  Point cloud completion concerns to predict missing part for incomplete 3D
shapes. A common strategy is to generate complete shape according to incomplete
input. However, unordered nature of point clouds will degrade generation of
high-quality 3D shapes, as detailed topology and structure of unordered points
are hard to be captured during the generative process using an extracted latent
code. We address this problem by formulating completion as point cloud
deformation process. Specifically, we design a novel neural network, named
PMP-Net++, to mimic behavior of an earth mover. It moves each point of
incomplete input to obtain a complete point cloud, where total distance of
point moving paths (PMPs) should be the shortest. Therefore, PMP-Net++ predicts
unique PMP for each point according to constraint of point moving distances.
The network learns a strict and unique correspondence on point-level, and thus
improves quality of predicted complete shape. Moreover, since moving points
heavily relies on per-point features learned by network, we further introduce a
transformer-enhanced representation learning network, which significantly
improves completion performance of PMP-Net++. We conduct comprehensive
experiments in shape completion, and further explore application on point cloud
up-sampling, which demonstrate non-trivial improvement of PMP-Net++ over
state-of-the-art point cloud completion/up-sampling methods.
