# A novel edge based embedding in medical images based on unique key generated using sudoku puzzle design

- B. Santhi
^{1}and - B. Dheeptha
^{1}Email author

**Received: **1 June 2016

**Accepted: **22 September 2016

**Published: **29 September 2016

## Abstract

The field of telemedicine has gained immense momentum, owing to the need for transmitting patients’ information securely. This paper puts forth a unique method for embedding data in medical images. It is based on edge based embedding and XOR coding. The algorithm proposes a novel key generation technique by utilizing the design of a sudoku puzzle to enhance the security of the transmitted message. The edge blocks of the cover image alone, are utilized to embed the payloads. The least significant bit of the pixel values are changed by XOR coding depending on the data to be embedded and the key generated. Hence the distortion in the stego image is minimized and the information is retrieved accurately. Data is embedded in the RGB planes of the cover image, thus increasing its embedding capacity. Several measures including peak signal noise ratio (PSNR), mean square error (MSE), universal image quality index (UIQI) and correlation coefficient (R) are the image quality measures that have been used to analyze the quality of the stego image. It is evident from the results that the proposed technique outperforms the former methodologies.

### Keywords

Telemedicine Edge based embedding XOR coding Stego image Least significant bit## Background

Information security has always been a matter of great concern with cyber threats on the rise. It is a vital aspect, especially in the field of telemedicine. Telemedicine utilizes telecommunication and information technology to provide health care. In such scenarios, the patient’s data must stay confidential, failing of which could result in a huge complication.

Steganography offers a viable solution to protect confidential information from unauthorized access by concealing the existence of data (Lou and Liu 2002). It is an art of hiding data inside any cover object (Amin et al. 2003). The cover object could be an image, a video or an audio file. The most commonly preferred cover object is an image. Different steganographic algorithms exist for different image formats (Morkel et al. 2005). Images can be either be a color image, or a grey image, or a binary image. The color images can again be in various formats like hue saturation value (HSV), luminance chrominance (YCbCr), red green blue(RGB), YUV, YIQ, etc.

A plethora of steganography techniques have been suggested in the erstwhile research works (Cheddad 2010). They can be broadly categorized on the basis of the embedding domain namely, spatial and frequency domain (transform domain). In the case of spatial domain, M is directly embedded in the pixels of C using the least significant bit (Canny 1986) or pixel value differencing (PVD). In the transform domain, many transforms are applied to the base image and M is embedded by altering the coefficient values obtained from transformation. The most commonly used transforms include DWT (discrete wavelet transform), SVD (singular value decomposition) and DCT (discrete cosine transform).

The steganography method used must offer imperceptibility, capacity, security and robustness (Cheddad 2010). The variations in the embedded image must be subtle enough to be inconspicuous to the human eye and have a good imperceptibility. This is achieved by utilizing the LSB of the pixels. This also facilitates easy retrieval of the embedded data. Coding methods like matrix coding, XOR coding etc., are incorporated to enhance the embedding efficiency. Generally, a random number is generated to improve the security of the algorithm. This also ensures that the key changes for every session.

This paper proposes a steganography method in the spatial domain for an RGB image. This method identifies the edge blocks of the cover image and combines with it an XOR coding function. It also generates a unique key for every session, thus ensuring robustness of the technique.

The remaining paper is structured in the following manner—"Related works" section briefs about the existing research works, analyzing their strengths and drawbacks. The detailed elaboration of the proposed methodology is elicited in "The proposed method" section along with the necessary flow charts. The experimental results are analyzed in "Experimental results and discussions" section and "Conclusion" section wraps up the entire paper work.

## Related works

This section briefs about the various methodologies that are used to perform steganalysis. Steganography methods can use any form of cover object to embed message bits. Cover objects include image, video and audio files. A video steganography algorithm was proposed by Mritha and Ashidi (2015) in which data is concealed in a video. This paper has succeeded in reducing the distortion in the cover video and securely embedding the message using scene-change detection. Similarly, an audio steganography scheme was proposed by Kar and Mulkey (2015) in 2015 which uses multiple threshold values to restrict the number of bits embedded in the sample audio.

