# Weighted Similarity-Confidence Laplacian Synthesis for High-Resolution Art Painting Completion
## 3 Methodology
### Our Proposed Algorithm  
In addressing the challenging task of completing missing regions in damaged art paintings, our proposed approach stands out as a proficient problem-solving strategy. The method seamlessly integrates Weighted Laplacian Synthesis and patch-based completion, collaborating consistently across multi-regions. Illustrated in Figure 1a, the process begins with the utilization of a high-resolution painting, denoted as \(I_{in}\). Through segmentation of \(I_{in}\) and its corresponding mask images \(M_{in}\) (Figure 1b), our approach ensures a more precise and specific completion of missing regions within the local area.  
The exploitation of Laplacian pyramid completion proves effective for high-resolution paintings, employing the abundance of pixels for consistent completion decisions across various resolutions. Inspired by [PERSON] et al. [32], Laplacian and upsampled Gaussian pyramids are combined, progressively enhancing completion quality from the coarsest to the finest layer. To address structure diffusion challenges, texture synthesis is introduced, employing Laplacian of a Gaussian pyramid at different levels. The process involves constructing a Gaussian pyramid to analyze base structure intensities and subsequently establishing a Laplacian pyramid for enhanced edge awareness (Figure 1c). Matching patches at different levels is achieved through an improved nearest neighbor search algorithm, ensuring a more accurate matching of areas for robust completion. The pursuit of determining the optimal pixel value for completing a missing region involves innovating the voting similarity function. Our method enhances this function by considering potential overlap of nearest neighbor pixels in color, even across different levels, resulting in a refined and accurate estimation of optimal pixel values.  
To address errors introduced by ambiguity in restored pixels, patch-based propagation is seamlessly integrated, applying an isophote-driven technique locally (Figure 1d). The propagation process ensures that matched patches align along the boundary of a hole between two distinct colored regions, with the best-matched patch duplicated into the target area based on confidence and data terms.  
In the quest for optimal patches, our approach employs a fused reaction that integrates the outcomes of Weighted Laplacian Synthesis and patch-based propagation through pyramid blending (Figure 1e,f). Pyramid blending emerges as a standout blending method, effectively handling scale differences between images and ensuring smoother transitions. Its hierarchical structure prevents noticeable seams in blended results, particularly advantageous when merging images with diverse content or structures. The computational efficiency of pyramid blending makes it suitable for real-time applications or large-scale image blending tasks.  
The proposed Algorithm 1 guides the entire process, beginning with segmentation and progressing through Weighted Laplacian Synthesis, patch-based propagation, and pyramid blending until multi-regions are empty. This comprehensive approach, applied to a high-resolution art painting with missing regions sized 1600 \(\times\) 2136 pixels, results in the completion of visually pleasing and artifact-free art paintings.  
```
Data: A damaged high-resolution art painting with a missing region \(I_{in}\) with a size of around 1600 \(\times\) 2136 pixels. Result: A restored high-resolution art painting \(I_{out}\). Segmentation  Divide the input image \(I_{in}\) and its mask image \(M_{in}\) into 16 multi-regions, each with a size of 400 \(\times\) 400 pixels (Figure 2b). do  Weighted Laplacian Synthesis (Figure 2c);  Patch-based Propagation (Figure 2d);  Pyramid Blending (Figure 2e,f); while\(multiregions!=empty\);
```  
**Algorithm 1**Weighted Similarity-Confidence Laplacian Synthesis