## 3 Proposed Method
### Message Embedding
#### 3.1.2 Phase-2: Weight Modulus Reversible Data-Hiding Embedding (WMRDHE)  
In Phase-2, we input a stego OWCT image, \(\mathbf{I}^{\prime\prime}_{\textit{oucet}}\), where every stego pixel, \(\mathbf{P}^{\prime\prime}_{\textit{oucet}}\) = (\(r^{\prime\prime}\), \(g^{\prime\prime}\), \(b^{\prime\prime}\)), has one secret message vector concealed, \(\mathbf{d_{\textit{sb}}}\), and one secret message conveyed, \(d_{\textit{wm}}\). Algorithm 2 shows the weight modulus reversible data-hiding embedding. The output of Phase-2 is two stego images: \(\mathbf{I}^{\prime\prime}_{\textit{s1}}\) and \(\mathbf{I}^{\prime\prime}_{\textit{s2}}\), which are produced by concealing a number of \(k\)-ary secret message vectors, \(\mathbf{d_{\textit{du}}}\) = \((d_{\textit{s1}}^{1},d_{\textit{s2}}^{2},\ d_{\textit{s3}}^{3})\), using the modulus operation with the 2-tuple weight vector, \(\mathbf{W_{b}}\) = [\(w_{1}\), \(w_{2}\)]. The message embedding consists of three steps, as detailed below:  
```
Input: \(\mathbf{I}^{\prime}_{\textit{oucet}}\), \(\mathbf{W_{b}}\) = [\(w_{1}\), \(w_{2}\)], and \(\mathbf{d_{\textit{du}}}\) = \((d_{\textit{s}}^{1},d_{\textit{s}}^{2},d_{\textit{s}}^{3})\)
```  
Output: \(\mathbf{I}^{\prime}_{\textit{s1}}\) and \(\mathbf{I}^{\prime\prime}_{\textit{s2}}\)  
1. Constructing the \"dual-pixel\", \(\mathbf{P}^{\prime\prime}_{\textit{du}}\). 2. Locating the distortion vector, \(\mathbf{V_{\textit{du}}}\), from Equation (9). 3. Producing the stego pair of components in three channels, \(\mathbf{P}^{\prime\prime}_{\textit{r1}}\), \(\mathbf{P}^{\prime\prime}_{\textit{s2}}\), and \(\mathbf{P}^{\prime\prime}_{\textit{b3}}\), from Equation (10), and producing the dual stego images: \(\mathbf{I}^{\prime\prime}_{\textit{s1}}\) and \(\mathbf{I}^{\prime\prime}_{\textit{s2}}\). ```  
**Algorithm 2** WMRDH algorithm  
**Step 1:** Constructing the \"dual-pixel.\" In this step, we first duplicate two images from \(\mathbf{I}^{\prime}_{\textit{oucet}}\) and rename them as \(\mathbf{I}^{\prime}_{\textit{s1}}\) and \(\mathbf{I}^{\prime\prime}_{\textit{s2}}\), respectively. Without loss of generality, we denote a pixel in \(I_{s1}^{\prime\prime}\) and \(I_{s2}^{\prime\prime}\) as \(\mathbf{P}_{s1}^{\prime\prime}=(I_{s1}^{\prime\prime},I_{s1}^{\prime\prime},I_{s1}^{ \prime\prime})\) and \(\mathbf{P}_{s2}^{\prime\prime}=(I_{s2}^{\prime\prime},I_{s2}^{\prime\prime},I_{s2}^ {\prime\prime})\), respectively. Then, we construct a dual-pixel, \(\mathbf{P}_{du}^{\prime}=((I_{s1}^{\prime\prime},I_{s2}^{\prime\prime}),(I_{s1}^{ \prime\prime},I_{s2}^{\prime\prime}),(I_{s1}^{\prime\prime},I_{s2}^{\prime \prime}))\), from \(\mathbf{P}_{s1}^{\prime\prime}\) and \(\mathbf{P}_{s2}^{\prime\prime}\). In other words, we select the component in the Red channel from \(\mathbf{P}_{s1}^{\prime\prime}\) in \(I_{s1}\) and \(\mathbf{P}_{s2}^{\prime\prime}\) in \(I_{s2}\), to construct a Red component pair, \((I_{s1}^{\prime\prime},I_{s2}^{\prime\prime})\). Similarly, we proceed with the same construction approach for the components in the Green and Blue channels. To simplify the notation, we represent each component in \(\mathbf{P}_{du}^{\prime}\) as \(\mathbf{P}_{r1}^{\prime\prime}\)= \((I_{s1}^{\prime\prime},I_{s2}^{\prime\prime})\), \(\mathbf{P}_{s2}^{\prime\prime}\)= \((I_{s1}^{\prime\prime},I_{s2}^{\prime\prime})\), \(\mathbf{P}_{s2}^{\prime\prime}\)= \((I_{s1}^{\prime\prime},I_{s2}^{\prime\prime})\). For example, if \(\mathbf{P}_{ouct}^{\prime\prime}\) = \((r^{\prime\prime},g^{\prime\prime},b^{\prime\prime})\)= (13, 5, 21), the dual-pixel constructed is \(\mathbf{P}_{du}^{\prime\prime}\) = ((13, 13), (5, 5), (21, 21)), and the component pairs in the Red, Green, and Blue channels will be \(\mathbf{P}_{r1}^{\prime\prime}\) = (13, 13), \(\mathbf{P}_{s2}^{\prime\prime}\) = (5, 5), and \(\mathbf{P}_{b3}^{\prime\prime}\) = (21, 21), respectively. **Step 2:** Locating the distortion vector, \(\mathbf{V}_{d_{k}}\).