## 4 Dataset and Evaluation Protocol
### Dataset Constructed with Poisson Blending and Relief Simulation
To address these limitations, we apply Poisson image blending [24], which is formulated as a gradient-preserving optimization problem. The goal is to retain the gradient field of the foreground image within a selected region \(\Omega\), while ensuring a smooth transition at the boundary \(\partial\Omega\) with the background. The problem is defined as follows:  
\[\min_{I}\int_{\Omega}\lVert\
abla I-\
abla S\rVert^{2}\quad\text{ subject to}\quad I|_{\partial\Omega}=B|_{\partial\Omega} \tag{8}\]  
Here, \(\
abla\) denotes the gradient operator, \(S\) is the source (foreground) image, \(B\) is the background image, and \(I\) is the output image. This formulation ensures that the gradients inside the pasted region match those of the source, while boundary values are constrained by the background. As a result, the output exhibits consistent illumination and texture continuity across the fusion boundary. As illustrated in Figure 5, the right image produced by Poisson blending demonstrates a more natural integration. The text appears to be part of the background surface, with preserved texture and no visible seams. Compared to alpha blending, Poisson blending yields improved edge smoothness, texture consistency, and overall visual coherence. To generate realistic and visually diverse stone inscription text images, we propose a synthesis method based on emboss filtering and alpha blending. Given a grayscale text image as input, the method simulates the visual characteristics of carved stone text, such as depth variation, edge shadows, material reflectivity, and surface texture. We first apply a directional emboss filter to the input text image using a convolution operation:  
\[I_{\text{emboss}}=S*K_{\text{emboss}} \tag{9}\]  
where \(S\) is the input grayscale text image, and \(*\) denotes the 2D convolution operator. The emboss kernel \(K_{\text{emboss}}\) is defined as follows:  
\[K_{\text{emboss}}= \begin{bmatrix}0&-1&-1\\ 1&0&-1\\ 1&1&0\end{bmatrix}  \tag{10}\]  
Figure 5: Comparison between (**a**) alpha blending with transparency \(\alpha=0.5\) and (**b**) Poisson image blending. The Chinese text is used as a representative example for evaluating the visual effectiveness of image blending techniques. No translation is provided, as the semantic content is not essential to the analysis. This operator enhances gradient edges in specific directions. It generates a pseudo-3D effect that mimics the appearance of chiseled text on stone surfaces. The embossed text image is then embedded into a resized stone background image. The placement is centered to ensure spatial alignment. We apply linear alpha blending to combine the text and background images:  
\[I(x,y)=(1-\alpha)\cdot B(x,y)+\alpha\cdot I_{\text{emboss}}(x,y) \tag{11}\]  
where \(B(x,y)\) is the background image and \(\alpha\in[0,1]\) controls the visibility of the text. The embedding position \((x_{0},y_{0})\) is computed as follows:  
\[x_{0}=\left\lfloor\frac{W-w}{2}\right\rfloor,\quad y_{0}=\left\lfloor\frac{H- h}{2}\right\rfloor \tag{12}\]  
where \((W,H)\) and \((w,h)\) denote the dimensions of the background and text images, respectively. This blending preserves the details of the stone texture while maintaining the visual coherence between text and background. To further enhance realism and variability, we introduce random perturbations in the HSV color space. This simulates natural variations in stone surfaces under different lighting and aging conditions. Specifically, the hue, saturation, and value channels are perturbed as follows:  
\[ \begin{split} H^{\prime}&=H+\delta_{h},\quad\delta _{h}\sim\mathcal{U}(-\Delta_{h},+\Delta_{h})\\ S^{\prime}&=S+\delta_{s},\quad\delta_{s}\sim \mathcal{U}(-\Delta_{s},+\Delta_{s})\\ V^{\prime}&=V+\delta_{v},\quad\delta_{v}\sim \mathcal{U}(-\Delta_{v},+\Delta_{v})\end{split}  \tag{13}\]  
where the variables \(\delta_{h},\delta_{s}\), and \(\delta_{v}\) are drawn from uniform distributions, and the parameters \(\Delta_{h}\), \(\Delta_{s}\), and \(\Delta_{v}\) denote the predefined perturbation ranges.