A High-Quality Image Authentication Scheme for AMBTC-compressed Images

Abstract

In this paper, we present a high-quality image authentication scheme based on absolute moment block truncation coding. In the proposed scheme, we use the parity of the bitmap (BM) to generate the authentication code for each compressed image block. Data hiding is used to authenticate whether the content has been altered or not. For image authentication, we embed the authentication code to quantization levels of each image block compressed by absolute moment block truncation coding (AMBTC) which will be altered when the host image is manipulated. The embedding position is generated by a pseudo-random number generator for security concerned. Besides, to improve the detection ability we use a hierarchical structure to ensure the accuracy of tamper localization. A watermarked image can be precisely inspected whether it has been tampered intentionally or incautiously by checking the extracted watermark. Experimental results demonstrated that the proposed scheme achieved high-quality embedded images and good detection accuracy, with stable performance and high expansibility. Performance comparisons with other block-based data hiding schemes are provided to demonstrate the superiority of the proposed scheme.

1. Introduction

With the rapid development of information technology, the Internet today is used to transmit massive digital images for various kinds of users. In order to speed up the file-transfer rate and decrease image storage space, digital images are always stored in a compressed format based on lossless compression [1] or lossy compression [1]. Lossless compression, does not lose any of the information from the original images, for example, run-length encoding (RLE), entropy encoding, chain codes, and so on. In contrast, lossy compression is subject to loss of some information from the original images in order to achieve a higher compression ratio than lossless compression. As a result, lossy compression is often used to compress general-purpose digital images.

Transform coding [1], block truncation coding (BTC) [1][2][3][4], and vector quantization (VQ) [1] are all typical lossy compression techniques. Among these techniques, BTC proposed by Delp and Ritcell [2] has low computational complexity and excellent reconstructed image quality. Later, Lema and Mitchell [3] redesigned the BTC algorithm by modifying the calculation method of two quantization levels of each AMBTC-compressed block to gain improved reconstructed image quality. This new scheme is called absolute moment block truncation coding (AMBTC) for both grayscale and color image compression.

Data transmitted over the Internet can be easily tampered or copied by malicious users. Image integrity protection has increasingly gained attention due to the rapid development of multimedia and the low security of the Internet. Many solutions have been proposed to ensure digital image authenticity, such as conventional cryptography, digital signatures based on image content, and fragile and semi-fragile watermarking. They could be divided into two groups depending on the service they provide. The first group is formed by strict authentication [5] in which it does not tolerate any manipulation of image data. The second group of applications is frequently addressed as selective authentication [5], which allow for some changes to image data from compression, different filtering algorithms, etc. In practice, however, it is necessary to compress an image to save either storage space or minimize transmission bandwidth/time. Therefore, strict image authentication solutions are less desirable in many practical circumstances.

There are two subgroups within strict authentication services, conventional cryptography based solutions [5][14][15] and fragile watermarking based solutions [5][16][17][18][19][20][21][22]. In general, image authentication solutions included in the conventional cryptography group compute a message authentication code using a hash function that can include message-digest algorithm 5 (MD5) or others. Hash computing for image pixels, rows or columns generates separate hash digests. Next, these hash digests are further encrypted by public key and then appended to the original image. When an image carrying encrypted hash digests is to be verified, receivers first decrypt and then compare the extracted hash digests and the calculated hash digests from the received image. If there are any differences, the image is determined as tampered or vice versa.

For fragile watermarking, there are three main processes for algorithms. First, watermark data are calculated from a set of pixels or other data of an image. Second, the calculated data are embedded into the original image, for example, as another set of pixels. Third, hidden data is extracted when the image is to be authenticated. During the watermark generation procedure, user specified keys are used for encryption and they must be known by senders and receivers in advance. Authenticity of an image can thus be verified. Generally, fragile watermarking algorithms have better performance than algorithms based on conventional cryptography.

