This study presents a self-prior-based mesh inpainting framework that requires only an incomplete mesh as input, without the need for any training datasets. Additionally, our method maintains the polygonal mesh format throughout the inpainting process without converting the shape format to an intermediate, such as a voxel grid, a point cloud, or an implicit function, which are typically considered easier for deep neural networks to process. To achieve this goal, we introduce two graph convolutional networks (GCNs): single-resolution GCN (SGCN) and multi-resolution GCN (MGCN), both trained in a self-supervised manner. Our approach refines a watertight mesh obtained from the initial hole filling to generate a completed output mesh. Specifically, we train the GCNs to deform an oversmoothed version of the input mesh into the expected completed shape. To supervise the GCNs for accurate vertex displacements, despite the unknown correct displacements at real holes, we utilize multiple sets of meshes with several connected regions marked as fake holes. The correct displacements are known for vertices in these fake holes, enabling network training with loss functions that assess the accuracy of displacement vectors estimated by the GCNs. We demonstrate that our method outperforms traditional dataset-independent approaches and exhibits greater robustness compared to other deep-learning-based methods for shapes that less frequently appear in shape datasets.

翻译：本文提出了一种基于自先验的网格补全框架，该框架仅需以不完整网格作为输入，无需依赖任何训练数据集。此外，我们的方法在补全过程中始终保持多边形网格格式，无需将形状格式转换为中间表示形式（如体素网格、点云或隐式函数），而这些中间形式通常被认为更易于被深度神经网络处理。为实现这一目标，我们引入了两种图卷积网络（GCN）：单分辨率图卷积网络（SGCN）与多分辨率图卷积网络（MGCN），两者均以自监督方式进行训练。我们的方法通过对初始孔洞填充得到的封闭网格进行优化，生成最终的完整输出网格。具体而言，我们训练图卷积网络将输入网格的过平滑版本变形为预期的完整形状。为了监督图卷积网络实现精确的顶点位移（尽管真实孔洞处的正确位移未知），我们利用多组网格，这些网格中多个连通区域被标记为伪孔洞。对于这些伪孔洞内的顶点，其正确位移是已知的，从而能够通过评估图卷积网络估计位移向量准确性的损失函数进行网络训练。实验表明，我们的方法优于传统不依赖数据集的方法，并且在处理形状数据集中出现频率较低的形状时，相比其他深度学习方法展现出更强的鲁棒性。