Hybrid Data Hiding Based on AMBTC Using Enhanced Hamming Code

Round 1

Reviewer 1 Report

Overall, this paper is engaging, well-structured, and self-contained. I think that the contribution herein introduced may have several and useful, practical implications. The paper appears to be sound and relies on well-known building blocks. Again, it is written by using an appropriate technical language. The mathematical notation is clearly defined and consistently applied within the whole paper.

However, I think that the paper is still affected by some minor drawbacks, which need to be necessarily addressed.

- In some parts of the paper, the clarity and editorial quality of the paper weaken. As a consequence, such parts result in being quite challenging to read. Therefore, I would suggest carefully improving the prose of writing to make this paper more comfortable.

- The title of Section 2 is quite misleading. This section should be titled "Background" or something similar.

- The authors should provide the rationale behind the proposed scheme to provide a clearer view of their proposal.

- In general, the work should be better contextualized with respect to state of the art, providing the appropriate connections. In this regard, authors should mention the following related papers:

[1] https://doi.org/10.1016/j.future.2018.07.051
[2] https://doi.org/10.1007/s11042-019-7519-2

- Accurate proofreading is strongly required since, in the paper, there are several typos and formatting issues.

Author Response

Reviewer#1

We appreciate the reviewer’s valuable comments. The followings are our point-by-point responses:

(1) I would suggest carefully improving the prose of writing to make this paper more comfortable.

Response: As suggested by the reviewer, we improved the prose of the writing to make easy to understand.

 (2) The title of Section 2 is quite misleading. This section should be titled "Background" or something similar.

Response: As suggested by the reviewer, we changed the title of Section 2 as “Preliminaries”.

(3) The authors should provide the rationale behind the proposed scheme to provide a clearer view of their proposal.

Response: (7, 4) Hamming code is effective for data hiding, which can conceal 3 bits into 7-pixels by flipping 1-bit of LSB in a pixel. However, there is a problem in applying this method directly to AMBTC. Because an image compressed with AMBTC is consists of two quantization levels and one bitmap, so it cannot provide sufficient redundant pixels. That is, since trio provides only two quantization levels, MSE can be greatly increased when a Hamming code is applied to two quantization levels like Bai & Chang’s method [30]. For improving performance, it is very important to find an optimized encoding method using Hamming code. In this paper, we propose a method to greatly reduce the errors that occur in the encoding process in the existing methods, and accordingly to improve the data hiding performance and image quality.

(4) In general, the work should be better contextualized with respect to state of the art, providing the appropriate connections. In this regard, authors should mention the following related papers:

Response: In Introduction Section, two papers suggested by reviewers were cited in the RDH methods below.

[1] https://doi.org/10.1016/j.future.2018.07.051,

[2] https://doi.org/10.1007/s11042-019-7519-2

(5) Accurate proofreading is strongly required since, in the paper, there are several typos and formatting issues.

Response: As suggested by the reviewer, we proofread to resolve typos and formatting issues.

Author Response File: Author Response.docx

Reviewer 2 Report

1. Mention the highlights of your work.
2. Rewrite the abstract with more numerical results.
3. The motivation for AMBTC has not been justified satisfactorily.
4. The way of explaining the proposed methodology is really good. Especially Fig 6.
5. From table 1, by considering the PSNR of the proposed work, it's supposed to be greater than 30 to achieve good hiding. Yet, your algorithm failed in that case with T = 20. What is your justification for this?
6. Kindly mention the unit for EC (Say bits or bytes, etc).
7. Perform histogram and NCC analysis to further verify your algorithm.
8. Perform timing analysis and compare it with earlier works.
9. Perform MSE and include results in the revised version.

Author Response

Reviewer#2

We appreciate that the reviewer’s valuable comments. The followings are our point-by-point responses:

(1) Mention the highlights of your work.
Response: As suggested by the reviewer, we added the contributions (highlights) in Introduction Section of our paper as follows.

