  Point cloud registration is a crucial technique in 3D computer vision with a
wide range of applications. However, this task can be challenging, particularly
in large fields of view with dynamic objects, environmental noise, or other
perturbations. To address this challenge, we propose a model called PosDiffNet.
Our approach performs hierarchical registration based on window-level,
patch-level, and point-level correspondence. We leverage a graph neural partial
differential equation (PDE) based on Beltrami flow to obtain high-dimensional
features and position embeddings for point clouds. We incorporate position
embeddings into a Transformer module based on a neural ordinary differential
equation (ODE) to efficiently represent patches within points. We employ the
multi-level correspondence derived from the high feature similarity scores to
facilitate alignment between point clouds. Subsequently, we use registration
methods such as SVD-based algorithms to predict the transformation using
corresponding point pairs. We evaluate PosDiffNet on several 3D point cloud
datasets, verifying that it achieves state-of-the-art (SOTA) performance for
point cloud registration in large fields of view with perturbations. The
implementation code of experiments is available at
https://github.com/AI-IT-AVs/PosDiffNet.
