  The task of point cloud completion aims to predict the missing part for an
incomplete 3D shape. A widely used strategy is to generate a complete point
cloud from the incomplete one. However, the unordered nature of point clouds
will degrade the generation of high-quality 3D shapes, as the detailed topology
and structure of discrete points are hard to be captured by the generative
process only using a latent code. In this paper, we address the above problem
by reconsidering the completion task from a new perspective, where we formulate
the prediction as a point cloud deformation process. Specifically, we design a
novel neural network, named PMP-Net, to mimic the behavior of an earth mover.
It moves each point of the incomplete input to complete the point cloud, where
the total distance of point moving paths (PMP) should be shortest. Therefore,
PMP-Net predicts a unique point moving path for each point according to the
constraint of total point moving distances. As a result, the network learns a
strict and unique correspondence on point-level, which can capture the detailed
topology and structure relationships between the incomplete shape and the
complete target, and thus improves the quality of the predicted complete shape.
We conduct comprehensive experiments on Completion3D and PCN datasets, which
demonstrate our advantages over the state-of-the-art point cloud completion
methods.
