# Weighted Similarity-Confidence Laplacian Synthesis for High-Resolution Art Painting Completion
## 4 Experimental Results
### Quantitative Comparison  
The evaluation of our results incorporates two distinct perceptual metrics: Learned Perceptual Image Patch Similarity (LPIPS) [34] and Deep Image Structure and Texture Similarity (DISTS) [35]. In contrast to commonly used metrics like Structural Similarity Index Measure (SSIM) [36] and Peak Signal to Noise Ratio (PSNR) [37], we opt for LPIPS, a metric rooted in deep feature networks that employs human perceptual similarity judgments. This metric involves the learning of linear weights for perceptual calibration, tuning configuration, and Gaussian weights as follows:  
\[d(x,x_{0})=\sum l\frac{1}{H^{l}W^{l}}\sum h,w\left|wt^{l}\odot(gh,w^{l}-\hat{ y}0h,w^{l})\right|_{2}^{2} \tag{7}\]  
Figure 3: Low-resolution art painting completion with a size of around 400 \(\times\) 400 pixels. The order of image names, from top to bottom, follows a structured sequence: Girl, Man, Seenery, and Woman. (**a**) Input, (**b**) [PERSON] et al. [1], (**c**) Laplacian [32], (**d**) EdgeConnect [27], (**e**) Ours, and (**f**) Ground Truth. In this equation, \(d(x,x_{0})\) represents the distance between the ground truth \(x\) and the restored images \(x_{0}\). The terms \(\hat{y}h,w^{l}\) and \(\hat{y}0h,w^{l}\epsilon\mathbb{R}^{H^{l}\times W^{l}\times C^{l}}\) denote feature stacks from \(l\) layers, each unit-normalized in the channel dimension. Here, \(H\), \(W\), and \(C\), respectively, indicate the number of height \(h\), weight \(w\), and channel dimension \(c\) of layers, while \(wt^{l}\epsilon\mathbb{R}^{C^{l}}\) serves as an activation channel-wise. Moreover, our evaluation includes the utilization of Deep Image Structure and Texture Similarity (DISTS) [36]. This approach, anchored in a Conventional Neural Network (CNN), seamlessly integrates spatial texture averages and feature structure maps to generate diverse texture patterns. Within this model, quality assessments are harmonized between convolution layers of texture, expressed by global means \(l\left(\hat{x}_{j}^{i},\hat{y}_{j}^{i}\right)\), and structure, represented by global correlations \(s\left(\hat{x}_{j}^{i},\hat{y}_{j}^{i}\right)\). The integration is accomplished through the computation of the weighted sum of different convolution layers, denoted as \(D(x,y;\alpha,\beta)\):  
\[l(\hat{x}_{j}^{i},\hat{y}_{j}^{i})=\frac{2\mu_{\hat{x}_{j}^{i}}\mu_{\hat{y}_{j} ^{i}}+c_{1}}{\left(\mu_{\hat{x}_{j}^{i}}\right)^{2}+\left(\mu_{\hat{y}_{j}^{i} }\right)^{2}+c_{1}} \tag{8}\]  
\[s(\hat{x}_{j}^{i},\hat{y}_{j}^{i})=\frac{2\sigma_{\hat{x}_{j}^{i}\hat{y}_{j}^{i }}+c_{2}}{\left(\sigma_{\hat{x}_{j}^{i}}\right)^{2}+\left(\sigma_{\hat{y}_{j} ^{i}}\right)^{2}+c_{2}} \tag{9}\]  
\[D(x,y;\alpha,\beta)=1-\sum_{i=0}^{m}\sum_{j=1}^{n_{i}}\left(\alpha_{ij}l\left( \hat{x}_{j}^{i},\hat{y}_{j}^{i}\right)\right)+\left(\beta_{ij}s\left(\hat{x}_{ j}^{i},\hat{y}_{j}^{i}\right)\right) \tag{10}\]  
where \(i\) and \(j\) refer to the convolution layers of the ground truth image \(x\) and the restored images \(y\), respectively. The variables \(\hat{x}_{j}^{i}\) and \(\hat{y}_{j}^{i}\) represent the convolution channels of \(x\) and \(y\). The terms \(m\) and \(n_{i}\) represent the number of convolution layers for \(x\) and \(y\) in the \(i\)-th layer, respectively. The weights \(\alpha\) and \(\beta\) are learned weights, satisfying the condition \(\sum_{i=0}^{m}\sum_{j=1}^{n_{i}}\alpha_{ij}+\beta_{ij}=1\). Additionally, \(\mu_{\hat{x}_{j}^{i}},\mu_{\hat{y}_{j}^{i}},\sigma_{\hat{x}_{j}^{i}}^{2},\sigma _{\hat{y}_{j}^{i}}^{2}\) denote the global means and variances of \(\hat{x}_{j}^{i}\) and \(\hat{y}_{j}^{i}\), while \(\sigma_{\hat{x}_{j}^{i}\hat{y}_{j}^{i}}\) represents the global covariance between \(\hat{x}_{j}^{i}\) and \(\hat{y}_{j}^{i}\). Constants \(c_{1}\) and \(c_{2}\) are introduced for numerical stability. Furthermore, our method stands out as a superior choice for high and low-resolution art painting completions due to several key factors that address and surpass the limitations of alternative approaches.