学习基于坐标的卷积核用于连续 SE(3) 等变且高效的点云分析
Learning Coordinate-based Convolutional Kernels for Continuous SE(3) Equivariant and Efficient Point Cloud Analysis
用坐标网络在双陪集空间上显式参数化卷积核，可在保持严格 SE(3) 等变的同时把显存开销压到可做大规模点云语义分割的程度，是替代组卷积做等变特征提取的可复用核架构。
原文依据 It acquires SE(3) equivariance from the kernel domain defined in a double coset space, and its explicit kernel design using coordinate-based networks
摘要译文
由模型翻译 · 术语统一 · 请对照原文核对关键结论刚体运动上的对称性是高效学习三维点云问题的显著因素之一。组卷积一直是提取等变特征的代表性方法，但其实现难以同时保持严格的对称性与可扩展性。我们主张利用 intertwiner 框架来化解这一权衡，但此前关于该框架的工作未能实现完整的 SE(3) 对称性或扩展到大规模问题，因而需要更先进的核架构。我们提出基于坐标的等变核卷积，即 ECKConv。它从定义于双陪集空间的核域中获得 SE(3) 等变性，其使用基于坐标的网络的显式核设计增强了学习能力与内存效率。在多种点云任务（如分类、位姿配准、部件分割和大规模语义分割）上的实验，验证了 ECKConv 的刚体等变性、内存可扩展性，以及相较于最优等变方法的出色性能。
英文原文摘要 1092 字符
A symmetry on rigid motion is one of the salient factors in efficient learning of 3D point cloud problems. Group convolution has been a representative method to extract equivariant features, but its realizations have struggled to retain both rigorous symmetry and scalability simultaneously. We advocate utilizing the intertwiner framework to resolve this trade-off, but previous works on it, which did not achieve complete SE(3) symmetry or scalability to large-scale problems, necessitate a more advanced kernel architecture. We present Equivariant Coordinate-based Kernel Convolution, or ECKConv. It acquires SE(3) equivariance from the kernel domain defined in a double coset space, and its explicit kernel design using coordinate-based networks enhances its learning capability and memory efficiency. The experiments on diverse point cloud tasks, e.g., classification, pose registration, part segmentation, and large-scale semantic segmentation, validate the rigid equivariance, memory scalability, and outstanding performance of ECKConv compared to state-of-the-art equivariant methods.