DMNet: Delaunay Meshing Network for 3D Shape Representation

Recently, there has been a growing interest in learningbased explicit methods due to their ability to respect the original input and preserve details. However, the connectivity on complex structures is still difficult to infer due to the limited local shape perception, resulting in artifacts and non-watertight triangles. In this paper, we present a novel learning-based method with Delaunay triangulation to achieve high-precision reconstruction. We model the Delaunay triangulation as a dual graph, extract local geometric information from the points, and embed it into the structural representation of Delaunay triangulation in an organic way, benefiting fine-grained details reconstruction. To encourage neighborhood information interaction of edges and nodes in the graph, we introduce a local graph iteration algorithm, which is a variant of graph neural network. Moreover, a geometric constraint loss further improves the classification of tetrahedrons. Benefiting from our fully local network, a scaling strategy is designed to enable large-scale reconstruction. Experiments show that our method yields watertight and high-quality meshes. Especially for some thin structures and sharp edges, our method shows better performance than the current state-of-the-art methods. Furthermore, it has a strong adaptability to point clouds of different densities.