the quantization level (3, 2), the element R(3, 3) is selected from the set CS due to R( 3, 3) = 4 = aci. Then, the current quantization levels (3, 2) are replaced by (3, 3).

Fig. 5.Example of the embedding authentication code phase

3.2 Tamper Detection Phase

Assume that the owner of the embedded BTC-compressed image I' suspects that a published image has been tampered from her/his embedded BTC-compressed image. In this scenario, this phase is used to authenticate that there is any modifications in the embedded BTC-compressed image I'.

To extract and verify the embedded authentication code, two parameters, b and K, are required in this phase. Fig. 6 shows the flowchart of main processes in the tamper detection phase.

Fig. 6.Flowchart of main processes in the tamper detection phase

The following algorithm shows the tamper detection phase in detail.

Input: The embedded BTC-compressed image I', the number of bits b of the authentication code, and the secret key K

Output: Tampered image

Step 1: Generate reference table R, and authentication code, AC, based on b and the secret key K, respectively.

Step 2: For each of the quantization levels (p', q') that is located on the reference matrix R at the row p' and the column q', the embedded authentication code, eaci, is extracted as the value of R(p', q') in the reference table R.

Step 3: Read the corresponding authentication code, aci, from the AC.

Step 4: If aci = eaci, the BTC-compressed image block is marked as a clear block; otherwise, the BTC-compressed image block is marked as a tampered block.

Step 5: Repeat Steps 2 through 4 until all quantization levels of the embedded BTC-compressed image I' have been processed completely and the roughly tampered image is generated by combining of all the clear blocks and tampered blocks.

Step 6: Estimate the roughly tampered image by using a morphological operation [21], and, then, the really-tampered areas are located correctly.

 

4. Experimental Classification Results and Analysis

To demonstrate the extensive experiments conducted with the proposed scheme, some of the experimental results are discussed in this section. Eight general gray images with sizes of 512×512 were test in these experiments. The eight gray images that were used were entitled F16, Boat, Goldhill, Lena, Couple, Clock, Peppers, and Sailboat, and they are shown in Fig. 7. In addition, the AMBTC scheme was used to compress the original images. This was done because the AMBTC scheme, which is a proven scheme, obtained the optimal value of MSE [6]. All computations were conducted on a computer with an Intel(R) Core™ i7-3770 CPU @ 3.4 GHz and an 8-GB RAM with Windows 7 Professional as the operating system, and Microsoft Visual Studio 2005 C# was used to implement the experiments.

Fig. 7.Eight grayscale test images with sizes of 512×512

To estimate the visual quality of the embedded image, the peak signal-to-noise ratio (PSNR) was defined in Equation (10):

The mean square error (MSE) for a W × H grayscale image was defined as shown in Equation (11):

where W and H are the dimensions of the images, and Xij and Y′ij are the pixel values of the original image and the embedded image, respectively. In principle, a lower value for MSE means less error, and, as considered in Equation (10), the inverse relationship between MSE and PSNR translates into a high value of PSNR, which is desirable. Here, the “signal” is the original image, and the “noise” is the error in the embedded image. Therefore, the lower the MSE (or the higher the PSNR) is, the better the visual quality of the image is.

Table 1.Qualities of images obtained by the AMBTC scheme [6].

Table 1 shows the visual qualities of images obtained by the AMBTC scheme [6] with three different values of n, i.e., 2, 4, and 8. Obviously, the visual quality of these images increase as the value of n decreases. When the values of n were 2, 4, and 8, the average visual qualities are achieved as 40.150 dB, 32.751 dB, and 29.530 dB, respectively, and the bit rates were 5 bits per pixel (bpp), 2 bpp, and 1.25 bpp, respectively.

