Learning Coordinate-based Convolutional Kernels for Continuous SE(3) Equivariant and Efficient Point Cloud Analysis

TL;DR

This paper introduces ECKConv, a novel coordinate-based kernel convolution method that achieves SE(3) equivariance, scalability, and high performance for diverse 3D point cloud tasks, addressing limitations of prior group convolution approaches.

Contribution

It proposes a new kernel architecture using coordinate-based networks within an intertwiner framework to improve scalability and symmetry in SE(3) equivariant point cloud analysis.

Findings

ECKConv achieves SE(3) equivariance and scalability.

It outperforms state-of-the-art methods in various point cloud tasks.

Demonstrates high memory efficiency and learning capability.

Abstract

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.