# PVO-Based Reversible Data Hiding Exploiting Two-Layer Embedding for Enhancing Image Fidelity

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

#### 2.1. PVO-Based RDH Scheme

_{1}× n

_{2}. Each block (x

_{1}, x

_{2}, …, x

_{n}) was sorted in an ascending order to arrange the pixel values (${x}_{\sigma \left(1\right)}$, ${x}_{\sigma \left(2\right)}$, …, ${x}_{\sigma \left(n\right)}$), where ${x}_{\sigma \left(n\right)}\text{}$ was the maximum value and ${x}_{\sigma \left(n-1\right)}$ was the second largest value. Prediction error PE

_{max}was then calculated by subtracting the second largest value from the maximum value, as follows:

_{max}, PE

_{max}histogram was generated (a positive value). Since PE

_{max}= 1 is usually the histogram peak value, Li et al. used PE

_{max}= 1 as the area in which the data was embedded in order to ensure reversibility. The revised prediction error was calculated as follows:

_{min}was calculated by subtracting the second smallest value from the minimum value as follows:

_{min}, PE

_{min}histogram was generated (a negative value). Li et al. used PE

_{min}= −1 as the area where the secret data was embedded. If the value was less than −1, the pixel values needed to be shifted in order to ensure reversibility. The revised prediction error was calculated as follows:

_{max}= 58 − 57 = 1. Because PE

_{max}is 1, the modified maximum value becomes 58 + b = 59, i.e., one secret bit data can be embedded. The minimum prediction error is PE

_{min}= 46 − 52 = −6. Because PE

_{min}is less than 1, the minimum value is modified to 46 − 1 = 45, and then shifted to left by 1. This pixel 46 cannot be used to hide any secret data.

#### 2.2. IPVO Method

_{u}= 117

_{(1)}, x

_{v}= 117

_{(3)}, and the maximum prediction error is PE

_{max}= x

_{u}− x

_{v}= 117

_{(1)}− 117

_{(3)}= 0. Because PE

_{max}is 0, the modified maximum value is ${x}_{\sigma \left(n\right)}+b$ = 117 + 1 = 118, and one bit secret data (b = 1) can be embedded in this pixel.

## 3. Proposed Method

#### 3.1. Embedding Procedure

_{1}× n

_{2}blocks. The second layer is divided from the second row of the second column. The threshold value t is set to a value ranging from 0 to 255. Each block (x

_{1}, x

_{2}, …, x

_{n}) is sorted in the ascending order to get the pixel values sorted (${x}_{\sigma \left(1\right)}$, ${x}_{\sigma \left(2\right)}$, …, ${x}_{\sigma \left(n\right)}$). NL is calculated using NL = ${x}_{\sigma \left(n-1\right)}\text{}$− ${x}_{\sigma \left(2\right)}$. If it is larger than t, than this block is not used for embedding secret data.$\text{}{x}_{\sigma \left(n\right)}\text{}$ is the maximum value, ${x}_{\sigma \left(n-1\right)}$ is the second largest value, and the prediction error is calculated using PE

_{max}= ${x}_{\sigma \left(n\right)}$ − ${x}_{\sigma \left(n-1\right)}.\text{}$ After calculating PE

_{max}, PE

_{max}histogram is generated. Similar to Li et al.’s method, we use PE

_{max}= 1 as the area in which the secret data is embedded. If PE

_{max}is larger than the peak value, then the pixel values are shifted.

_{min}is calculated by subtracting ${x}_{\sigma \left(1\right)}$ (minimum value) from ${x}_{\sigma \left(2\right)}$ (second smallest value) using $P{E}_{min}$ = ${x}_{\sigma \left(1\right)}$ − ${x}_{\sigma \left(2\right)}$. After calculating PE

_{min}, histogram of PE

_{min}is generated. Similar to Li et al.’s method, we use PE

_{min}= −1 as the area of embedded data. If the value is less than −1 then the PVO method shifts the pixel values.