We introduce a general framework for DH based on AMBTC with minimal square error by optimal Hamming code using Look Up Table (LUT). Our method calculates the codeword corresponding to the minimum distance from the standard array of the (7,4) Hamming code table, and then extracts the corresponding code. The method has little effect on program performance and can be easily conducted. We provide a comparative analysis and evaluate their efficiency based on the specified criteria. The sufficient experimental results are used to show the effectiveness and advantages of the proposed method.

(2) Rewrite the abstract with more numerical results.

Response: As suggested by the reviewer, we have included numerical results in Abstract.

Abstract: Image-based data hiding method is a technology used for the purpose of secretly transmitting confidential information. Especially, since images (e.g., grayscale image) usually have sufficient redundancy information, they are a very suitable medium for hiding data secretly. Absolute Moment Block Truncation Coding (AMBTC) is one of several compression methods and is suitable for embedding data due to its very low complexity and acceptable distortion. However, there is not enough redundant data compared to grayscale scale images, so the studies to embed data in the compressed image is a very challenging research topic. Meanwhile, Hamming code is a grayscale image-based coding method that is frequently used in the study of data hiding methods. However, in the case of AMBTC-based images, there is a lack of sufficient redundant data, so it is necessary to study how to overcome these limitations. In this paper, we present an effective data hiding method at two quantization levels representing blocks based on AMBTC using Hamming code. AMBTC is expressed in the format , where  and  are quantization levels and BM are a bitmap. The quantization level is the pixel value used as the representative value when dividing the image into 4´4 blocks. The Hamming (7, 4) is a method to embed 3 secret bits by flipping only 1 bit when a codeword is composed of 7 bits. An image compressed by AMBTC has only two quantization levels, so it is difficult to use directly. Bai & Chang introduced a codeword that combines the lower 4 bits in  and the lower 3 bits in , but the image distortion error is high. Therefore, in this paper, we introduce an effectively way to conceal 3 bits as well as to reduce the distortion that occurs in the data hiding stage. In the experiments, when concealing 150,000 bits in the Lena image, the averages of the normalized cross correlation (NCC) and Mean-Squared Error (MSE) of our proposed method were 0.9952 and 37.9460, respectively, which were the highest. The sufficient experiments confirmed that the performance of the proposed method is satisfactory in terms of image embedding capacity and quality.

(3) The motivation for AMBTC has not been justified satisfactorily.

Response: As suggested by the reviewer, we added the motivation in Introduction Section as follows:

The motivations to propose a DH method using the Hamming code based on the image compressed with AMBTC are as follows. First, AMBTC is suitable for data hiding because it has reasonable compression performance, very low computational complexity, and (although not many) (although not many) redundant bits. In addition, data hiding based on AMBTC was relatively less studied than that of grayscale images. Second, Meanwhile, Hamming code is a very efficient for redundant bits, such as a grayscale image. This has been demonstrated in previous studies (quoting my paper). However, since the image compressed with AMBTC has fewer redundancy bits than the grayscale image, the embedding enough secret bits on two quantization levels results in a negative effect on the image in the decoding the bitmap. Third, Bai & Chang[30] attempted to conceal data at two quantization levels, but did not meet the optimized performance. Therefore, it is essential to develop an optimized method in the data hiding process.

(4) The way of explaining the proposed methodology is really good. Especially Fig 6.

Response: To make the example easier to understand, a number was added to each step of the process in Figure 6, and the description of the number was written step by step in the paper.

The two quantization levels of a given trio are assigned to variables and , and then converted to binary, i.e., = 103 = 011001112 and  = 109 = 011011012. For the two converted binary numbers, the 4 LSB ( = (011001112) of and the 3 LSB (  = (011011012)) of  are extracted. To form a codeword, the extracted binary numbers are combined. That is, y = (0111||101)2. Calculate y’ = (bin2dec(0111) bin2dec(101)) = (7 5). After converting the bit m(= 101) to decimal, The value d = 5 is retrieved from the coset leaders of standard array of HC (7,4). Using Equation 9, the codeword having the minimum distance from the given codewords is retrieved from the table. Here, ( −7)2 + ( −4)2 = 1 corresponds to the minimum distance. The new codeword is = (7||4) = (0111||100)2 = (0111100)2. Two quantization levels to embed 3 secret bits are recovered by using the codeword . A new quantization level is obtained by replacing the upper 4 bits and the lower 3 bits of  obtained in the process of (7), respectively, with 4LSB and 3LSB of two quantization levels. That is, the recovered codewords are  = 103 and  = 108.

