  Latest methods represent shapes with open surfaces using unsigned distance
functions (UDFs). They train neural networks to learn UDFs and reconstruct
surfaces with the gradients around the zero level set of the UDF. However, the
differential networks struggle from learning the zero level set where the UDF
is not differentiable, which leads to large errors on unsigned distances and
gradients around the zero level set, resulting in highly fragmented and
discontinuous surfaces. To resolve this problem, we propose to learn a more
continuous zero level set in UDFs with level set projections. Our insight is to
guide the learning of zero level set using the rest non-zero level sets via a
projection procedure. Our idea is inspired from the observations that the
non-zero level sets are much smoother and more continuous than the zero level
set. We pull the non-zero level sets onto the zero level set with gradient
constraints which align gradients over different level sets and correct
unsigned distance errors on the zero level set, leading to a smoother and more
continuous unsigned distance field. We conduct comprehensive experiments in
surface reconstruction for point clouds, real scans or depth maps, and further
explore the performance in unsupervised point cloud upsampling and unsupervised
point normal estimation with the learned UDF, which demonstrate our non-trivial
improvements over the state-of-the-art methods. Code is available at
https://github.com/junshengzhou/LevelSetUDF .