**Step 1**

**:**Get a cover image of size W × H.

**Step 2**

**:**Get secret data.

**Step 3**

**:**Divide the cover image into blocks of size ${n}_{1}$×${n}_{2}$. And set the best threshold t, t ranges from 0 to 255.

**Step 4**

**:**Sort each block (x

_{1}, x

_{2}, …, x

_{n}) in the ascending order and get the sorted pixel values (${x}_{\sigma \left(1\right)}$, ${x}_{\sigma \left(2\right)}$, …, ${x}_{\sigma \left(n\right)}$).

**Step 5**

**:**Calculate NL = ${x}_{\sigma \left(n-1\right)}$ − ${x}_{\sigma \left(2\right)}.\text{}$ If NL > t, then the block is not used for embedding secret data.

**Step 6**

**:**Embed secret data:

_{max}= ${x}_{\sigma \left(n\right)}$ − ${x}_{\sigma \left(n-1\right)}$, $P{E}_{min}$ = ${x}_{\sigma \left(1\right)}$ − ${x}_{\sigma \left(2\right)}.$

- If ${x}_{\sigma \left(n\right)}$ − ${x}_{\sigma \left(n-1\right)}$ = 1, do embedding. If ${x}_{\sigma \left(n\right)}$ − ${x}_{\sigma \left(n-1\right)}\text{}$> 1, do pixel shifting.$${\tilde{x}}_{\sigma \left(n\right)}\text{}={x}_{\sigma \left(n-1\right)}+{\tilde{PE}}_{max}=\{\begin{array}{c}{x}_{\sigma \left(n\right)},\text{}if\text{}P{E}_{max}=0,\text{}\\ {x}_{\sigma \left(n\right)}+b,\text{}if\text{}P{E}_{max}=1,\\ {x}_{\sigma \left(n\right)}+1,\text{}if\text{}P{E}_{max}1,\text{}\end{array}$$
- If ${x}_{\sigma \left(1\right)}$ − ${x}_{\sigma \left(2\right)}$ = −1, do embedding. If ${x}_{\sigma \left(1\right)}$ − ${x}_{\sigma \left(2\right)}$ > 1, do pixel shifting.$${\tilde{x}}_{\sigma \left(1\right)}\text{}={x}_{\sigma \left(n\right)}+{\tilde{PE}}_{min}=\{\begin{array}{c}{x}_{\sigma \left(1\right)},\text{}if\text{}P{E}_{min}=0,\text{}\\ {x}_{\sigma \left(1\right)}-b,\text{}if\text{}P{E}_{min}=-1,\\ {x}_{\sigma \left(1\right)}-1,\text{}if\text{}P{E}_{min}-1,\text{}\end{array}$$

**Step 7**

**:**After finishing the first-layer embedding, a marked image is obtained. Use this marked image to execute second-layer embedding starting from the blocks at the second row and second column.

**Step 8**

**:**Repeat Steps 3 to 7.

#### 3.2. Data Extraction and Image Recovery Procedure

**Step 1**

**:**Restore pixel values from the second layer, second row and second column. Divide the image into blocks of size ${n}_{1}$ × ${n}_{2}$.

**Step 2**

**:**Sort each block (x

_{1}, x

_{2}, …, x

_{n}) in the ascending order to get the sorted pixel values (${x}_{\sigma \left(1\right)}$, ${x}_{\sigma \left(2\right)}$, …, ${x}_{\sigma \left(n\right)}$).

**Step 3**

**:**Check whether secret data is embedded or not. Calculate NL = ${x}_{\sigma \left(n-1\right)}$ − ${x}_{\sigma \left(2\right)}$. If NL > t, then the block is not used for hiding secret data.

**Step 4**

**:**Extract secret data:

- ${x}_{\sigma \left(n\right)}$ − ${x}_{\sigma \left(n-1\right)}$:

- ${x}_{\sigma \left(1\right)}$ − ${x}_{\sigma \left(2\right)}$:

**Step 5**

**:**Restore the first layer and divide the image from the first row and first column to the block of size ${n}_{1}$ × ${n}_{2}$.$\text{}{n}_{1}$,${n}_{2}\in \left\{2,\text{}3,\text{}4,\text{}5\right\}.$

**Step 6**

**:**Repeat Steps 2 to 4.

## 4. Experimental Results

## 5. Discussion, Future Research, and Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**The partition modes used in the proposed method. (

**a**) is Model A used by the first layer, and (

**b**) is Model B used by the second layer.

**Table 1.**The embedding capacity (bits) of the proposed method in different dividing modes. (Refer to Figure 3 for the first and second layer embedding).

