  Implicit function based surface reconstruction has been studied for a long
time to recover 3D shapes from point clouds sampled from surfaces. Recently,
Signed Distance Functions (SDFs) and Occupany Functions are adopted in
learning-based shape reconstruction methods as implicit 3D shape
representation. This paper proposes a novel method for learning occupancy
functions from sparse point clouds and achieves better performance on
challenging surface reconstruction tasks. Unlike the previous methods, which
predict point occupancy with fully-connected multi-layer networks, we adapt the
point cloud deep learning architecture, Point Convolution Neural Network
(PCNN), to build our learning model. Specifically, we create a sampling
operator and insert it into PCNN to continuously sample the feature space at
the points where occupancy states need to be predicted. This method natively
obtains point cloud data's geometric nature, and it's invariant to point
permutation. Our occupancy function learning can be easily fit into procedures
of point cloud up-sampling and surface reconstruction. Our experiments show
state-of-the-art performance for reconstructing With ShapeNet dataset and
demonstrate this method's well-generalization by testing it with McGill 3D
dataset \cite{siddiqi2008retrieving}. Moreover, we find the learned occupancy
function is relatively more rotation invariant than previous shape learning
methods.
