  3D point clouds acquired by scanning real-world objects or scenes have found
a wide range of applications including immersive telepresence, autonomous
driving, surveillance, etc. They are often perturbed by noise or suffer from
low density, which obstructs downstream tasks such as surface reconstruction
and understanding. In this paper, we propose a novel paradigm of point set
resampling for restoration, which learns continuous gradient fields of point
clouds that converge points towards the underlying surface. In particular, we
represent a point cloud via its gradient field -- the gradient of the
log-probability density function, and enforce the gradient field to be
continuous, thus guaranteeing the continuity of the model for solvable
optimization. Based on the continuous gradient fields estimated via a proposed
neural network, resampling a point cloud amounts to performing gradient-based
Markov Chain Monte Carlo (MCMC) on the input noisy or sparse point cloud.
Further, we propose to introduce regularization into the gradient-based MCMC
during point cloud restoration, which essentially refines the intermediate
resampled point cloud iteratively and accommodates various priors in the
resampling process. Extensive experimental results demonstrate that the
proposed point set resampling achieves the state-of-the-art performance in
representative restoration tasks including point cloud denoising and
upsampling.