(5) From table 1, by considering the PSNR of the proposed work, it's supposed to be greater than 30 to achieve good hiding. Yet, your algorithm failed in that case with T = 20. What is your justification for this?

Response: Thank you for your good question. Here are our thoughts and justifications for your question.

T (a - b) =30 means that the difference between the two quantization levels of the block is 30. In (Table 1), when T=20, the ECs of Ou & Sun and Bai & Chang for Lena are less than our proposed method. Therefore, the PSNRs of the two methods are relatively high. Bai & Chang's EC is less than half that of our proposed method. However, EC and PSNR of Hong and our proposed method show similar performance. When T=30, Bai & Chang's method in Figure 8(a) cannot hide more than 150,000 secret bits. The PSNR of Ou & Sun's method degrades below 30dB when concealing approximately 250,000 bits. In Hong and our method, PSNR is reduced to less than 30dB when concealing more than 280000 bits. For the comparison between the original image and the stego image, the maximum value of the data concealment amount is compared when it is usually 30 dB or more. When the PSNR is reduced to less than 30dB, the quality of the image is deteriorated enough to be detected by the human visual system, so performance at T=30 is not important.

(6) Kindly mention the unit for EC (Say bits or bytes, etc).

Response: Yes, we use bits for EC. To clearly show this, we modify EC --> EC (bits) and dB --> PSNR (dB) in Table 1.

(7) Perform histogram and NCC analysis to further verify your algorithm. Perform MSE and include results in the revised version.

Response: As suggested by the reviewer, we added the histogram analysis (Figure 9) and the NCC and MSE experiments (Table 3).

Figure 9 shows the evaluation by comparing the histograms of stego images generated from the proposed method and existing methods, i.e., W Hong, Ou & Sun and Bai & Chang. Here, stego images are generated after concealing 150,000 bits in a cover Lena image by existing and proposed methods. The pixel values range on x-axis is [95, 115]. In Figure 9, the curves of our proposed method and the existing two methods (i.e., W Hong and Ou & Sun) are similar, while Bai &Chang’s histogram curve has a larger amplitude than other methods. The reason is that the maximum EC of Bai & Chang’s method is up to 150000 bits. In other words, we can see that the quality of the image is dropping because of exhausting all possible resources. The histogram does not show much difference because our proposed method and the existing two methods keep more than 33dB in common when concealing 150000 bits. As shown in Figure 8, as the EC increases, the histogram of the stego image also becomes far from the original histogram.

Table 3 shows the MSE and NCC simulation results for the existing and the proposed method for the four images. The average MSE value of the proposed method is lower than those of the other three methods. The MSE value of Airplane image in our proposed method is slightly higher than those of Ou & Sun [29] and W Hong [33]. However, from the NCC scores, there is no difference, so it is objectively proven that there is no problem with the performance of our proposed method. Also, when the maximum EC of Ou & Sun reaches 270000 bits, the PSNR drops to 23dB. On the other hand, our proposed method can maintain the PSNR higher than 30dB, so the DH performance for our proposed method is useful. Our proposed method can obtain better performance by creating a look up table to obtain more optimal values than W Hong’s method.

(8) Perform timing analysis and compare it with earlier works.

Table 4 shows the CPU times for the proposed and the existing methods.

