## 3 Proposed Algorithm
\tag{35}\]  
where \(x\in\{0,\ 1,\ 2,\ 3\}\)  
* At location 6, if edge(0), or edge(1), or edge(2), or edge(3) has the value strong_edge, the predicted value \(V_{4S}(x_{i},\ y_{j})\) is calculated using Equation (36). Thereafter, as shown in Equation (37), if the absolute value of the difference between \(V_{2}(x_{i},\ y_{j})\) and \(V_{4S}(x_{i},\ y_{j})\) is equal to or less than the difference threshold (8), the rounded value of \(V_{4S}(x_{i},\ y_{j})\) is used as the predicted pixel value. In Equation (37), the value of \(V_{2}(x_{i},\ y_{j})\) is \((T+U+V+A^{\prime})/4\). When the absolute value of the difference between \(V_{2}(x_{i},\ y_{j})\) and \(V_{4S}(x_{i},\ y_{j})\) exceeds \(\delta\), the pixel value of the cover image becomes the predicted pixel value. In Equation (37), \(V(x_{i},\ y_{j})\) represents the predicted pixel value at location \((x_{i},\ y_{j})\) and \(C(x_{i},\ y_{j})\) represents the pixel value of the cover image at location \((x_{i},\ y_{j})\). \[ \begin{array}{ll}V_{4S}\big{(}x_{i},y_{j}\big{)}&=\big{\{}R_{S}\text{.V}_{2} \big{(}x_{i},y_{j}\big{)}+P\big{(}x_{i+1},y_{j}\big{)}\text{-edge}(0)+P\big{(} x_{i+1},y_{j-1}\big{)}\text{-edge}(1)\\ &+P\big{(}x_{i},y_{j-1}\big{)}\text{-edge}(2)+P\big{(}x_{i-1},y_{j-1}\big{)} \text{-edge}(3)\big{\}}/\{R_{S}+\text{edge}(0)\\ &+\text{edge}(1)+\text{edge}(2)+\text{edge}(3)\}\end{array} \] (36)  
\[V\big{(}x_{i},y_{j}\big{)}=\left\{ \begin{array}{ll}V_{4X}\big{(}x_{i},y_{j} \big{)}&\text{if (}\left|V_{2}\big{(}x_{i},y_{j}\big{)}-V_{4X}\big{(}x_{i},y_{j}\big{)}\right| \leq\delta\right)\\ C\big{(}x_{i},y_{j}\big{)}&\text{otherwise}\end{array} \right. \tag{37}\]  
where \(x\in\{S,\ N,W\}\)
* If strong_edge is absent in edge(0), edge(1), edge(2), and edge(3), and at least one of them has normal_edge, then the predicted value \(V_{4N}(x_{i},\ y_{j})\) is calculated using Equation (38). The predicted pixel value \(V(x_{i},\ y_{j})\) is obtained in the same manner as shown in Step 1.C by applying \(V_{4N}(x_{i},\ y_{j})\) to Equation (37). \[ \begin{array}{ll}V_{4N}\big{(}x_{i},y_{j}\big{)}&=\big{\{}R_{N}\text{.V}_{2} \big{(}x_{i},y_{j}\big{)}+P\big{(}x_{i+1},y_{j}\big{)}\text{-edge}(0)+P\big{(} x_{i+1},y_{j-1}\big{)}\text{-edge}(1)\\ &+\text{P}\big{(}x_{i},y_{j-1}\big{)}\text{-edge}(2)+P\big{(}x_{i-1},y_{j-1} \big{)}\text{-edge}(3)\big{\}}/\{R_{N}+\text{edge}(0)\\ &+\text{edge}(1)+\text{edge}(2)+\text{edge}(3)\}\end{array} \] (38)
* If there is no strong_edge nor normal_edge in edge(0) to (3), and at least one of them has weak_edge, the predicted value \(V_{4W}(x_{i},\ y_{j})\) is calculated using Equation (39). The predicted pixel value \(V(x_{i},\ y_{j})\) is obtained in the same manner as shown in Step 1.C by applying \(V_{4W}(x_{i},\ y_{j})\) to Equation (37). If edge(0) to (3) are not strong edges, normal edges, and weak edges, the pixel value of the cover image becomes the predicted pixel value. \[ \begin{array}{ll}V_{4W}\big{(}x_{i},y_{j}\big{)}&=\big{\{}R_{W}\text{.V}_{2} \big{(}x_{i},y_{j}\big{)}+P\big{(}x_{i+1},y_{j}\big{)}\text{-edge}(0)+P\big{(} x_{i+1},y_{j-1}\big{)}\text{-edge}(1)\\ &+P\big{(}x_{i},y_{j-1}\big{)}\text{-edge}(2)+P\big{(}x_{i-1},\ y_{j-1}\big{)} \text{-edge}(3)\big{\}}/\{R_{W}+\text{edge}(0)\\ &+\text{edge}(1)+\text{edge}(2)+\text{edge}(3)\}\end{array} \] (39)Using the obtained predicted pixel values, a prediction image is generated as shown in Figure 7g. The display rule used in Figure 7f,g is as follows: The general number displayed in the top row represents the pixel value of the cover image. The italic number indicates the rounded value of V1. The underlined italic number indicates the rounded value of V2. The italic bold number indicates the rounded value of V3C. The underlined italic bold number indicates the rounded value of V4S. The underlined bold number indicates the rounded value of V4N, and the double underlined bold number indicates the rounded value of V4W.