  It is an important task to reconstruct surfaces from 3D point clouds. Current
methods are able to reconstruct surfaces by learning Signed Distance Functions
(SDFs) from single point clouds without ground truth signed distances or point
normals. However, they require the point clouds to be dense, which dramatically
limits their performance in real applications. To resolve this issue, we
propose to reconstruct highly accurate surfaces from sparse point clouds with
an on-surface prior. We train a neural network to learn SDFs via projecting
queries onto the surface represented by the sparse point cloud. Our key idea is
to infer signed distances by pushing both the query projections to be on the
surface and the projection distance to be the minimum. To achieve this, we
train a neural network to capture the on-surface prior to determine whether a
point is on a sparse point cloud or not, and then leverage it as a
differentiable function to learn SDFs from unseen sparse point cloud. Our
method can learn SDFs from a single sparse point cloud without ground truth
signed distances or point normals. Our numerical evaluation under widely used
benchmarks demonstrates that our method achieves state-of-the-art
reconstruction accuracy, especially for sparse point clouds.