Two-Layer Embedding by Different Models. | Lena | F16 | Baboon | Boat | Peppers | Elaine |
---|---|---|---|---|---|---|

First layer uses Model A Second layer uses Model A | 48,100 | 58,563 | 19,842 | 36,332 | 42,229 | 32,154 |

First layer uses Model A Second layer uses Model B | 62,839 | 76,653 | 25,751 | 46,716 | 53,929 | 41,456 |

**Table 2.**Comparison of PVO method and the proposed method in terms of numbers of shift. used by Lena image for a fixed embedding capacity (EC).

Method | EC(bits) | Shift Unit | Total Shifts (Bits) | |||
---|---|---|---|---|---|---|

+1 | −1 | +2 | −2 | |||

Original PVO method | 32,000 | 46,305 | 46,921 | 0 | 0 | 93,226 |

Proposed method based on PVO method | 32,000 | 36,929 | 37,305 | 1616 | 1765 | 80,996 |

**Table 3.**Comparison of peak signal-to-noise ratio (PSNR) values using different block sizes for Baboon image.

Image | Payload (Bits) | PVO | IPVO | PVO-k | Proposed_ PVO | Proposed_ IPVO | Proposed_ PVO-k |
---|---|---|---|---|---|---|---|

2*2 | 13,000 | 51.65 | 51.53 | 51.49 | 52.19 | 51.96 | 52.56 |

3*3 | 7500 | 55.33 | 55.23 | 55.25 | 56.39 | 56.17 | 56.60 |

4*4 | 4800 | 57.94 | 57.88 | 57.90 | 58.47 | 58.31 | 58.82 |

5*5 | 3300 | 60.06 | 60.03 | 59.96 | 60.24 | 60.18 | 60.57 |

**Table 4.**Comparison of PVO series methods and the proposed method in terms of different threshold values and block size used by Baboon image.

Image | Payload (Bits) | Block Size | Threshold | PSNR (dB) |
---|---|---|---|---|

PVO | 13,000 | 2 × 2 | 70 | 51.688 |

Proposed_PVO | 13,000 | 2 × 2 | 4 | 52.178 |

IPVO | 13,000 | 2 × 2 | 45 | 51.598 |

Proposed_ IPVO | 13,000 | 3 × 2 | 16 | 51.931 |

PVO-k | 14,000 | 2 × 2 | 76 | 51.248 |

Proposed_PVO-k | 14,000 | 3 × 2 | 15 | 52.549 |

PPVO | 14,000 | 2 × 2 | 86 | 51.213 |

Proposed_ PPVO | 14,000 | 2 × 2 | 86 | 51.062 |

PVO | IPVO | PVO-k | PPVO | SSPVO | ||||||
---|---|---|---|---|---|---|---|---|---|---|

EC (Bits) | PSNR (dB) | EC (Bits) | PSNR (dB) | EC (Bits) | PSNR (dB) | EC (Bits) | PSNR (dB) | EC (Bits) | PSNR (dB) | |

Lena | 32,000 | 52.674 | 37,000 | 51.942 | 38,000 | 51.610 | 44,000 | 51.099 | 40,000 | 48.33 |

F16 | 38,000 | 53.617 | 50,000 | 52.129 | 49,000 | 51.897 | 67,000 | 51.208 | 50,000 | 48.94 |

Baboon | 13,000 | 51.651 | 13,000 | 51.598 | 14,000 | 51.248 | 14,000 | 51.213 | 16,000 | 47.53 |

Boat | 24,000 | 52.164 | 26,000 | 51.613 | 27,000 | 51.382 | 29,000 | 51.216 | 30,000 | 47.67 |

