# Efficient Data Hiding Based on Block Truncation Coding Using Pixel Pair Matching Technique

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## Abstract

**:**

## 1. Introduction

## 2. Related Works

#### 2.1. AMBTC Compression Technique

#### 2.2. Adaptive Pixel Pair Matching Technique

#### 2.3. Huang et al.’s Method

_{2}, the values of ${a}_{i}^{\prime}$ and ${b}_{i}^{\prime}$ are swapped and bitmap ${B}_{i}^{\prime}={\overline{B}}_{i}$ is set, where ${\overline{B}}_{i}$ is the flipped version of ${B}_{i}$. Otherwise, ${a}_{i}^{\prime}$ and ${b}_{i}^{\prime}$ are kept unchanged and set ${B}_{i}^{\prime}={B}_{i}$.

_{2}. Because ${d}_{i}={b}_{i}-{a}_{i}=5>T$, the block is complex, and we have $D={10}_{2}=2$, ${R}_{i}=\mathrm{mod}({d}_{i},T)=1$. According to Equation (4), because ${R}_{i}\le D$, we have ${a}_{i}^{\prime}={a}_{i}-\lfloor (D-{R}_{i})/2\rfloor =25-\lfloor (2-1)/2\rfloor =25$, ${b}_{i}^{\prime}=30+\lceil (2-1)/2\rceil =31$. To extract the embedded bits, which is the binary representation of $\mathrm{mod}({d}_{i}^{\prime},T)$, we calculate ${d}_{i}^{\prime}={b}_{i}^{\prime}-{a}_{i}^{\prime}=6$. Because $\mathrm{mod}({d}_{i}^{\prime},T)=2$, the embedded bits are 10

_{2}.

## 3. Proposed Method

#### 3.1. Optimal Quantization Level Adjustment

#### 3.2. Embedment Using APPM

#### 3.3. Division-Switching Technique

#### 3.4. Lossless Embedment Technique

_{2}, the trio is unmodified. If the to-be-embedded bit is 1

_{2}, the trio is modified to $({b}_{i},{a}_{i},{\overline{B}}_{i})$, where ${\overline{B}}_{i}$ is the flipped version of ${B}_{i}$. Note that the decoded blocks $I({a}_{i},{b}_{i},{B}_{i})$ and $I({b}_{i},{a}_{i},{\overline{B}}_{i})$ are identical. As a result, the embedment in the complex blocks results in no distortion but contribute one bit to payload per block.

#### 3.5. Embedding Procedures

- Step 1:
- Use Equation (11) to determine the smallest threshold T.
- Step 2:
- Scan the AMBTC trios ${\{{a}_{i},{b}_{i},{B}_{i}\}}_{i=1}^{N}$.
- Step 3:
- If ${b}_{i}-{a}_{i}\le T$, the scanned trio is smooth. The following three steps are performed to embed ${\mathrm{log}}_{2}\sigma +m\times m$ bits into the scanned trio:
- (1)
- Extract $m\times m$ bits ${S}_{j}$ from S, and replace ${B}_{i}$ with ${S}_{j}$.
- (2)
- Adjust the quantization pair $({a}_{i},{b}_{i})$ to $({\widehat{a}}_{i},{\widehat{b}}_{i})$ by solving the Equation (6) given in Section 3.1.
- (3)
- Extract ${\mathrm{log}}_{2}\sigma $ bits from S, convert the extracted bits to a digit ${s}_{\sigma}$ in $\sigma -\text{ary}$ notational system, and perform the APPM embedding technique to embed ${s}_{\sigma}$ into the quantization pair $({\widehat{a}}_{i}^{\prime},{\widehat{b}}_{i}^{\prime})$ by solving Equation (9). In case the solution cannot be found, return the previously extracted ${\mathrm{log}}_{2}\sigma +m\times m$ to S, modify $({a}_{i},{b}_{i})$ to $({a}_{i}^{\prime},{b}_{i}^{\prime})$ according to the Equation (10), and go to Step 4 for embedding one additional bit.

- Step 4:
- If ${b}_{i}-{a}_{i}>T$, the scanned trio is complex. Extract one bit from S and losslessly embed the extracted bit, as described in Section 3.4.
- Step 5:
- Steps 2–4 are repeated until all bits in S are embedded.

#### 3.6. Extraction Procedures

- Step 1:
- Scan the stego codes ${\{{a}_{i}^{S},{b}_{i}^{S},{B}_{i}^{S}\}}_{i=1}^{N}$ sequentially.
- Step 2:
- If $|{a}_{i}^{S}-{b}_{i}^{S}|\text{\hspace{0.17em}}\le T$, extract $m\times m$ bits from the bitmap. Other ${\mathrm{log}}_{2}\sigma $ bits can be extracted by obtaining ${s}_{\sigma}={R}_{\sigma}({a}_{i}^{S},{b}_{i}^{S})$ first, and then convert ${s}_{\sigma}$ to its binary representation.
- Step 3:
- If $|{a}_{i}^{S}-{b}_{i}^{S}|\text{\hspace{0.17em}}>T$, one bit is embedded in this block. If ${a}_{i}^{S}<{b}_{i}^{S}$, a bit 0
_{2}is extracted. If ${a}_{i}^{S}>{b}_{i}^{S}$, a bit 1_{2}is extracted. - Step 4:
- Repeat Steps 2–4 until all the embedded data are extracted.

