# Survey on Data Hiding Based on Block Truncation Coding
## 3 Survey of Related Works
### Non-Reversible Data Hiding
#### 3.1.2 Exploit Modification Direction  
[PERSON] [32] introduced a DH method based on Pixel Pair Matching (PPM) [33], which is originated from the Exploit Modification Direction (EMD) [26]. The EMD method belongs to the superior method among spatial domain-based DH methods. PPM is a technique that embeds digits in \(\sigma\)-ary notational system into pixel pairs by matching the secret digits with entities in a reference table, which is a table that fills with digits ranging from 0 to \(\sigma-1\). Let us assume that \(R_{\sigma}(i,j)\) is the entity located at the \(i\)-th column and the \(j\)-th row of the reference table \(R_{\sigma}(i,j)=mod(c_{\sigma}x+y,\sigma)\), where \(c_{\sigma}\) is a constant. For instance, when \(\sigma=4,8,16,32\) and 64, \(c_{\sigma}=2,3,6,7\), and 14, respectively. Let \(p_{1}=35\), \(p_{2}=23\), and the secret digits in 16-ary notational system be embedded as \(d_{16}=15_{16}\). The reference table can be constructed using \(R_{\sigma}(x,y)\). The design of the reference table affects the embedding performance of the PPM-based method. As this method is applied to two quantized pixels per block, when a small amount of data are hidden, the quality of the cover image can be guaranteed, but when a large amount of data are hidden, the quality of the image can greatly deteriorate.  
[PERSON] et al. [34] introduced a difference matching technique to minimize distortion caused by inserting secret data into the quantization levels. This technique adjusts the quantization values to minimize. Thus, the quality of the cover image and DH capacity were improved.  
[PERSON] et al. [35] proposed an authentication method for AMBTC. First, after dividing each block into two sub-bitmaps, a 6-bit authentication code is allocated to the two sub-codes. In order to hide the 6-bit authentication code, each separated bitmap is allocated as a codeword, and then 3 bits are inserted using matrix encoding, respectively. To overcome the distortion caused by bitmap modifications, instead of directly flipping these bits in the bitmap, the corresponding bit position information to be flipped is written. Then, the bit position is inserted into the quantization level based on the adjusted quantization level matching.  
[PERSON] et al. [36] proposed a method of hiding data by applying the EMD method [26] (Equation (5)) to two divided parts of a bitmap block. First of all, each divided bitmap converted to decimal number is required before performing DH.  
\[f(\mu_{0},\mu_{1})=\left[\sum_{i=1}^{2}(\mu_{i}\cdot i)\right]\bmod 5 \tag{5}\]No modification is needed if a secret digit \(d\) equals the extraction function of the original pixel group. When \(d\
eq f\), calculate \(s=d-f\) mod 5. If \(s\) is greater than or equal to 2, increase the value of \(\mu_{s}\) by 1; otherwise, decrease the value of \(\mu_{5-s}\) by 1.  
[PERSON] et al. [37] proposed a turtle shell method that is derived from EMD [26]. It has proven to be effective against AMBTC as well as having excellent DH performance, especially in spatial domain-based images. This method requires a turtle shell table for data hiding and extraction. The merit of this method is that it is strong against security attacks. That is, even if the attacker knows that the data is hidden, it is difficult to infer the hidden data in this way.  
**Example 3**.: _Suppose two AMBTC trios \((\mu_{0},\mu_{1},BM)_{i=1}^{2}=(146,149,00110101110100)\) are to be embedded with secret data \(d=4\). For example, consider the quantization levels \((\mu=[146\;\;149])\) and the threshold is \(T=5\). We may obtain \(f=\text{mod}((146\times 1+149\times 2),5)=4\) in a 5-ary notational system. Since \(d=f\) in this example, no correction is needed for the two quantization levels in this example._