# Pixel-Value-Ordering based Reversible Information Hiding Scheme with Self-Adaptive Threshold Strategy

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Works

_{1}and T

_{2}. In this way, the displacement extent of high complexity blocks can be reduced, and hence image quality is enhanced [20]. First, the image is cut into many blocks 4 × 4 in size. Further, the pixels in each block are divided into four sets of sub-blocks 4 × 4 in size and sorted in ascending order. Next, in each block, complexity computation is using the second smallest pixel value ${x}_{\Delta \left(2\right)}$ and the second largest pixel value ${x}_{\Delta \left(3\right)}$. The equation for complexity computation is as follows:

_{1}and T

_{2}are used to judge the block complexity, and the threshold values are between –1 $\le $ T

_{2}$\le $ T

_{1}$\le $ 255. Blocks of different complexity are processed as either one of the following three Cases to process:

- Case 1: When NL > T
_{1}, it indicates that the block is a high complexity area. There will not be any message embedding and displacement. - Case 2: When T
_{2}< NL $\le $ T_{1}, it indicates that the block is a common complex area. Since the block is not smooth, the errors generated in the four blocks will mostly fall in the Outer Region; their displacements cannot increase the hiding capacity and may even lead to image distortion; Hence the 4 × 4 block is sorted directly and Peng’s method is used to generate error values, and confidential information embedding and pixels displacement are performed. - Case 3: When NL $\le $ T
_{2}, it indicates that the block is a smooth block, and embedding and displacement may be performed on each of the four sub-blocks individually; hence they are sorted in 2 × 2 blocks. Peng’s method is used for embedding.

_{2}= 15 and T

_{1}= 60. When the four sub-block pixel combination in the first 4 × 4 block is ${X}^{1}$ = {5, 4, 7, 17}, ${X}^{2}$ = {15, 19, 17, 54}, ${X}^{3}$ = {13, 19, 89, 56}, and ${X}^{4}$ = {19, 17, 56, 56}, and each sub-blocks are sorted individually; through Equation (8), the computed block complexity is NL = max(7, 19, 56, 56) − min(5, 17, 19, 19) = 51. When T

_{2}< NL $\le $ T

_{1}, it conforms to the general complexity block in Case 2, hence the entire block is reordered. Using Equations (4) and (5) the computed maximum error value $P{E}_{max}$ = 89 − 56 = 33 and the minimum error value $P{E}_{min}$ = 5 − 4 = 1. Finally, Equations (6) and (7) are used to generate the camouflaged pixel values ${{x}^{\prime}}_{\Delta \left(n\right)}$ = 89 + 1 = 90 and ${{x}^{\prime}}_{\Delta \left(1\right)}$ = 4 − 1 = 3. When the four sub-block pixel combination in the second block are ${X}^{1}$ = {19, 17, 20, 21}, ${X}^{2}$ = {15, 14, 14, 18}, ${X}^{3}$ = {22, 22, 20, 24}, and ${X}^{4}$ = {16, 14, 10, 12}, sort each sub-block individually and use Equation (8) to compute the block complexity NL = max(20, 15, 22, 14) − min(19, 14, 22, 12) = 10. When NL $\le $ T

_{2}, it conforms to the smooth block in Case 3. Therefore, embedding and displacement will be conducted in each sub-block individually. Take $X{}_{sorted}^{2}$ = {14, 14, 15, 18} as an instance. Through Equations (4) and (5), the computed error values are $P{E}_{max}^{2}$ = −3 and $P{E}_{min}^{2}$ = 0. Finally, using Equations (6) and (7), the confidential information s = 0 is embedded and displaced to give ${{x}^{\prime}}_{\Delta \left(n\right)}$ = 18 + 1 = 19 and ${{x}^{\prime}}_{\Delta \left(1\right)}$ = 14 − 0 = 14. The camouflaged pixel values of the four sub-blocks can be obtained in the same way.

_{1}, it means that the block complexity is high, the computed difference values $P{E}_{max}$ and $P{E}_{min}$, will not fall in the Inner Region where embedding may be performed and instead fall in the Outer Region, resulting in pixel value modification and hence serious image distortion. When T

_{2}< NL $\le $ T

_{1}, it means that the block is of general complexity and it is possible to embed confidential information. In order to reduce the amount of pixel modifications, all the pixels in the 4 × 4 block are directly sorted in sequence and the difference $P{E}_{max}$ and $P{E}_{min}$ are obtained, reducing the variation amount to 2. On the other hand, when the NL $\le $ T

_{2}, it means that the block is very smooth and many error values will fall in the Inner Region. It is suitable for volume information embedding. The 4 × 4 block is thus converted to 2 × 2 sub-blocks for individual embedding and displacement so as to enhance the hiding capability.