Selective authentication service can be grouped into two subgroups, semi-fragile watermarking based solutions [5][23][24][25] and digital-signature based solutions [5][26]. Semi-fragile watermarking solutions aim to insert a watermark into the original image, and differs from fragile watermarking techniques, where the falsification of the protected image can be detected even when the image has undergone some specific image processing operations, i.e., compression, different filtering algorithms, etc. A signature based on image content solutions generally has four main phases. First, high-level characteristics are extracted from the original image. Second, a hash function is used to reduce the size of these characteristics and generate a hash digest. Third, a signature algorithm is used to sign the hash digest to increase security. Finally, the signature to the original image is inserted or attached to the image. When it is necessary to verify the authenticity of the image, the generated image signature is compared to the extracted one. Both signatures should be calculated by the same algorithm.

In 2001, Wong and Memon [6] proposed secret and public key image watermarking solutions for ownership verification and image authentication. Lin and Chang [7] designed a semi-fragile watermarking method that can be used for lossy compressed JPEG images. A compression-domain method [8] that provides JPEG images dual protection was proposed by Lie et al. in 2006. In 2008, Lee and Lin [9] designed a new watermark method for detecting image tamper and recovering the tampered area of the original image. In 2010, a hash-based authentication method [10] was proposed by Ahmed and Siyal to verify the image. In 2011, two additional schemes were proposed, one an adaptive image authentication scheme [11] introduced by Chung and Hu, and the other a quantization-based semi-fragile watermark [12] introduced by Qi and Xin. The former for VQ compressed image authentication and the latter for image content authentication.

In 2013, Hu et al. [13] proposed a new image authentication scheme to verify the tampered areas of AMBTC-compressed images. Hu et al. used a pseudo-random sequence to generate the authentication data. Users determined the number of embedding bits for each AMBTC-compressed image block. Then the authentication code was embedded into certain positions of a bitmap (BM) of each AMBTC-compressed image block. Hu et al.’s method achieved good detection accuracy, however, the visual quality of the embedded image was a little low. The highest quality was 37.8 dB.

As a result, in this paper we propose a new image authentication scheme for AMBTC-compressed images to obtain higher image visual quality and to maintain the detection capability for a watermarked image. In the proposed scheme, the authentication code is embedded into quantization levels of each AMBTC-compressed image block. The experimental results demonstrated that this new authentication scheme achieves both high detection accuracy and high visual quality for the watermarked images.

The rest of the paper is organized as follows. The absolute moment block truncation coding (AMBTC) is provided in Section 2. Section 3 describes a detailed algorithm of our scheme. Experimental results and analysis are shown in Section 4. Finally, conclusions are concluded in Section 5.

 

2. AMBTC

Based on the BTC, Lema and Mitchell [3] presented a new technique called absolute moment block truncation coding (AMBTC), which provides an improvement in reconstructed image quality. In AMBTC, an image is first partitioned into n×n blocks. Each block can be treated as a vector x1, x2, …, xk of dimension k, where k= n×n. The mean value for each pixel block is computed as

The mean value is regarded as a threshold that separates the pixels of a block into two groups. If xi ˂ , then xi is classified into the first group G0; otherwise the pixel is classified into the second group G1. For each block, all the pixels will be stored in a bitmap BM. If xi is in group G0, xi will be stored in the bitmap as value 0; otherwise, xi will be stored in the bitmap as value 1. Then, for each AMBTC-compressed block, the two quantization levels a and b are calculated as

where m is the number of pixels in group G1. A compressed trio is then generated, (a, b, BM). The decoding method of AMBTC is very simple, and presented as follows.

where bm1, bm2, …, bmk are the values in BM of each compressed trio, and let r1, r2, …, rk are the values of reconstructed vector of each image block.

 

3. Proposed Scheme

In Hu et al.’s scheme [13], the authentication code is embedded into the bitmap of each AMBTC-compressed block (a, b, BM). This way, the original image is damaged to a large extent, and the visual quality of reconstructed watermarked images is not so good. To improve image quality, we embed the authentication code into quantization levels of each AMBTC-compressed image block so as to create less distortion of the original image. Note that it is necessary to keep quantization level a smaller than quantization level b even after authentication code embedding. In general, two principles are followed in the embedding operations: (1) never change the bits in two quantization levels that are used to generate sequence ab; (2) always choose the bit that causes less influence to the quantization level(s) to obtain the higher image quality. Hence, as shown in Fig. 1, there are some operations that must be done before embedding watermarks. Having explained our motivation, we now outline the principle of the proposed data hiding algorithm including position code generation procedure, authentication code generation procedure, embedding procedure, and tamper detection procedure.

