## 2 Related Works
### Adaptive MSB Prediction
In a given location map, where '0' represents an unusable block and '1' represents a usable block, the inversion of this rearrangement is enabled, which also spends more redundant space to represent the location map. The method [14] proposed by [PERSON] et al. combines AQP with MSB prediction. The basic idea of quadtree segmentation is to iteratively and adaptively divide the square image (if the carrier image is not square, it can be extended by filling in the background) according to pre-set rules until all sub-blocks of the image satisfy these rules. The entire quadtree partitioning structure can be depicted using a binary group (\(I\), rule). In each iteration, the current image is partitioned into four sub-blocks: upper left, upper right, lower left, and lower right. Each sub-block corresponds to a node within the quadtree partitioning structure. Sub-blocks that do not meet the predefined rules are further divided into the next node level, while those that meet the rules remain undivided and become leaf nodes. This process continues until the division stops at the smallest unit, resulting in the final quadtree partitioning structure. The rule is set, such that if the pixel difference within a block is less than or equal to the threshold (\(T\)) then no further partitioning occurs. If it exceeds \(T\), further partitioning continues until blocks of size 2 \(\times\) 2 are reached, which are not subdivided further, 2 \(\times\) 2 blocks being the smallest units. \(T\) represents the minimum number of MSB bits shared by all pixels in the pixel block with the upper-left pixel. As shown in Figure 4, when \(T\) is set to 3, (a) depicts an 8 \(\times\) 8 pixel block from the top-left corner of the Peppers image before partitioning, and (b) shows the block after quadtree partitioning. Through such a threshold setting, blocks of different sizes can be divided according to the different smoothness of the image. Compared with simply dividing the image into 2 \(\times\) 2 sub-blocks, more embedding space can be freed up based on the different texture distributions of each image. During the encryption, an \(M\times N\) sized image is divided into 64 \(\times\) 64 pixel blocks. For each 64 \(\times\) 64 pixel block, after AQP based on a given \(T\), the blocks are assigned four sizes: 16 \(\times\) 16, 8 \(\times\) 8, 4 \(\times\) 4, and 2 \(\times\) 2, represented by \(dim\). Subsequently, the image is  
Figure 3: Example of pixel bit reconstruction. Figure 2: Pixel bit reconstruction. encrypted at the block level. Next, four blocks of the same level within each \(64\times 64\) sub-block are permuted according to the permutation key, which serves to resist analysis of the encrypted image and enhance its security. After receiving the encrypted image, the data hider initially employs adaptive MSB prediction, in conjunction with AQP, to vacate space for data-hiding. We discuss here [14], the case where the partition size is larger than 2 after AQP. The pixel bit reconstruction for a pixel block of this kind is divided into the following three steps:  
1. Eight bits of the upper-left pixel \(P\), two bits of \(dim\) type (the sizes \(16\times 16\), \(8\times 8\), \(4\times 4\), \(2\times 2\) are denoted by \(00\), \(01\), \(10\), \(11\), respectively), and three bits of \(MD\). 2. Arrange the prediction errors \(e_{i}\) (\(i=1,...\), \(dim^{2}-1\)), respectively, where \(e_{i}\) is the remainder of \(C_{i}\) after removing the shared MSBs. 3. The remaining \([md\ \times\ (dim^{2}-1)-5]\) bits are the space available for data-hiding represented by \(n_{c}\). A \(4\times 4\) sized block of pixels is used as an example, to specifically discuss pixel bit reconstruction. As shown in Figure 5, \(P=162=(10100010)_{2}\), \(dim=(10)_{2}\), \(MD=md-1=5=(101)_{2}\). In method [13], the same situation requires 56 tagging bits to represent the same pixel block after pixel bit reconstruction, while [14] only needs 43 bits.