## 3. Proposed Scheme

#### 3.1. Improvement of Peng et al.’s Hiding Scheme

#### 3.2. Adaptive Threshold Generation Strategy

#### 3.3. Proposed Data Embedding Procedures

- Divide the host image into several non-overlaping blocks sized $2\times 2$. Let $X=\left\{{x}_{1},{x}_{2},{x}_{3},{x}_{4}\right\}$ be the block and total number of blocks is $N$.
- Sort each block in ascending order to get ${X}_{sorted}=\left\{{x}_{\Delta \left(1\right)},{x}_{\Delta \left(2\right)},{x}_{\Delta \left(3\right)},{x}_{\Delta \left(4\right)}\right\}$.
- Generate a location map $LM=\left\{L{M}_{1},L{M}_{2},\cdots ,L{M}_{N}\right\}$ to record whether the block has an overflow (or underflow) problem or not. For each block, if ${x}_{\Delta \left(1\right)}$ = 0 or ${x}_{\Delta \left(4\right)}$ = 255, then $L{M}_{i}$ = 1 which means the block may have the problem. On the contrary, if $L{M}_{i}$ = 0, the location map is then compressed by the data algorithm (such as arithmetic coding or JBIG2 and so on). The compressed results are then concatenated with the secret message to embed it into the host image.
- Compute the variance of each block by using Formulas (9)–(11).
- Calculate the predefined threshold $T$ using the adaptive threshold generation strategy which was introduced in Section 3.2.
- Detect whether the block is embeddable or not.
- If $L{M}_{i}$ = 1, then the block is non-embeddable.
- If the variance ${\sigma}^{2}>T$ and $L{M}_{i}$ = 0, then the block is non-embeddable.
- If the variance ${\sigma}^{2}\le T$ and $L{M}_{i}$ = 0, then the block is embeddable.

- Conceal the secret message into the embeddable block.
- Compute ${d}_{max}={x}_{u}-{x}_{v}$, where:$$\{\begin{array}{c}u=min\left(\Delta \left(n\right),\Delta \left(n-1\right)\right),\\ v=max\left(\Delta \left(n\right),\Delta \left(n-1\right)\right).\end{array}$$
- Calculate the stego pixel by:$${x}_{\Delta \left(n\right)}^{\prime}=\{\begin{array}{c}\begin{array}{cc}{x}_{\Delta \left(n\right)}+s,& \mathrm{if}{d}_{max}=1,\end{array}\\ \begin{array}{cc}{x}_{\Delta \left(n\right)}+1,& \mathrm{if}{d}_{max}1,\end{array}\\ \begin{array}{cc}{x}_{\Delta \left(n\right)}+s,& \mathrm{if}{d}_{max}=0,\end{array}\\ \begin{array}{cc}{x}_{\Delta \left(n\right)}+1,& \mathrm{if}{d}_{max}0.\end{array}\end{array}$$
- Compute ${d}_{min}={x}_{s}-{x}_{t}$, where:$$\{\begin{array}{c}s=min\left(\Delta \left(1\right),\Delta \left(2\right)\right),\\ t=max\left(\Delta \left(1\right),\Delta \left(2\right)\right).\end{array}$$
- Calculate the stego pixel by:$${x}_{\Delta \left(1\right)}^{\prime}=\{\begin{array}{c}\begin{array}{cc}{x}_{\Delta \left(1\right)}-s,& \mathrm{if}{d}_{min}=1,\end{array}\\ \begin{array}{cc}{x}_{\Delta \left(1\right)}-1,& \mathrm{if}{d}_{min}1,\end{array}\\ \begin{array}{cc}{x}_{\Delta \left(1\right)}-s,& \mathrm{if}{d}_{min}=0,\end{array}\\ \begin{array}{cc}{x}_{\Delta \left(1\right)}-1,& \mathrm{if}{d}_{min}0.\end{array}\end{array}$$

- Continue the steps until all secret messages are embedded.

