# FAmesh: Generating Frequency Adaptive Meshes from Single Images under 2D Hole Constraints
## 4 Result and Discussion
### Comparisons with the State-of-the-Arts  
In this section, we compare the proposed method with SOTA models, including Pixel2 Mesh [16], Atlasnet [37], TMNET [18], and Vanet [22]. We measure the performance of the proposed method by calculating the chamfer distance and F-score. However, the existing quantitative indicators cannot fully reflect the reconstructed shape quality, so we demonstrate the advantages of the proposed method in detail recovery and topology correction by visualizing the reconstruction results. Figure 6 demonstrates the visualization results. In this experiment, we aligned the output results uniformly. As can be seen from Figure 6, Pixel2 Mesh and Vanet are incapable of reconstructing non-zero-genus objects and lack correct details in high-curvature parts, while low-curvature parts are not sufficiently smooth. The reconstruction results of Atlasnet suffer from severe self-intersection and cannot recover the correct topology (such as the hole in the chair back). Benefiting from the application of the mesh adaptive pruning strategy, TMNET can generate more complex topological structures; however, it is incapable of handling holes with a small surface area or infrequent locations. Our method can reconstruct more intricate topologies than TMNET and Atlasnet (such as holes in chairs, benches, and tables). Moreover, the large results of our method are smoother than those of other methods in areas with low curvatures, such as the chair's seat surface and the monitor's screen, and have more detail in the lamp's areas with high curvature. We compare the performance of the proposed method and SOTA models quantitatively. The results are shown in Table 1, and we use \(\Delta\) to denote the difference between the quantitative results of our method and TMNET. It should be noted that methods such as Pixel2 Mesh reduce the shape by a factor of 0.57, which causes inconsistency between our quantitative results and those obtained by these methods. In terms of CD and F-score values, our method outperforms other methods in the majority of categories and averages, with average CD and F-scores that are 0.418 and 3.20 better than the state-of-the-art methods, respectively. Quantitative and qualitative experiments demonstrate that the proposed method outperforms other approaches. Benefiting from the mesh pruning strategy under the 2D hole constraints, our method is able to reconstruct a more correct topology. Due to the sparseness of point clouds, existing mesh pruning methods by learning point errors cannot reconstruct holes with small areas, and it is difficult for neural network-based methods to migrate to uncommon hole locations. Based on the experimental findings, our method overcomes the above shortcomings. This is due to the fact that the 2D contour contains the hole position information in this view, bypassing the limitation of point cloud sparsity, and it is better for holes with smaller areas. In addition, the introduction of 2D hole contour as an absolute constraint can complement the shortcomings of the neural network, and holes with uncommon locations can be determined through manual experience. Moreover, it is evident from the results that our method is superior to others in its ability to handle the mesh's high and low curvature regions. By utilizing a dual-branch local patch refinement structure, we address high- and low-curvature portions independently. Due to the differences in data between the two branches, the parameters they learn are also distinct. The high-curvature branch tends to learn a high-pass filter to preserve appropriate high-frequency details, while the low-curvature branch learns a low-pass filter to filter out high-frequency noise and make the part smoother. In addition, we also introduce skip connections and FAGCN to adaptively achieve the balance of different frequencies.