  We present a method for reconstructing triangle meshes from point clouds.
Existing learning-based methods for mesh reconstruction mostly generate
triangles individually, making it hard to create manifold meshes. We leverage
the properties of 2D Delaunay triangulations to construct a mesh from manifold
surface elements. Our method first estimates local geodesic neighborhoods
around each point. We then perform a 2D projection of these neighborhoods using
a learned logarithmic map. A Delaunay triangulation in this 2D domain is
guaranteed to produce a manifold patch, which we call a Delaunay surface
element. We synchronize the local 2D projections of neighboring elements to
maximize the manifoldness of the reconstructed mesh. Our results show that we
achieve better overall manifoldness of our reconstructed meshes than current
methods to reconstruct meshes with arbitrary topology. Our code, data and
pretrained models can be found online:
https://github.com/mrakotosaon/dse-meshing
