  The reconstruction of a discrete surface from a point cloud is a fundamental
geometry processing problem that has been studied for decades, with many
methods developed. We propose the use of a deep neural network as a geometric
prior for surface reconstruction. Specifically, we overfit a neural network
representing a local chart parameterization to part of an input point cloud
using the Wasserstein distance as a measure of approximation. By jointly
fitting many such networks to overlapping parts of the point cloud, while
enforcing a consistency condition, we compute a manifold atlas. By sampling
this atlas, we can produce a dense reconstruction of the surface approximating
the input cloud. The entire procedure does not require any training data or
explicit regularization, yet, we show that it is able to perform remarkably
well: not introducing typical overfitting artifacts, and approximating sharp
features closely at the same time. We experimentally show that this geometric
prior produces good results for both man-made objects containing sharp features
and smoother organic objects, as well as noisy inputs. We compare our method
with a number of well-known reconstruction methods on a standard surface
reconstruction benchmark.