This paper has classified the steganography techniques based on the domain (Spatial or transform) used for implementation. In 2004, Chan and Chen (2004) presented a data hiding technique in spatial domain using plain LSB substitution. Optimal pixel adjustment process was applied to the stego image to improve its quality. However, such simple LSB substitution methods are easily prone to attacks. Another spatial domain technique that is often used is based on pixel value differencing(PVD).This was proposed by Da-Chun Wu and Wen-Hsiang Tsai (2003) in 2003. The message was embedded based on the differences obtained between two consecutive pixels. The range of difference values chosen depends on the human vision’s sensitivity to variations in the image. Although PVD can be used to conceal a large number of secret bits, the histogram plotted for pixel differences can expose the presence of the secret message. To overcome such anomalies, Zhang and Wang (2003) presented a modified version of the method in 2004 wherein a pseudo random number generated from an embedding key was used for any pair of successive pixels.

Another alternative advancement to the PVD technique was the utilization of the edge pixels to embed message bits. Edge blocks are employed in accordance to the human visual system since human eyes are more sensitive to changes in smooth areas rather than sharp, contrast regions. The intensity of edge pixels was either higher or lower than their neighboring pixels, thus causing a sharp variation in the image. Hence edge blocks are most suitable to hide secret information in an image. Numerous edge detection methods have been elicited over the years. In 1986, Canny (1986) proposed a computational approach to edge detection which involved satisfying a few localization conditions, detection and response criteria on a class of edges. Li et al. (2009) used sobel operator to generate edge image. Edge detection was performed on all the three (R, G, B) planes and the corresponding LSB of each pixel are utilized to embed data. Finally, the stego planes were merged to obtain the stego image. But, this method did not ensure high embedding capacity. Chen et al. (2010) introduced a hybrid edge detector by combining fuzzy edge detector and the canny edge detector, thus effectively achieving a good quality stego image. However, this method brings about unnecessary modifications in the stego image.

Bassil (2012) proposed an image steganography for color images based on canny edge detection in 2012. Three least significant bits of every edge pixel identified by the canny edge detector are replaced by message bits. In addition to this, the algorithm is characterized by three parameters that help to yield different outputs for the same image and data. However, it does not guarantee the correct retrieval of the hidden message. In 2013, Modi et al. (2013) applied canny edge detection to color images. The least two significant bits of every edge pixel are used for embedding data. Edges are selected depending on the length of the secret message to be embedded.

All the mentioned works utilized canny edge detector which, unfortunately, does not produce the same set of edge pixels for a pair of cover image and stego image. Consequently, the message extracted could turn out to be incorrect. To evade from such inconsistencies, Dmour and Ani (2016) proposed an embedding technique using edge based detection and XOR coding. The cover image is broken down into non-overlapping blocks. The edge blocks of the cover image and the stego image are identified using a threshold value. The current paper is an improvisation of Dmour’s work to improve the security of the algorithm by generating an exclusive key matrix for every session.

To augment the embedding efficiency, a myriad of coding theories have been proposed. They include matrix encoding, chaotic sequencing and parity bit check. In 2007, Liu and Xi (2007) used chaotic sequencing concept for information hiding. In 1998, Crandall et al. (1998) applied matrix embedding to minimize the disparities between the original image and the stego image. XOR operation is used to hide two message bits in a block of three pixels. F5 algorithm, a transform domain implementation was then introduced by Westfeld (2001) in 2001. This algorithm serves two purposes—improving embedding efficiency and minimizing the change of DCT coefficients. K bits of secret data is concealed in 2^{
k
}
*−*1 cover bits using hamming code. Despite the improvements in embedding efficiency, matrix encoding has certain drawbacks such as, limited embedding capacity and high computational cost. Hou et al. (2011) proposed a tree based parity check approach that utilizes a tree structure to minimize the distortions in the cover image. This method can hide 2^{n} bits of message bits in n-level binary tree.

This paper proposes an embedding technique based on XOR coding. XOR coding reduces the computational cost to a great extent and also helps in easy retrieval of the message bits.

## The proposed method

### Identification of edges

The human eyes are less affected by changes in image regions containing edges and sharp transitions in comparison to smooth regions. Consequently, the message is camouflaged in the edge areas to render the steganography algorithm imperceptible.