Table 4 shows the comparison of CPU execution time between the proposed and the existing methods. The computer for the experiment is YOGA 730 and the CPU processor is Intel(R) Core(TM) i5-8250U CPU 1.6Ghz. The software is Matlab R2019a. Here, we measure the cpu time to conceal a random number from 20000bits to 200000bits in the Lena image by using four ways (i.e., Ou & Sun, W Hong, Bai & Chang, Our proposed method). The process in the measurement includes AMBTC compression, data embedding, and AMBTC decompression. The most time-consuming method is Bai & Chang, and the least consumption method is Ou & Sun. The method we proposed is faster than Bai & Chang’s, but it is time consuming compared to the other two. However, if we code using C language, the required time will be less than 1 second.

 

 

Author Response File: Author Response.docx

Reviewer 3 Report

The authors improved Bai & Chang method for hiding data using Hamming code.  Experimental results show that the improvement is successful.  This is a contribution to our field.

 

The abstract is terrible and should be improved in terms of logic.  In the current version, the abstract starts with the contribution of this study, followed however with background information.  Then, the Bai & Chang method was mentioned and improved.  It reads strange.

 

What is the limitation of the proposed method?

 

I want to suggest adding some recommendations for future research.

Author Response

Reviewer #3
We appreciate that the reviewer’s valuable comments. The followings are our point-by-point responses:

(1) The abstract is terrible and should be improved in terms of logic. In the current version, the abstract starts with the contribution of this study, followed however with background information. Then, the Bai & Chang method was mentioned and improved. It reads strange.

Response: Thank you for your good comments. We improved Abstract as follows:

Abstract: Image-based data hiding method is a technology used for the purpose of secretly transmitting confidential information. Especially, since images (e.g., grayscale image) usually have sufficient redundancy information, they are a very suitable medium for hiding data secretly. Absolute Moment Block Truncation Coding (AMBTC) is one of several compression methods and is suitable for embedding data due to its very low complexity and acceptable distortion. However, there is not enough redundant data compared to grayscale scale images, so the studies to embed data in the compressed image is a very challenging research topic. Meanwhile, Hamming code is a grayscale image-based coding method that is frequently used in the studies of data hiding. However, in the case of AMBTC-based images, there is a lack of sufficient redundant data, so it is necessary to study how to overcome these limitations. AMBTC is expressed in the format , where  and  are quantization levels and BM is a bitmap. The quantization level is the pixel value used as the representative value when dividing the image into 4´4 blocks. In this paper, we present an effective data hiding method at two quantization levels representing blocks based on AMBTC using Hamming code. The Hamming (7, 4) is a method to embed 3 secret bits by flipping only 1 bit when a codeword is composed of 7 bits. An image compressed by AMBTC has only two quantization level, so it difficult to use data hiding directly. Bai & Chang introduced a codeword that combines the lower 4 bits in  and the lower 3 bits in , but the image distortion error is high. Therefore, in this paper, we introduce an effectively way to conceal 3 bits as well as to reduce the distortion that occurs in the data hiding. In the experiments, when concealing 150000 bits in the Lena image, the averages of the normalized cross correlation (NCC) and Mean-Squared Error (MSE) of our proposed method were 0.9952 and 37.9460, respectively, which were the highest. The sufficient experiments confirmed that the performance of the proposed method is satisfactory in terms of image embedding capacity and quality.

(2) What is the limitation of the proposed method?

Response: The performance of data hiding based on AMBTC-compressed images depends entirely on the exploitation level of both bitmap and two quantization levels. Since data hiding is accompanied by increasing errors as much as the secret bits, in the case of a low-frequency image, even though allowable secret information may be concealed, the quality of the cover image may not deteriorate excessively. On the other hand, the proposed method and the existing methods are vulnerable to high-frequency images. Therefore, more research is needed on this problem.

(3) I want to suggest adding some recommendations for future research.

Response: As suggested by the reviewer, we added future research as follows: In the future, we will devise a method to calculate a more optimal distance when applying HC (7,4) to two quantization levels, and conduct the research to find a way to minimize data concealment errors. 

 

 

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

The authors addressed all the issues I pointed out by carefully revising the paper. The paper has been substantially improved with respect to the relative previous version. In my opinion, the paper is now ready to be accepted for publication.

Author Response

Thank you!

Reviewer 2 Report

The authors solved ALL the comments 

Author Response

Thank you!