#### 3.7. A Simple Example

_{2}. The two trios and the corresponding AMBTC block are shown in Figure 6a–c, respectively. Let $T=20$ and $\sigma =16$ be the embedding parameters used, and the required reference table ${R}_{16}$ is shown in Figure 2. In this example, the bitmap is capable of carrying 16 bits while the pair of quantization levels are able to carry ${\mathrm{log}}_{2}16=4$ bits.

_{2}of S. Since the bitmap is replaced, a pair of quantization levels $({\widehat{a}}_{1},{\widehat{b}}_{1})$ has to find such that the distortion due to the bitmap replacement is the smallest. ${\widehat{a}}_{1}=31$ and ${\widehat{b}}_{1}=23$ can be obtained by solving Equation (6) with few calculations. Now, ${\widehat{a}}_{1}$ and ${\widehat{b}}_{1}$ can be modified to carry four additional bits. Extract the 17-th to 20-th bits 1011

_{2}from S and convert it to the 16-ary notational system, we have ${s}_{16}=11$. Because the coordinate (33, 23) is the nearest coordinate to (31, 23) satisfying ${R}_{16}(33,23)=11$ and $|23-33|\text{\hspace{0.17em}}<20$, we have ${\widehat{a}}_{1}^{\prime}=33$ and ${{\widehat{b}}^{\prime}}_{1}=23$. As a result, the final stego trio for the first AMBTC block is $({a}_{1}^{S},{b}_{1}^{S},{B}_{1}^{S})=(33,23,0010\text{\hspace{0.17em}}0010\text{\hspace{0.17em}}0110\text{\hspace{0.17em}}{0000}_{2})$. For the second block, because ${b}_{2}-{a}_{2}=86-65=21>T$, one bit can be embedded into this block losslessly. Because the 21-th bit is 1

_{2}, swapping the value of ${a}_{2}$ and ${b}_{2}$, and flipping the bitmap of ${B}_{2}$, we have the stego code $({a}_{2}^{S},{b}_{2}^{S},{B}_{2}^{S})=(86,65,0011\text{\hspace{0.17em}}00110000\text{\hspace{0.17em}}{1111}_{2})$. The final stego trios and the corresponding stego AMBTC block are shown in Figure 6d–f.

_{2}. Moreover, because ${R}_{16}(33,23)={11}_{16}={1011}_{2}$, four bits 1011

_{2}can be extracted. For the second block, since $|{a}_{2}^{S}-{b}_{2}^{S}|\text{\hspace{0.17em}}=\text{\hspace{0.17em}}|86-65|\text{\hspace{0.17em}}>T$ and ${a}_{2}^{S}>{b}_{2}^{S}$, a bit 1

_{2}is extracted. Concatenate these extracted bits, the embedded secret data 001000100110000010111

_{2}can then be successfully extracted.

## 4. Experimental Results

#### 4.1. Performance of the Proposed Method

#### 4.2. Comparison with Previous Schemes

## 5. Conclusions

## Conflicts of Interest

## References

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**Figure 4.**Distribution of the proposed embedding techniques. (

**a**) $T=3,\text{\hspace{0.17em}}\sigma =32$; (

**b**) $T=5,\text{\hspace{0.17em}}\sigma =32$.

**Figure 6.**Examples of the proposed method. (

**a**) ${a}_{1}=23,{b}_{1}=39$; (

**b**) ${a}_{2}=65,{b}_{2}=86$; (

**c**) AMBTC compressed block; (

**d**) ${a}_{1}^{S}=33,{b}_{1}^{S}=23$; (

**e**) ${a}_{2}^{S}=86,{b}_{2}^{S}=65$; (

**f**) Stego image block.

**Figure 7.**Eight test images. (

**a**) Lena; (

**b**) Jet; (

**c**) Tiffany; (

**d**) Peppers; (

**e**) Tank; (

**f**) Boat; (

**g**) House; (

**h**) Baboon.

**Figure 9.**Performance comparison of the related works. (

**a**) Lena; (

**b**) Boat; (

**c**) Baboon; (

**d**) Averaged results.

**Figure 10.**Stego AMBTC images. (

**a**–

**c**) Huang et al.’s method; (

**d**) The proposed method. (

**a**) T = 4, 136,647 bits 35.30 dB; (

**b**) T = 8, 219,721 bits 34.19 dB; (

**c**) T = 16, 283,145 bits 31.54 dB; (

**d**) T = 16, 283,125 bits 33.53 dB ($\sigma =32$).

**Figure 11.**Performance comparison of 200 test images. (

**a**) PSNR comparisons at payload = 200,000 bits; (

**b**) PSNR comparison at payload = 262,144 bits.

**Table 1.**Image quality (in dB) of the absolute moment block truncation coding (AMBTC) compressed images.

Image | Lean | Jet | Tiffany | Peppers | Tank | Boat | House | Baboon |
---|---|---|---|---|---|---|---|---|

PSNR | 33.27 | 31.97 | 35.77 | 33.42 | 34.73 | 31.16 | 30.89 | 26.98 |

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**MDPI and ACS Style**

Hong, W.
Efficient Data Hiding Based on Block Truncation Coding Using Pixel Pair Matching Technique. *Symmetry* **2018**, *10*, 36.
https://doi.org/10.3390/sym10020036

**AMA Style**

Hong W.
Efficient Data Hiding Based on Block Truncation Coding Using Pixel Pair Matching Technique. *Symmetry*. 2018; 10(2):36.
https://doi.org/10.3390/sym10020036

**Chicago/Turabian Style**

Hong, Wien.
2018. "Efficient Data Hiding Based on Block Truncation Coding Using Pixel Pair Matching Technique" *Symmetry* 10, no. 2: 36.
https://doi.org/10.3390/sym10020036