The gamut of traditional edge detection algorithms described earlier result in edge images that are susceptible to changes in the original cover image, in spite of the changes being minor or insignificant. The common edge detection algorithms that are in use include Sobel, Canny, Prewitt, Roberts and fuzzy logic methods. Since the concealment of information in edge images generated by these methods would result in changes to the cover image, the algorithm proposed in (Al-Dmour 2016) has been adopted.

Algorithm: Edge detection | |
---|---|

Input: | C, a cover image |

th, a threshold value between 4 and 96. Choose the highest value of 96 initially | |

Output: | E, an edge image. |

1. Divide C into non-overlapping blocks, each of size 3 × 3 | |

2. Compute the absolute mean difference between the left and right columns of the block. Repeat the same to find the horizontal, first diagonal and the second diagonal’s magnitude. Figure 2 depicts this calculation | |

3. The maximum of the four values is assigned to a variable e. If e > th, the block is considered to be an edge block. Else, the block is a non-edge block | |

4. Construct a matrix E with the value e for edge blocks and a value of 0 for non-edge blocks | |

5. The message is embedded only in the edge blocks as shown in Fig. 3 |

Only the five of the nine pixels of the identified edge block are used for hiding the secret message. The remaining four pixels are not disturbed since they are used in estimating the edge strength. This ensures that the edge strength of the blocks in the cover image and stego image remains unchanged.

### Message embedding

No. of edge pixels \(\ge \frac{{4 * {\text{message length}}}}{3}\)

_{1}, MP

_{2}and MP

_{3}are embedded in the last bit of the first edge pixel group P

_{1}, P

_{2}, P

_{3}and P

_{4}in the following manner:

Algorithm: Message embedding |
---|

1. The three key values to be compared with the message bits are computed as follows: KP |

2. The obtained values of KP |

3. The threshold value is also embedded in the cover image since it will be required during retrieval process. Conventionally, the threshold value is embedded in the last pixel of the cover image |

### Message extraction

For all sets of four stego edge bits QP_{1}, QP_{2}, QP_{3} and QP_{4}, the message bits MP_{1}, MP_{2} and MP_{3} are retrieved thus:

MP_{1} = QP_{1} XOR QP_{2}

MP_{2} = QP_{3} XOR QP_{4}

MP_{3} = QP_{1} XOR QP_{3}

These equations guarantee the correct result for any combination of message bits and edge bits. Thus the message is accurately reinstated.

### Key generation

This 9 × 9 block is replicated along the rows and columns to obtain the final key matrix whose dimensions are the same as that of the edge image, E. Suppose the edge image has a size of 81 × 81. The 9 × 9 block has to be replicated nine times along the row and nine times along the column to produce the final key matrix.

This kind of key generation has been adopted to enhance the security of the algorithm. Firstly, the entire key need not be passed to the embedding or the extracting algorithm. It would be adequate to pass the first element of the key matrix to the two algorithms for efficient operation. The matrix can then be generated as described above. Besides, the inclusion of the key matrix in this algorithm helps in randomizing the selection of the edge blocks for embedding the message bits. In this paper, when a key matrix value of 1 or 9 is encountered, the edge block is utilized for hiding the message bits. In the absence of the key matrix, the edge blocks are selected sequentially to embed information. This might increase the probability of attacks.

### Improving the embedding capacity

To improve the embedding capacity of the cover image, all the three planes namely, the red plane, the blue plane and the green plane of the RGB image are utilised to conceal the payload. The edge image and the key matrix are obtained for each plane using the algorithms in the proposed algorithm. The threshold value may vary for each plane. Hence, the threshold value is embedded in the last pixel of each plane. The message bits are embedded in the three planes in the order of red, green and blue.

In the retrieval process, the edge images and the key matrix for the stego image are generated for each plane. The XOR operations are then applied to extract three message bits at a time and finally the entire message is restored.

### An example

Here, the output of edge detection algorithm is greater than the threshold value. Hence the block is an edge block and suitable for embedding. At this stage, it is ensured that the corresponding key matrix value for the edge block is either 1 or 9.

Consider the same block as given in Fig. 7. According to the embedding algorithm, three message bits can be embedded in four edge pixels.

_{1}is complemented. P

_{1}= 0.

Embedding conditions

Condition | Action to be taken | ||
---|---|---|---|

MP | MP | MP | No change |

MP | MP | MP | Complement P |

MP | MP | MP | Complement P |

MP | MP | MP | Complement P |

MP | MP | MP | Complement P |

MP | MP | MP | Complement P |

MP | MP | MP | Complement P |

MP | MP | MP | Complement P |

Thus the first pixel value of the group becomes 160 and the other pixel values remain the same.