#### 3.4. Extraction and Recovering Procedures

- Divide the stego image into several non-overlap blocks sized $2\times 2$. Let ${X}^{\prime}=\left\{{{x}^{\prime}}_{1},{{x}^{\prime}}_{2},{{x}^{\prime}}_{3},{{x}^{\prime}}_{4}\right\}$ be the block and total number of blocks is $N$.
- Sort each block in ascending order to get ${{X}^{\prime}}_{sorted}=\left\{{{x}^{\prime}}_{\Delta \left(1\right)},{{x}^{\prime}}_{\Delta \left(2\right)},{{x}^{\prime}}_{\Delta \left(3\right)},{{x}^{\prime}}_{\Delta \left(4\right)}\right\}$.
- Extract the location map $LM=\left\{L{M}_{1},L{M}_{2},\cdots ,L{M}_{N}\right\}$ from the stego image by using Wang et al.’s scheme. For each block, if $L{M}_{i}$ = 1 which means the block is non-embeddable.
- Compute the variance of each block by using Formulas (9)–(11).
- Detect whether the block is embeddable or not.
- If $L{M}_{i}$ = 1, then the block is non-embeddable.
- If the variance ${\sigma}^{2}>T$ and $L{M}_{i}$ = 0, then the block is non-embeddable.
- If the variance ${\sigma}^{2}\le T$ and $L{M}_{i}$ = 0, then the block is embeddable.

For the non-embeddable block, the proposed scheme will skip the block. The original block is the same as the stego block. - Extract the secret message from the embeddable block.
- Compute ${{d}^{\prime}}_{max}={{x}^{\prime}}_{u}-{{x}^{\prime}}_{v}$, where$$\{\begin{array}{c}u=min\left(\Delta \left(n\right),\Delta \left(n-1\right)\right),\\ v=max\left(\Delta \left(n\right),\Delta \left(n-1\right)\right).\end{array}$$
- Obtain the secret message$$s=\{\begin{array}{ll}{{d}^{\prime}}_{max}-1,\hfill & \mathrm{if}{{d}^{\prime}}_{max}=1\mathrm{or}2,\hfill \\ none,\hfill & \mathrm{if}{{d}^{\prime}}_{max}2,\hfill \\ -{{d}^{\prime}}_{max},\hfill & \mathrm{if}{{d}^{\prime}}_{max}=0\mathrm{or}-1,\hfill \\ none,\hfill & \mathrm{if}{{d}^{\prime}}_{max}-1.\hfill \end{array}$$
- Calculate the original pixel by$${x}_{\Delta \left(1\right)}=\{\begin{array}{ll}{{x}^{\prime}}_{\Delta \left(1\right)}-s,\hfill & \mathrm{if}{{d}^{\prime}}_{max}=1\mathrm{or}2,\hfill \\ {{x}^{\prime}}_{\Delta \left(1\right)}-1,\hfill & \mathrm{if}{{d}^{\prime}}_{max}2,\hfill \\ {{x}^{\prime}}_{\Delta \left(1\right)}-s,\hfill & \mathrm{if}{{d}^{\prime}}_{max}=0\mathrm{or}-1,\hfill \\ {{x}^{\prime}}_{\Delta \left(1\right)}-1,\hfill & \mathrm{if}{{d}^{\prime}}_{max}\le -1.\hfill \end{array}$$
- Compute ${{d}^{\prime}}_{min}={{x}^{\prime}}_{s}-{{x}^{\prime}}_{t}$, where$$\{\begin{array}{c}s=min\left(\Delta \left(1\right),\Delta \left(2\right)\right),\\ t=max\left(\Delta \left(1\right),\Delta \left(2\right)\right).\end{array}$$
- Obtain the secret message$$s=\{\begin{array}{ll}{{d}^{\prime}}_{min}-1,\hfill & \mathrm{if}{{d}^{\prime}}_{min}=1\mathrm{or}2,\hfill \\ none,\hfill & \mathrm{if}{{d}^{\prime}}_{min}2,\hfill \\ -{{d}^{\prime}}_{min},\hfill & \mathrm{if}{{d}^{\prime}}_{min}=0\mathrm{or}-1,\hfill \\ none,\hfill & \mathrm{if}{{d}^{\prime}}_{min}-1.\hfill \end{array}$$
- Calculate the original pixel by$${x}_{\Delta \left(1\right)}=\{\begin{array}{ll}{{x}^{\prime}}_{\Delta \left(1\right)}+s,\hfill & \mathrm{if}{{d}^{\prime}}_{min}=1\mathrm{or}2,\hfill \\ {{x}^{\prime}}_{\Delta \left(1\right)}+1,\hfill & \mathrm{if}{{d}^{\prime}}_{min}2,\hfill \\ {{x}^{\prime}}_{\Delta \left(1\right)}+s,\hfill & \mathrm{if}{{d}^{\prime}}_{min}=0\mathrm{or}-1,\hfill \\ {{x}^{\prime}}_{\Delta \left(1\right)}+1,\hfill & \mathrm{if}{{d}^{\prime}}_{min}\le -1.\hfill \end{array}$$