Peppers | 28,000 | 52.309 | 30,000 | 51.711 | 32,000 | 51.396 | 33,000 | 51.216 | 35,000 | 48.06 |

Elaine | 21,000 | 52.178 | 23,000 | 51.917 | 23,000 | 51.590 | 27,000 | 51.289 | 29,000 | 47.64 |

Average | 26,000 | 52.432 | 29,833 | 51.818 | 30,500 | 51.520 | 35,666 | 51.206 | 33,333 | 48.03 |

Proposed Based on PVO | Proposed Based on IPVO | Proposed Based on PVO-k | Proposed Based on PPVO | Proposed Based on SSPVO | ||||||
---|---|---|---|---|---|---|---|---|---|---|

EC (Bits) | PSNR (dB) | EC (Bits) | PSNR (dB) | EC (Bits) | PSNR (dB) | EC (Bits) | PSNR (dB) | EC (Bits) | PSNR (dB) | |

Lena | 32,000 | 53.017 | 37,000 | 52.102 | 38,000 | 52.746 | 44,000 | 51.136 | 40,000 | 49.45 |

F16 | 38,000 | 54.273 | 50,000 | 52.235 | 49,000 | 53.475 | 67,000 | 51.127 | 50,000 | 51.16 |

Baboon | 13,000 | 52.865 | 13,000 | 51.931 | 14,000 | 52.549 | 14,000 | 51.143 | 16,000 | 49.87 |

Boat | 24,000 | 52.531 | 26,000 | 51.644 | 27,000 | 51.908 | 29,000 | 51.216 | 30,000 | 48.97 |

Peppers | 28,000 | 52.474 | 30,000 | 51.748 | 32,000 | 51.646 | 33,000 | 51.306 | 35,000 | 49.17 |

Elaine | 21,000 | 52.178 | 23,000 | 51.939 | 23,000 | 51.819 | 27,000 | 51.306 | 29,000 | 48.57 |

Average | 26,000 | 52.889 | 29,833 | 51.933 | 30,500 | 52.357 | 35,666 | 51.205 | 33,333 | 49.53 |

**Table 7.**Comparison of elapsed time for PVO series methods using our proposed method with a fixed block size of 2 × 2.

Image | PVO | IPVO | PVO-k | PPVO | SSPVO | Proposed_ PVO | Proposed_ IPVO | Proposed_ PVO-k | Proposed_ PPVO | Proposed_ SSPVO | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Time | T | Time | T | Time | T | Time | T | Time | T | ||||||

Lena | 0.749508 | 0.356481 | 0.291244 | 1.163397 | 2.402814 | 1.851007 | 5 | 10.429027 | 9 | 0.672309 | 1 | 1.166460 | - | 4.239199 | 5 |

F16 | 0.336530 | 0.336282 | 0.329327 | 1.215053 | 2.375948 | 0.393720 | 1 | 4.703645 | 4 | 0.719459 | 1 | 1.417945 | - | 3.104335 | 3 |

Baboon | 0.342171 | 0.337842 | 0.333449 | 1.159332 | 2.463345 | 1.699404 | 4 | 4.307921 | 4 | 2.620159 | 4 | 1.187693 | - | 9.360498 | 14 |

Boat | 0.350143 | 0.394626 | 0.335444 | 1.155205 | 2.508979 | 1.322694 | 3 | 16.537310 | 15 | 1.459243 | 2 | 1.184053 | - | 6.254179 | 8 |

Peppers | 0.366290 | 0.340776 | 0.337090 | 1.160963 | 2.351799 | 1.274811 | 3 | 14.027471 | 12 | 8.211449 | 9 | 1.151029 | - | 4.619279 | 6 |

Elaine | 0.338726 | 0.330346 | 0.319696 | 1.386960 | 2.471801 | 3.649546 | 10 | 9.970896 | 9 | 1.458494 | 2 | 1.379967 | - | 9.743423 | 10 |

Average | 0.413895 | 0.349392 | 0.324375 | 1.206818 | 2.429114 | 1.69853 | 9.996045 | 2.523519 | 1.247858 | 6.220152 |

**Table 8.**Performance comparison in terms of PSNR (dB) on six test images from Kodak image database for an embedding capacity of 10,000 bits.