They are the exact message bits that were initially embedded. Thus the message is reinstated successfully.

## Experimental results and discussions

Conventionally Zhou (2004), three standard tests are carried out to analyze the efficiency of any steganography algorithm. The first test is used to evaluate the embedding efficiency (change rate) of the stego image; the second one is used to assess the embedding payload of the cover image and lastly the security level of the proposed technique is determined. The proposed method has been implemented in MATLAB R2013a. An RGB image of size 246 × 246 × 3 has been used for implementing the algorithm. This paper exploits the red plane for all the operations on the image. Hence all the measures have been described in terms of two-dimensional images. The method can be extended to the other planes to increase the embedding capacity. This section presents the results and analysis of the proposed method.

### Embedding capacity evaluation

Embedding capacity

Image | Embedding capacity |
---|---|

Image1 | 0.0146 |

Image2 | 0.0286 |

Image3 | 0.1585 |

Image4 | 0.0279 |

Image5 | 0.0931 |

### Embedding distortion evaluation

Image quality measures

Measures | Formula |
---|---|

PSNR | 10log |

MSE | \(\frac{{\mathop \sum \nolimits_{{{\text{i}} = 1}}^{\text{m}} \mathop \sum \nolimits_{{{\text{j}} = 1}}^{\text{n}} ({\text{A}}\left( {{\text{i}},{\text{j}}} \right) - {\text{B}}({\text{i}},{\text{j}}))^{2} }}{m*n}\) |

SSIM | \(\frac{{(2 * {{\upmu }}_{\text{A}} * {{\upmu }}_{\text{B}} + {\text{c}}_{1} ) (2 * {{\upsigma }}_{\text{AB}} + {\text{c}}_{2} ) }}{{ ({{\upmu }}_{\text{A}}^{2} + {{\upmu }}_{\text{B}}^{2} + {\text{c}}_{1} )({{\upsigma }}_{\text{A}}^{2} + {{\upsigma }}_{\text{B}}^{2} + {\text{c}}_{2} )}}\) |

UIQI | \(\frac{{4 * {{\upsigma }}_{\text{AB}} * {{\upmu }}_{\text{A}} * {{\upmu }}_{\text{B}} }}{{({{\upsigma }}_{\text{A}}^{2} + {{\upsigma }}_{\text{B}}^{2} )({{\upmu }}_{\text{A}}^{2} + {{\upmu }}_{\text{B}}^{2} ) }}\) |

R | \(\frac{{\mathop \sum \nolimits_{{{\text{i}} = 1}}^{\text{N}} \left( {\frac{{{\text{A}}_{\text{i}} - {{\upmu }}_{\text{A}} }}{{{{\upsigma }}_{\text{A}} }}} \right)\left( { \frac{{{\text{B}}_{\text{i}} - {{\upmu }}_{\text{B}} }}{{{{\upsigma }}_{\text{B}} }}} \right)}}{{{\text{N}} - 1}}\) |

The peak signal to noise ratio is evaluated using the equation mentioned in Table 2. MSE is the mean square error between the cover image A and the stego image B, each of size m × n.

A higher value of PSNR and a lower value of MSE signify a better quality.

The structural similarity index metric (SSIM) evaluates the visual impact of three characteristics of an image- luminance, contrast and structure. Structural information reveals that pixels that are spatially close have stronger interdependencies.

\(\mu_{\text{A}} , \, \mu_{\text{B}} ,\;\sigma_{A} ,\;\sigma_{B}\) in the equation are the local means, standard deviations of images A, B, and σ_{AB} is the cross variance of A and B.

c_{1} = (L_{1}X)^{2} and c_{2} = (L_{2}X)^{2} are two constants used to avoid null denominator.

X is the dynamic range and is typically equal to (2^{no. of bits per pixel} − 1), where L_{1} = 0.01 and L_{2} = 0.03.

The range of SSIM is between –1 and 1. Identical images yield a maximum value of 1.

Universal image quality index (UIQI) is also used as an image quality measure (Wang 2002). It is a product of three factors: loss of correlation, contrast distortion and luminance distortion.