- Continue the steps until all the secret messages are extracted and the pixels are recovered.

## 4. Experimental Results

#### 4.1. Adaptive Threshold Detection

#### 4.2. Quantified Number $Q$ Evaluation

#### 4.3. Comparison Results

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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$\mathit{r}\mathit{o}\mathit{u}\mathit{n}\mathit{d}({\mathit{\sigma}}^{\mathbf{2}})$ | 0 | 3 | 4 | 8 | 11 | 12 | 16 | 19 | 20 | … |

$\mathit{H}({\mathit{\sigma}}^{\mathbf{2}})$ | 5195 | 14,148 | 8770 | 6001 | 7238 | 1780 | 1269 | 1986 | 2109 | … |

$\mathit{P}({\mathit{\sigma}}^{\mathbf{2}})$ | 7.93% | 21.59% | 13.38% | 9.16% | 11.04% | 2.72% | 1.94% | 3.03% | 3.22% | … |

$\mathit{C}\mathit{P}$ | 7.93% | 29.52% | 42.90% | 52.05% | 63.10% | 65.81% | 67.75% | 70.78% | 74.00% | … |

Image | 70% | 80% | ||
---|---|---|---|---|

T | CP(%) | T | CP(%) | |

Airplane | 13 | 71.73 | 36 | 80.14 |

Lake | 57 | 70.98 | 105 | 80.52 |

Lena | 20 | 71.33 | 36 | 80.46 |

Mandrill | 265 | 70.39 | 453 | 80.91 |

Pepper | 21 | 70.11 | 36 | 80.72 |

Tiffany | 13 | 72.41 | 28 | 80.33 |

Image | Method | Hiding Rate | T | PSNR | bpp | Capacity | Increased |
---|---|---|---|---|---|---|---|