Fig. 1.Flowchart of authentication code embedding procedure

3.1 Position Code Generation Procedure

To ensure that the embedding may not change the features of AMBTC, we first use the authentication index and position index to generate the position code where the authentication data is embedded into.

We use a pseudo-random number generator to generate the authentication index and position index for security concerned. The authentication index ai and the position index pi are computed as

where rv_ai and rv_pi are the random values generated by a pseudo-random number generator, and eb denotes the number of bits of authentication code.

Then, we ues the authentication index and position index to generate the position code pc that indicates which bit of quantization level will be used for embedding authentication code ac. To ensure the safety of our proposed authentication code embedding procedure, we generate a new sequence called ab from two quantization levels to determine the position code pc.

Assume that the two quantization levels are transformed to binary formats denoted as a=(a1, a2, …, a8) and b=(b1, b2, …, b8). The ab sequence (ab1, ab2, …, ab8) is computed as ab = derived from two quantization levels, a and b. The position code pc is calculated as

where pi is the position index computed by Eq. 1 and abi is an element in sequence ab which is chosen by position index pi.

The example of generation of sequence ab shown in Fig. 2 is set as a=134, b=231. The two quantization levels can be presented as two binary sequences: a=10000110, b=11100111. Then the sequence ab is obtained as ab=01110001. The position code pc is computed as Fig. 3 according to eb. If eb equals 1 or 2, the possible value of pc is 7 or 8; otherwise, if eb equals 3 or 4, the possible value of pc is 6 or 7. For eb=4, we need four bits of two quantization levels to embed watermarks. Therefore, variable position code is used in proposed embedding rather than fix LSB embedding in order to ensure the safety of watermark embedding.

Fig. 2.Example of generation of sequence ab

Fig. 3.Example of computing position code pc

3.2 Authentication Code Generation Procedure

Unlike general watermarking method, instead of external watermarks, we embed features of the image as a watermark into itself for unique authentication. In such self embedding technique the image features are embedded into itself as an authentication data. The features are of course image dependent data and therefore are able to prevent watermarking copy attacks or similar. As a result, the use of image-dependent watermark provides better security as compared to traditional watermarking where a random sequence is used as a watermark for all images [27].

For block-based image authentication, we use the parity of the bitmap (BM) to generate the authentication code for each compressed image block. We first divide the bitmap BM = bm1, bm2, …, bmn×n into eb sub-blocks with a size

The sub-block SDBMi can be presented in the following way

The parity pi of SDBMi can be computed by

Thus, the authentication code ac is generated by

where aci is the ith bit of authentication code ac.

3.3 Authentication Code Embedding Procedure

In the proposed scheme, we embed an eb−bit watermark consists of the authentication data into each AMBTC compressed image block. Note that the authentication data is used to identify any modification made to the authenticated image. The proposed watermarking procedure is described as follows.

Input: AMBTC-compressed image I, authentication seed, position seed.

Output: Watermarked AMBTC-compressed image Iʹ.

Step 1. Generate authentication index ai and position index pi according to Eq. 1.

Step 2. Generate position code pc according to Eq. 2.

Step 3. Generate authentication code ac according to Eq. 3.

Step 4. If eb equals 1, hide ac1 into quantization levels as

Step 5. If eb equals 2, hide ac1 and ac2 into quantization levels as

Step 6. If eb equals 3, hide ac1, ac2, and ac3 into quantization levels as

Step 7. If eb equals 4, hide ac1, ac2, ac3, and ac4 into quantization levels as

Step 8. If quantization level a is bigger than quantization level b,

Step 9. Repeat Steps 1 to 8 until all AMBTC-compressed blocks have been processed.

