提出新型点云卷积，兼具旋转平移对称性与高效内存占用。
Learning Coordinate-based Convolutional Kernels for Continuous SE(3) Equivariant and Efficient Point Cloud Analysis
- 基于坐标构建卷积核，通过双陪集空间实现严格对称性。
- 在多个点云任务中达到领先性能，且内存消耗更低。
- 适合需要高精度几何对称性的3D视觉任务，如工业检测。
刚体运动对称性是高效处理3D点云的关键因素。群卷积虽能提取等变特征，但难以同时满足严格的对称性和可扩展性。本文提出等变坐标基卷积（ECKConv），其卷积核定义在双陪集空间中，实现完整的SE(3)等变性；通过基于坐标的网络显式设计卷积核，提升学习能力与内存效率。在点云分类、姿态配准、部件分割及大规模语义分割等任务上的实验表明，ECKConv在保持刚性等变性的同时，具备出色的性能和内存可扩展性，优于当前最先进的等变方法。
原文摘要 · Abstract (English)
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.
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