  In this paper, we present 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 one, 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 complete output mesh. Specifically, we
train the GCNs to deform an oversmoothed version of the input mesh into the
expected complete shape. The deformation is described by vertex displacements,
and the GCNs are supervised to obtain accurate displacements at vertices in
real holes. To this end, we specify several connected regions of the mesh as
fake holes, thereby generating meshes with various sets of fake holes. The
correct displacements of vertices are known in these fake holes, thus enabling
training GCNs with loss functions that assess the accuracy of vertex
displacements. We demonstrate that our method outperforms traditional
dataset-independent approaches and exhibits greater robustness compared with
other deep-learning-based methods for shapes that infrequently appear in shape
datasets. Our code and test data are available at
https://github.com/astaka-pe/SeMIGCN.