μ_{A}, μ_{B}, σ
_{A}
^{2}
, σ
_{B}
^{2}
in the equation are the mean values and variance of images A and B respectively.

The dynamic range of UIQI is between −1 and 1. A value of 1 is obtained for identical images.

The correlation coefficient (R) is also an essential measure to predict the quality of the stego image. μ_{A} and σ_{A} in the equation are the mean and standard deviation of A, respectively, and μ_{B} and σ_{B} are the mean and standard deviation of B, respectively.

The image quality measures of five images for the same embedding capacity

Cover image 246 × 246 × 3 | PSNR in dB | MSE | UIQI | R |
---|---|---|---|---|

Image1 | 80.9320 | 5.2879e−04 | 1.0 | 1.0 |

Image2 | 71.3896 | 0.0048 | 1.0 | 0.9995 |

Image3 | 80.6687 | 5.6183e−04 | 1.0 | 1.0 |

Image4 | 80.5428 | 5.7836e−04 | 1.0 | 1.0 |

Image5 | 71.2268 | 0.0049 | 1.0 | 1.0 |

Comparison of the proposed method with the Al-Dmour’s method using PSNR and MSE values

Image | Proposed method | Hayat Al-Dmour & Ahmed Al-Ani’s method | ||
---|---|---|---|---|

PSNR | MSE | PSNR | MSE | |

Image1 | 80.9320 | 5.2879e−04 | 80.6687 | 5.6183e−04 |

Image2 | 71.3896 | 0.0045 | 71.3595 | 0.0048 |

Image3 | 80.6687 | 2.3134e−04 | 80.1857 | 6.2793e−04 |

Image4 | 80.5428 | 1.9829e−04 | 80.4205 | 5.9488e−04 |

Image5 | 71.2268 | 0.0046 | 71.1834 | 0.0050 |

Image quality measures of the edge images

Cover image 246 × 246 | PSNR in dB | MSE | UIQI | R |
---|---|---|---|---|

Image1 | ∞ | 0 | 1.0 | 1.0 |

Image2 | 95.9835 | 1.6525e−05 | 0.9985 | 0.9985 |

Image3 | ∞ | 0 | 1.0 | 1.0 |

Image4 | ∞ | 0 | 1.0 | 1.0 |

Image5 | 95.9835 | 1.6525e−05 | 0.9995 | 0.9995 |

We observe an increase of 0.327, 0.042, 0.602, 0.152 and 0.06 % in the PSNR values of Image1, image2, image3, image4, image5, respectively, using the proposed method. A higher PSNR value indicates minimized distortions in the cover image. This analysis suggests that the proposed method is superior to the former method (Al-Dmour 2016).

The above table indicates that there are no differences between the cover edge images and the stego edge images for Image1, Image3, Image4 and very slight differences in Image2 and Image5. This eventually proves that the edge detection algorithm adopted is the most effective algorithm implemented till date.

## Conclusion

This paper presents a robust steganography method which conceals patients’ information in the edge blocks of any medical image like X-ray or EEG or ECG. It exploits the fact that human eyes are less liable to changes in sharp regions of the image and hence uses the high contrast edge pixels to embed data, thereby minimizing the distortions in the stego image. The embedding capacity is improved by extending the algorithm to all the three planes of the image.

The stego images thus obtained were analyzed using measures like PSNR, MSE, R and SSIM. The algorithm achieved a maximum PSNR value of 87.5325, which is higher compared to the other established methodologies. Thus the proposed technique exhibits higher level of security and imperceptibility. The algorithm is implemented in the spatial domain to avoid the shortcomings of transform domain. Although the efficiency is higher for transform domain implementation, it suffers from a severe setback due to lower embedding capacity and higher computational cost. Hence, a spatial domain approach has been chosen.

Moreover, the generation of the unique key matrix randomizes the selection of the edge blocks required to embed the patient’s information. Moreover, the key matrix changes for every session. This enhances the security of the entire steganography method. The above arguments prove that the proposed technique is robust, secure and offers a fairly high embedding capacity.

## Declarations

### Authors’ contributions

Identifying pixel positions to embed secret data without using a key, which improves the security level of the algorithm. Using the concept of Sudoku puzzle design to generate a unique key for every session. Implementing the algorithm in MATLAB to achieve the required results. Both authors read and approved the final manucsript.