Airplane | Peng | 100% | ∞ | 52.11 | 0.20 | 52,546 | 1.79 |

Peng_VAR | 70% | 13 | 53.90 | 0.18 | 48,132 | - | |

Peng_VAR | 80% | 36 | 53.19 | 0.19 | 50,223 | 0.71 | |

Wang | 100% | (241,117) | 52.21 | 0.20 | 52,007 | 1.69 | |

Lake | Peng | 100% | ∞ | 51.60 | 0.10 | 26,365 | 1.64 |

Peng_VAR | 70% | 57 | 53.24 | 0.09 | 24,076 | - | |

Peng_VAR | 80% | 105 | 52.65 | 0.10 | 25,038 | 0.59 | |

Wang | 100% | (220,51) | 52.28 | 0.10 | 25,265 | 0.96 | |

Lena | Peng | 100% | ∞ | 51.84 | 0.15 | 38,938 | 1.47 |

Peng_VAR | 70% | 20 | 53.31 | 0.13 | 35,033 | - | |

Peng_VAR | 80% | 36 | 52.83 | 0.14 | 36,903 | 0.48 | |

Wang | 100% | (155,49) | 52.20 | 0.15 | 38,279 | 1.11 | |

Mandrill | Peng | 100% | ∞ | 51.37 | 0.05 | 13,656 | 1.6 |

Peng_VAR | 70% | 265 | 52.97 | 0.05 | 12,129 | - | |

Peng_VAR | 80% | 453 | 52.37 | 0.05 | 12,665 | 0.6 | |

Wang | 100% | (212,80) | 51.97 | 0.05 | 13,020 | 1 | |

Pepper | Peng | 100% | ∞ | 51.73 | 0.13 | 33,173 | 1.57 |

Peng_VAR | 70% | 21 | 53.30 | 0.11 | 28,754 | - | |

Peng_VAR | 80% | 36 | 52.66 | 0.12 | 31,022 | 0.64 | |

Wang | 100% | (149,19) | 52.68 | 0.11 | 30,008 | 0.62 | |

Tiffany | Peng | 100% | ∞ | 51.94 | 0.17 | 44,047 | 1.7 |

Peng_VAR | 70% | 13 | 53.64 | 0.15 | 38,923 | - | |

Peng_VAR | 80% | 28 | 52.97 | 0.16 | 41,348 | 0.67 | |

Wang | 100% | (220,51) | 52.18 | 0.16 | 42,289 | 1.46 |

Image | Method | PSNR | bpp | Capacity | overflow |
---|---|---|---|---|---|

1063 | Peng_VAR (80%) | 52.24 | 0.02 | 4519 | 0 |

Peng_VAR (70%) | 52.82 | 0.02 | 4242 | 0 | |

Peng | 51.25 | 0.03 | 4943 | 0 | |

Wang | 56.32 | 0.02 | 4039 | 453 | |

1030 | Peng_VAR (80%) | 52.27 | 0.03 | 5687 | 0 |

Peng_VAR (70%) | 52.86 | 0.03 | 5393 | 0 | |

Peng | 51.28 | 0.03 | 6164 | 0 | |

Wang | 56.33 | 0.02 | 4340 | 281 | |

1050 | Peng_VAR (80%) | 52.29 | 0.03 | 6436 | 0 |

Peng_VAR (70%) | 52.89 | 0.03 | 6231 | 0 | |

Peng | 51.29 | 0.03 | 6748 | 0 | |

Wang | 55.09 | 0.03 | 6054 | 1969 | |

84 | Peng_VAR(80%) | 52.33 | 0.04 | 8306 | 0 |

Peng_VAR(70%) | 52.94 | 0.04 | 7925 | 0 | |

Peng | 51.34 | 0.05 | 8900 | 0 | |

Wang | 53.32 | 0.03 | 6813 | 283 |

File Name | Method | Percentage | PSNR | bpp | Capacity | Overflow | Increased |
---|---|---|---|---|---|---|---|

1.jpg | Peng_VAR | 80 | 53.12 | 0.17 | 32,728 | 0 | 0.62 |

Peng_VAR | 70 | 53.74 | 0.16 | 31,854 | 0 | - | |

Peng | 70 | 51.95 | 0.17 | 33,628 | 0 | 1.79 | |

Wang | 52.79 | 0.15 | 29,172 | 897 | 0.95 | ||

2.jpg | Peng_VAR | 80 | 53.23 | 0.18 | 35,910 | 0 | 0.69 |

Peng_VAR | 70 | 53.92 | 0.18 | 35,041 | 0 | - | |

Peng | 70 | 52.04 | 0.19 | 36,956 | 0 | 1.88 | |

Wang | 52.86 | 0.18 | 36,062 | 68 | 1.06 | ||

3.jpg | Peng_VAR | 80 | 52.63 | 0.09 | 18,119 | 0 | 0.63 |

Peng_VAR | 70 | 53.26 | 0.09 | 17,491 | 0 | - | |

Peng | 70 | 51.58 | 0.10 | 18,807 | 0 | 1.68 | |

Wang | 53.18 | 0.09 | 16,845 | 61 | 0.08 |

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**MDPI and ACS Style**

Lu, T.-C.; Tseng, C.-Y.; Huang, S.-W.; Nhan Vo., T.
Pixel-Value-Ordering based Reversible Information Hiding Scheme with Self-Adaptive Threshold Strategy. *Symmetry* **2018**, *10*, 764.
https://doi.org/10.3390/sym10120764

**AMA Style**

Lu T-C, Tseng C-Y, Huang S-W, Nhan Vo. T.
Pixel-Value-Ordering based Reversible Information Hiding Scheme with Self-Adaptive Threshold Strategy. *Symmetry*. 2018; 10(12):764.
https://doi.org/10.3390/sym10120764

**Chicago/Turabian Style**

Lu, Tzu-Chuen, Chun-Ya Tseng, Shu-Wen Huang, and Thanh Nhan Vo.
2018. "Pixel-Value-Ordering based Reversible Information Hiding Scheme with Self-Adaptive Threshold Strategy" *Symmetry* 10, no. 12: 764.
https://doi.org/10.3390/sym10120764