Tables 2 to 4 present the qualities of the embedded images of the proposed scheme and that of Hu et al.’s scheme [20] when using different values of n, i.e., 2, 4, and 8. As can be seen from Table 2, when the value of n was 2, and b had the values of 2, 3, and 4. The average visual qualities of the embedded images obtained by our proposed scheme were 40.146, 39.140, and 36.884 dB, respectively. It means that the losses of image quality by our proposed scheme were 0.004, 1.010, and 3.266 dB, for b values of 2, 3, and 4, respectively. In the same configuration, the losses for Hu et al.'s scheme were 1.504, 3.829, and 7.136 dB, respectively. Our scheme performed better than Hu et al.’s scheme because their scheme embeds the b bits of authentication code into the quantization values (p, q) by modifying the difference value between p and q. In Hu et al.’s scheme, two candidates, q1 and q2, are generated by using Equations (4) and (5), and the different value between q1 and q2 is 2b. The quantization level q will be in the middle of q1 and q2. Then, to embed ac into the quantization levels, q is replaced by the closer candidate, meaning that the value of q will be changed from 0 to 2b/2. Therefore, the different value between the original quantization levels (p, q) and the embedded quantization values (p', q') also is changed from 0 to 2b/2. For example, when b is equal to 3, the amount of the change will be from 0 to 4. Conversely, the proposed scheme is based on the reference table to ensure that the smallest change of quantization levels. For example, to embed the b bits of authentication code, (p, q) is located in the reference table R, and the candidate set is determined as shown in Fig. 4. Fig. 4 shows that when b is equal to 3, the embedded quantization value (p', q') will be located in the range [p-1, q-1] and [p+1, q+1], meaning that the difference value between the original quantization values (p, q) and the embedded quantization values (p', q') is from 0 to . Obviously, the embedded quantization levels in the proposed scheme will be closer to the original quantization levels than they are in Hu et al.’s scheme. Therefore, we can conclude that the proposed scheme achieved better visual quality of reconstructed images than Hu et al.’s scheme.

Table 2.Comparison of the image quality of our proposed scheme and Hu et al.’s scheme when n was 2.

Table 3.Comparison of the image quality of our proposed scheme and Hu et al.’s scheme when n was 4.

Table 4.Comparison of the image quality of our proposed scheme and Hu et al.’s scheme when n was 8.

In Tables 3 and 4, it is clear that, when the values of n were 4 and 8, our proposed scheme provided better image quality than Hu et al.’s scheme in all cases. The results in Tables 3 and 4 shows that, as the value of b increased, the better the quality of the embedded image became in the proposed scheme. For example, in Table 3, when the value of b was 2, an average image quality of our proposed scheme is greater than that of Hu et al.’s scheme. The average gain rate is 0.307 dB. However, when the value of b is increased to 4, the average image quality of the proposed scheme was 2.24 dB greater than that of Hu et al.’s scheme. This can be explained by the fact that a reference table was used in the proposed scheme. In addition, in the proposed scheme, when the smaller block size n is used, the better quality of the embedded image is obtained. The quantization levels are utilized to compress image block. Therefore, if the block size n is small, the quantization levels will be closer to the original pixel value. Consequently, the higher quality of BTC-compressed images is achieved. However, more bits are required to compress the image.

Fig. 8.Tampered image used in tamper detection test

In the tamper test, Fig. 8(a) was inserted on the wall of the embedded image. Fig. 8(b) shows the binary version of the tamper area of the tampered object.

Fig. 9.Tamper test of embedded image "F16" when the value of n was 4, and b was equal to 3: (a) embedded compressed image with a PSNR of 33.075 dB; (b) tampered image; (c) raw detected image; (d) really-detected image after morphology operation

Fig. 9 shows the tamper test result of the proposed scheme for image “F16” when the value of n was 4, and b was equal to 3. Fig. 9(d) shows the refined detected image after the morphology operation. Normalized correlation coefficient (NC) is used to measure the similarity between the tamper binary image and the detected image. Basically, the nearer the value NC to value 1 is obtained, the more accuracy the detected image is achieved. It is easy to see that the proposed scheme provides the high accuracy of tamper detection, when the NC value is larger than 0.96. Here, NC is calculated using Equation (12)

where TI is the tamper binary image, DI is the detected image, and TIh and TIw are the height and width of the tamper binary image, respectively.

Table 5.Comparison of the proposed scheme and Hu et al.’s scheme when the value of n was 2 and b was equal to 2.

Table 5 shows the comparison of the proposed scheme and Hu et al.’s scheme [20] when n was equal to 2 and the value of b was 2. It is apparent that the proposed scheme and Hu et al.’s schemes can be used for tamper detection. However, the quality value of the embedded image obtained in the proposed scheme is better than that obtained in Hu et al.’s scheme.

 

5. Conclusion

In this paper, we propose a new tamper detection scheme for BTC-compressed images that can detect and locate the tamper areas in such images. Our proposed scheme achieved high-quality images due to its use of the reference table, which was generated by using an extraction function. The experimental results show that our scheme obtained better visual quality of the embedded images than Hu et al.’s scheme irrespective of the size of blocks used in the AMBTC compression technique. For example, the image quality loss of the proposed scheme (0.004 dB) is much less than that of Hu et al.’s scheme (1.504 dB) when the b value is set to 2 and the value of n is 2. In addition, the proposed scheme achieves a clear tampered area. In the future, approaches capable of recovering the original information will be studied.