Learning Coordinate-based Convolutional Kernels for Continuous SE(3) Equivariant and Efficient Point Cloud Analysis
This work addresses the problem of efficient and scalable 3D point cloud learning for applications in computer vision and robotics, representing a novel method for a known bottleneck rather than an incremental improvement.
The paper tackled the challenge of achieving both rigorous SE(3) symmetry and scalability in point cloud analysis by introducing Equivariant Coordinate-based Kernel Convolution (ECKConv), which demonstrated rigid equivariance, memory scalability, and outperformed state-of-the-art equivariant methods across tasks like classification and segmentation.
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.