### Acknowledgements

The authors would like to thank the Deapartment of Science and Technology, India for their financial support through Fund for Improvement of S&T Infrastructure (FIST) programme SR/FST/ETI-349/2013.

### Competing interests

The authors declare that there are no competing interests.

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

## Authors’ Affiliations

## References

- Al-Dmour H, Al-Ali A (2016) Steganography embedding method based on edge identification and XOR coding. Expert Syst Appl 46:293–306View ArticleGoogle Scholar
- Amin, Muhalim Mohamed, et al, Information hiding using steganography, Telecommunication technology, NCTT 2003 Proceedings. 4th National conference on IEEE, 2003Google Scholar
- Bassil Y (2012) Image steganography based on a parameterized canny edge detection algorithm. Int J Comput Appl 60(4):35–40Google Scholar
- Canny J (1986) A computational approach to edge detection. IEEE Trans Pattern Anal Mach Intell 8(6):679–698View ArticlePubMedGoogle Scholar
- Chan CK, Chen LM (2004) Hiding data in images by simple LSB substitution. Pattern Recognit. 37(3):469–474MathSciNetView ArticleMATHGoogle Scholar
- Cheddad A, Condell J, Curran K, Mc Kevitt P (2010) Digital image steganography: survey and analysis of current methods. Signal Processing 90(3):727–752View ArticleMATHGoogle Scholar
- Chen WJ, Chang CC, Le TH (2010) High payload steganography mechanism using hybrid edge detector. Expert Syst Appl 37(4):3292–3301View ArticleGoogle Scholar
- Crandall R (1998) Some notes on steganography, Posted on steganography mailing listGoogle Scholar
- Hou C-L, Lu C, Tsai S-C, Tzeng W-G (2011) An optimal data hiding scheme with tree-based parity check. IEEE Trans Image Process 20(3):880–886ADSMathSciNetView ArticlePubMedGoogle Scholar
- Kar DC, Mulkey CJ (2015) A multi threshold based audio steganography scheme., Journal of information security and applications 23:54–67View ArticleGoogle Scholar
- Li L, Luo B, Li Q, Fang X (2009) A color Images steganography method by multiple embedding strategy based on Sobel operator. In: 2009 International Conference on Multimedia Information Networking and Security (Vol. 2, pp 118-121). IEEEGoogle Scholar
- Liu Z, Xi L (2007) Image information hiding encryption using chaotic sequence, In: Proc. of the 11th International Conference on Knowledge-Based Intelligent Information and Engineering Systems and the XVII Itallian Workshop on Neural Networks, pp 202–208Google Scholar
- Lou DC, Liu JL (2002) Steganography Method for Secure Communications. Elsevier Science on Computers & Security 21(5):449–460View ArticleGoogle Scholar
- Modi, Islam, Gupta, M.R. Modi, S. Islam, P. Gupta (2013) Edge based steganography on colored images, Intelligent computing theories pp 593–600Google Scholar
- Morkel T, Eloff JHP, Oliver MS (2005) An Overview of Image Steganography, In: Proc. of the Fifth Annual Information Security South Africa Conference (ISSA2005), Sandton, South AfricaGoogle Scholar
- Ramalingam M, Isa NA (2015) A data hiding technique using scene-change detection for video steganography. Computers and Electrical EngineeringGoogle Scholar
- Wang Z (2002) A universal image quality index. IEEE Signal Process Lett 9(3):81–84ADSView ArticleGoogle Scholar
- Wang Z, Bovik AC, Sheikh HR, Simoncelli EP (2004) Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process 13(4):600–612ADSView ArticlePubMedGoogle Scholar
- Westfeld A (2001) F5–a steganographic algorithm: high capacity despite better steganalysis, Proceedings of fourth international workshop on information hiding, lecture notes in computer science 2137, Springer-Verlag, pp 289–302Google Scholar
- Wu DC, Tsai WH (2003) A steganographic method for images by pixel value differncing. Pattern Recogn Lett 24:1613–1626View ArticleMATHGoogle Scholar
- Zhang Xinpeng, Wang Shuozhong (2003) Vulnerability of pixel value differncing steganography to histogram analysis and modification for enhanced security. Pattern Recogn Lett 25:331–339View ArticleGoogle Scholar