Based on definitions of AMBTC, the quantization level a is smaller than quantization level b. Note that Step 8 is used to make sure that quantization level a is still lower than quantization level b after embedding the watermark. A watermarking embedding example is provided for eb=2. Suppose that ai = 01, pi = 5, and the block trio is (10000110, 11100111, 0100111010111100). According to Eq.2, the authentication code ac is computed as 00. The position code pc is calculated as pc=8-(1-ab6)=8. We embed ac1 into apc and ac2 into b8 since ac1=0, that is, a8=0 and b8=0. Step 8 is skipped since the quantization level a is smaller than quantization level b in this case. The final watermarked compressed trio is (10000110, 11100110, 0100111010111100).

3.4 Tamper Detection Procedure

The flowchart of tamper detection is shown in Fig. 4. Tamper detection detects whether the received AMBTC-compressed image has been tampered. The proposed tamper detection procedure is described as follows.

Fig. 4.Flowchart of tamper detection procedure

Input: The watermarked AMBTC-compressed image Iʹ, authentication seed, position seed.

Output: Tampered part of the image.

Step 1. Generate authentication index ai and position index pi according to Eq. 1.

Step 2. Generate position code pc according to Eq. 2.

Step 3. Generate authentication code ac according to Eq. 3.

Step 4. Extract authentication code eac from quantization levels according to authentication code ac and position code pc

Step 5. Compare eac with ac. If they are not equal, mark this block erroneous and complete the detection for it; otherwise, mark it valid.

Step 6. Repeat Steps 1 to 5 until all the blocks have been tested.

To improve the detection ability, we use a hierarchical structure to ensure the accuracy of tamper localization. In the level-2 detection, a valid center block is further marked erroneous if there are two erroneous blocks in its 3×3 block-neighborhood shown in Fig. 5.

Fig. 5.The 3×3 block-neighborhood of a valid center block

 

4. Experimental Results

The test images of size 512×512, “Lenna,” “Airplane,” “Girl,” “Peppers,” “Tiffany,” and “Zelda,” are shown in Fig. 6. To measure the quality of the watermarked images, the peak signal-to-noise ratio (PSNR) is introduced as

where the mean squared error (MSE) is defined as

where Ii, j denotes a pixel value of the original image, Iʹi, j denotes a pixel value of the watermarked image, and H×W is the image size.

Fig. 6.Test images with size 512×512

Table 1 shows the PSNR values for the six test images compressed by the AMBTC algorithm with blocks of size 2×2, 4×4, and 8×8. Clearly, the image quality decreases when the block size increases. The average visual qualities are 42.073 dB, 34.969 dB, 31.367 dB when the original image was divided into 2×2, 4×4, and 8×8 blocks, respectively. Note that a higher PSNR value resulted in higher image visual quality.

Table 1.Image quality of AMBTC-compressed images with different block sizes

Tables 2 to 4 compares image quality in PSNR for test images delivered by the proposed scheme and Hu et al.’s scheme [13] with block sizes 2×2, 4×4, and 8×8, respectively. The number of bits that are embedded into a block are 1, 2, 3, and 4, respectively. In Table 2, our proposed scheme performs better than Hu et al.’s scheme with results that are 3.65 dB, 5.95 dB, 5.16 dB, and 4.92 dB higher, respectively, for different number of embedding bits. The reason is that their scheme embeds the authentication code into the BM by modifying the least eb distortion bits of BM, and also changes the quantization levels of a block. Our scheme, however, only changes the quantization levels of a block. When eb=1 and eb=2, the maximum distortion for the quantization levels a and b is no more than two. When eb=3 or eb=4, maximum distortion for the quantization levels a and b is no more than six. Therefore, our scheme results in less distortion.

Table 2.Performance comparison for test images with scheme [13] for block size 2×2

Table 3.Performance comparison for test images with scheme [13] for block size 4×4

Table 4.Performance comparison for test images with scheme [13] for block size 8×8

In Table 3, the PSNRs are still higher than that of the Hu et al. scheme [13] when the size of a block size is 4×4. It was 0.26 dB, 0.9 dB, 1.33 dB, 1.96 dB higher for 1 bit, 2 bit, 3 bit, and 4 bit embedding, respectively. However, in Table 4 when the number eb are 1 and 3, our proposed scheme performs worse than Hu et al.’s scheme. The losses of our scheme are 0.06 dB, and 0.04 dB, respectively. It is obvious that if the size of block increases, the superiority of the PSNR in our scheme decreases. This is because the larger the block size, the bigger the bitmap of a block. Whereas, in the meanwhile the quantization levels are still two. Under this condition, if one changes bit information of the bitmap, the loss of image information is significant, and will be shared with the other 63 pixels. However, if you change the quantization levels of an image block, the loss of information is not that significant, but 64 or 32 pixels may have the same loss. Therefore, if the block is larger, the advantage of our scheme is smaller.

