## 1 Introduction  
With the emergence and development of 3D scanners and computer graphics technology, the way that cultural heritage artifacts (CHarts) are preserved has changed considerably. For example, CHarts can be restored in digital space and presented through the Internet. The virtual presentation of CHarts can be divided into three steps: obtaining the 3D fragments by 3D scanners, reassembling the 3D fragments, and finally transferring the virtual CHarts to the Internet. However, due to the physical and chemical erosion of the contact surfaces, the CHarts were often broken into fragments when they were discovered and the edges of the discovered fragments were often incomplete, resulting in the existence of holes on the reassembled 3D CHarts. Thus, how to fill these holes effectively and reconstruct high-quality 3D CHarts is an important issue in the field of archeology. The traditional hole-filling methods are based on the structural information of 3D mesh models [1, 2, 3, 4, 5]. These methods can be generally categorized as template-based methods and mesh-based methods. The former methods are suitable when the holes are relatively large, and a similar 3D model from the 3D model database is selected to be the underlying surface and then used to fill the holes [6, 7]. An effective template database is very important; the more 3D models of different shapes, the better the hole-filling effect. [PERSON] et al. [8], proposed an online 2D depth database; they projected the 3D hole region into a 2D depth map, then searched the best-matched depth map from the depth-based database to complete the 2D hole region, and finally restored the 3D mesh model. Some studies [9, 10, 11] focus on the creation of 3D shape databases, which are used to retrieve the most relevant shape with holes to fill the missing region. However, if the best-matched template does not exist in the database, the completed task will fail. Other works used the non-local self-similarity of 3D mesh models to complete hole regions [12; 13]. This method implicitly assumes there are local structures similar to the missing parts on the same model. [PERSON] et al. [14] segmented a point cloud into cubes with a fixed size and iteratively searched for the most similar cubes from the non-hole area to fill the missing region. The main drawback of the template-based method is that it works only with an analogous template. Different from the template-based methods, the mesh-based methods can reconstruct the hole regions based on the topological information, and these methods can obtain a satisfactory restoration result when the hole regions are relatively small. These methods [15; 16; 17] interpolated values in the hole to generate the latent surfaces directly. [PERSON] et al. [18] applied the Poisson equation to global fitting the input model surface to obtain the hole patch, and then adjusted the normal vectors of the hole boundary region to stitch better to the original hole model. [PERSON] et al. [19] reconstructed incomplete feature curves by extending salient features around the hole regions, and then split the original hole regions into smaller and more planar sub-holes, and completed those sub-holes. Similarly, [PERSON] et al. proposed a surface-fitting reconstruction method based on tensor voting. By combining the fringe projection-based 3D reconstruction method [20; 21] and the SFM method, [PERSON] et al. [22] proposed an SFM-based hole-filling algorithm. They first extracted the hole boundary points based on the 2D phase map, and then recovered geometry information with SFM point cloud, which can effectively restore the complicated surface hole regions. However, if large curvature variations exist in the hole regions, the surface-based methods also cannot reconstruct the hole regions very well. Recently, with the development of deep learning, learning-based methods have been proposed to process point clouds, as well as 3D models. These methods can generate 3D models from the learned latent features [23; 24; 25; 26].