  Non-rigid point cloud registration is a key component in many computer vision
and computer graphics applications. The high complexity of the unknown
non-rigid motion make this task a challenging problem. In this paper, we break
down this problem via hierarchical motion decomposition. Our method called
Neural Deformation Pyramid (NDP) represents non-rigid motion using a pyramid
architecture. Each pyramid level, denoted by a Multi-Layer Perception (MLP),
takes as input a sinusoidally encoded 3D point and outputs its motion
increments from the previous level. The sinusoidal function starts with a low
input frequency and gradually increases when the pyramid level goes down. This
allows a multi-level rigid to nonrigid motion decomposition and also speeds up
the solving by 50 times compared to the existing MLP-based approach. Our method
achieves advanced partialto-partial non-rigid point cloud registration results
on the 4DMatch/4DLoMatch benchmark under both no-learned and supervised
settings.