As shown in Tables 2 to 4, when the number of bits of the authentication code increases, the visual quality of the watermarked image decreases. The visual quality that can be achieved depends on the nature of the image itself. It is also very apparent that the visual quality decreases fast with increased compressed block size.When the size of block is 2×2 or 4×4, our scheme has better PSNR values. However, when the block size is increased to 8×8 our PSNR value is a little less than that of Hu et al.’s scheme. As such, different authentication schemes may best suited to different block sizes.

Fig. 7 shows the visual impacts of watermarked “Airplane” images at various real hiding capacities for block size 4×4. In general, the watermarked image hardly can be distinguished from the original image. Fig. 8 compares the visual impacts of the zoomed-in watermarked “Airplane” image for eb=4 delivered by the proposed scheme and Hu et al.’s scheme [13]. Clearly, Hu et al.’s scheme destroys the smoothness in many points around edges. The reasion is that Hu et al. scheme transforms a bit in the bitmap from 0 to 1 or 1 to 0 that results in the smooth pixels may become very distinct in the reconstructed image. Usually, the blocks containing the edges may have two quantization levels with a large difference, and sometimes the difference between quantization level a and b can be more than 100. With this condition, the value of a reconstructed pixel according the transformed bit will turn from quantization level a to quantization level b or from b to a. As a result, this pixel may become very distinct in the reconstructed image since it is different from the other pixels around it. Our scheme only changes the value of quantization levels, and thus does not suffer from the same problem.

Fig. 7.Watermarked “Airplane” image

Fig. 8.Performance comparison for the zoomed-in “Airplane” image with scheme [13] for eb=4; (a) AMBTC-compressed image, (b) watermarked image using our proposed scheme, and (c) watermarked image using Hu et al.’s scheme

In our experiment, the watermarked image is tampered with by a small cherry image. Fig. 9 shows the tamper detection result. In our proposed scheme, when embedding an one-bit authentication code into each image block, about half of all tampered blocks can be detected only during the level-1 detection procedure, and only a few blocks around the edges of a tamper image fail to be detected after level-2 detection. From Fig. 10, when the bit number of an embedding authentication code is larger, more tampered blocks can be detected after level-2 detection, that is, the failed detected blocks are fewer. Our proposed scheme embeds the authentication code into quantization levels instead of BM to achieve good detection accuracy. In our proposed scheme, when embedding a one-bit authentication code into each image block, about half of all tampered blocks can be detected only during the raw detection procedure, and only a few blocks around the edges of a tamper image fail to be detected after tamper refinement. When embedding a two-bit authentication code into each image block, about 3/4 of all tampered blocks can be detected only during the raw detection procedure and the failed tampered blocks are fewer. If the bits of an authentication code is three, about 7/8 of tampered blocks can be detected only during the raw detection procedure. If the bits of an authentication code is four, about 15/16 of the tampered blocks can be detected only during the raw detection procedure, and the failed detected blocks are the fewest.

Fig. 9.Tamper detection results for eb=1; (a) tampered “Airplane”, (b) level-1 detection, (c) level-2 detection, and (d) Failed detected blocks

Fig. 10.Failed detected results for various hiding capacity; (a) eb=1, (b) eb=2, (c) eb=3, and (d) eb=4

 

5. Conclusion

In this paper, we present a high-quality image authentication scheme to protect the security of AMBTC-compressed images. The authentication code derived from the BM information is protected by the random numbers. Our proposed scheme embeds the authentication code into quantization levels instead of BM to obtain higher visual quality in the embedded image. Our scheme has better visual quality in comparison to Hu et al., which results in some abrupt points appearing around the edges of an embedded image. In the future, we will try to propose an adaptive image authentication scheme for AMBTC compressed images, which can offer high quality for AMBTC compressed images with different block sizes.