Image | PVO | IPVO | PVO-k | PPVO | SSPVO | Proposed_ PVO | Proposed_ IPVO | Proposed_ PVO-k | Proposed_ PPVO | Proposed_ SSPVO |
---|---|---|---|---|---|---|---|---|---|---|

kodim1 | 59.26 | 62.63 | 60.42 | 63.76 | 59.50 | 60.80 | 62.63 | 61.13 | 63.78 | 59.63 |

kodim2 | 62.84 | 63.38 | 62.60 | 62.48 | 60.72 | 62.85 | 63.42 | 62.60 | 62.47 | 61.60 |

kodim3 | 63.87 | 64.78 | 63.40 | 64.85 | 62.20 | 63.89 | 64.80 | 63.45 | 64.85 | 62.23 |

kodim4 | 62.12 | 63.15 | 62.21 | 63.89 | 60.82 | 62.20 | 63.21 | 62.25 | 63.86 | 60.87 |

kodim5 | 60.51 | 61.95 | 60.88 | 63.01 | 59.51 | 60.95 | 61.95 | 61.17 | 63.00 | 59.94 |

kodim6 | 63.13 | 64.96 | 63.28 | 65.64 | 61.75 | 63.13 | 64.97 | 63.22 | 65.64 | 62.21 |

Average | 61.955 | 63.475 | 62.131 | 63.938 | 60.75 | 62.303 | 63.496 | 62.303 | 63.933 | 61.08 |

**Table 9.**PSNR values of difference expansion (DE) and reduced difference expansion (RDE) methods, and our proposed method based on DE and RDE methods.

Image | Layer | DE | Proposed based on DE | RDE | Proposed based on RDE | ||||
---|---|---|---|---|---|---|---|---|---|

PSNR (dB) | EC (Bits) | PSNR (dB) | EC (Bits) | PSNR (dB) | EC (Bits) | PSNR (dB) | EC (Bits) | ||

Lena | Layer2 | 25.21 | 260,211 | 29.90 | 261,361 | 36.05 | 262,137 | 40.17 | 261,632 |

F16 | Layer2 | 25.81 | 259,114 | 30.77 | 261,069 | 35.60 | 261,850 | 38.90 | 261,625 |

Baboon | Layer2 | 19.76 | 255,449 | 23.01 | 260,126 | 30.45 | 262,105 | 33.52 | 261,622 |

Boat | Layer2 | 23.35 | 257,206 | 25.90 | 259,167 | 33.80 | 261,655 | 35.75 | 261,271 |

Peppers | Layer2 | 26.01 | 258,257 | 29.27 | 260,192 | 36.82 | 261,658 | 39.24 | 261,456 |

Average | Layer2 | 24.03 | 258,047 | 27.77 | 260,383 | 34.54 | 261,881 | 37.52 | 261,521 |

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**MDPI and ACS Style**

Lee, C.-F.; Shen, J.-J.; Wu, Y.-J.; Agrawal, S.
PVO-Based Reversible Data Hiding Exploiting Two-Layer Embedding for Enhancing Image Fidelity. *Symmetry* **2020**, *12*, 1164.
https://doi.org/10.3390/sym12071164

**AMA Style**

Lee C-F, Shen J-J, Wu Y-J, Agrawal S.
PVO-Based Reversible Data Hiding Exploiting Two-Layer Embedding for Enhancing Image Fidelity. *Symmetry*. 2020; 12(7):1164.
https://doi.org/10.3390/sym12071164

**Chicago/Turabian Style**

Lee, Chin-Feng, Jau-Ji Shen, Yi-Jhen Wu, and Somya Agrawal.
2020. "PVO-Based Reversible Data Hiding Exploiting Two-Layer Embedding for Enhancing Image Fidelity" *Symmetry* 12, no. 7: 1164.
https://doi.org/10.3390/sym12071164