HEGN: Hierarchical Equivariant Graph Neural Network for 9DoF Point Cloud Registration

Given its wide application in robotics, point cloud registration is a widely researched topic. Conventional methods aim to find a rotation and translation that align two point clouds in 6 degrees of freedom (DoF). However, certain tasks in robotics, such as category-level pose estimation, involve non-uniformly scaled point clouds, requiring a 9DoF transform for accurate alignment. We propose HEGN, a novel equivariant graph neural network for 9DoF point cloud registration. HEGN utilizes equivariance to rotation, translation, and scaling to estimate the transformation without relying on point correspondences. Based on graph representations for both point clouds, we extract equivariant node features aggregated in their local, cross-, and global context. In addition, we introduce a novel node pooling mechanism that leverages the cross-context importance of nodes to pool the graph representation. By repeating the feature extraction and node pooling, we obtain a graph hierarchy. Finally, we determine rotation and translation by aligning equivariant features aggregated over the graph hierarchy. To estimate scaling, we leverage scale information in the vector norm of the equivariant features. We evaluate the effectiveness of HEGN through experiments with the synthetic ModelNet40 dataset and the real-world ScanObjectNN dataset. The results show the superior performance of HEGN in 9DoF point cloud registration and its competitive performance in conventional 6DoF point cloud registration.