# FAmesh: Generating Frequency Adaptive Meshes from Single Images under 2D Hole Constraints
## 1 Introduction  
Reconstructing the 3D structure of an object from a single image is an important task in computer vision and graphics. However, due to the ill-posed nature of single-view 3D reconstruction, additional prior knowledge or appropriate constraints are required to restore the correct 3D shape of an object. In recent years, the development of deep learning and the popularization of 3D shape datasets [1; 2; 3] have enabled neural networks to encode the hidden structural information of images effectively, resulting in significant advancements in the field of 3D reconstruction. Existing research on single-view reconstruction employs various 3D shape representations, including implicit functions [4; 5; 6; 7], voxels [8; 9; 10; 11], point clouds [12; 13; 14], meshes [15; 16; 17; 18; 19; 20; 21; 22; 23], and others. Voxel-based methods are challenging to reconstruct high-precision shapes due to the large amount of memory and computational time required to apply 3D CNN. The point cloud representation lacks connection information between points, making it difficult to represent the surface details of 3D objects. Methods based on implicit functions often require the execution of expensive post-processing steps, such as the Marching cube algorithm [24], to generate functional 3D structures. Compared with other representations, the mesh adopted in this paper is a compact, seamless, and coherent surface representation capable of representing finer surface details with smaller data sizes. However, methods using mesh representation face significant challenges:  
The first challenge is dealing with objects with complex topological structures. Most mesh-based single-view reconstruction methods mainly rely on the free deformation of the initial mesh, which limits the reconstruction to meshes with 0-genus topology. According to topology theory [25], the topological properties of meshes remain unchanged underhomeomorphic morphism. As shown in Figure 1, the reconstruction results of the mesh-based method [16] are topologically equivalent to the 0-genus initial template, and the lack of correct holes in the reconstruction results has become a shortcoming that affects the visual effect. Recent studies [18] have begun to explore mesh pruning to generate corresponding holes by estimating the sampling point error; however, smaller holes cannot be handled due to the sparseness of the sampling point cloud. Moreover, data-driven methods have difficulty recovering uncommon holes in the dataset. Thus, achieving the correct topology of the reconstruction result remains a significant problem in the field. The second challenge of mesh reconstruction is the difficulty of generating smooth surfaces with precise details. As shown in Figure 2, the plane lacks sufficient detail in the high-curvature wing parts to reconstruct the engine, and the lower-curvature parts, such as the fuselage, are not smooth enough when compared to the ground truth. This issue can be explained in terms of frequency: the high-curvature part of the mesh contains a large number of high-frequency features, while the high-frequency information in the low-curvature part is mainly noise. Thus, the neural network should retain the high-frequency signal as much as possible in the high-curvature part while suppressing the high-frequency information in the low-curvature part. However, existing methods do not differentiate between high- and low-curvature meshes, which may lead to the worst-case scenario of lacking detail in high-curvature and too much noise in low-curvature. In order to address these challenges, we propose a framework for global-to-local single-view mesh reconstruction that can independently fine-tune high-frequency and low-frequency local meshes and introduce 2D hole constraints to restore the correct mesh topology.