Shape completion with azimuthal rotations using spherical gidding-based invariant and equivariant network

Point cloud completion aims to restore full shapes of objects from their partial views obtained by 3D optical scanners. In order to make point cloud completion become more robust to azimuthal rotations and more adaptive to real-world scenarios, we propose a novel network for simultaneous rotation invariant and equivariant completion with no need of data augmentation, while other existing approaches require separately trained models for different completion types. Our method includes several main steps: First, Density Compensation Mapping (DCM) as well as Aggregative Gaussian Gridding (AGG) modules are introduced to transfer partial point clouds to spherical signals and avoid unbalanced sampling. Second, an encoder based on group correlation is designed to extract rotation invariant global features and equivariant azimuthal features from spherical signals. Third, parallel groups of decoders are proposed to realize rotation invariant completion based on feature fusion. Finally, a feature remapping module as well as Pose Voting Alignment (PVA) algorithm are proposed to unify feature space and realize rotation equivariant completion. Based on these modules, we find that the application of group correlation can be extended to the domain of shape completion; equivariant and invariant completions can be unified in one pipeline, and our inherent rotation equivariant and invariant framework can achieve competitive performances when comparing with existing representative methods. © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2024.