Features that are equivariant to a larger group of symmetries have been shown
to be more discriminative and powerful in recent studies. However, higher-order
equivariant features often come with an exponentially-growing computational
cost. Furthermore, it remains relatively less explored how rotation-equivariant
features can be leveraged to tackle 3D shape alignment tasks. While many past
approaches have been based on either non-equivariant or invariant descriptors
to align 3D shapes, we argue that such tasks may benefit greatly from an
equivariant framework. In this paper, we propose an effective and practical
SE(3) (3D translation and rotation) equivariant network for point cloud
analysis that addresses both problems. First, we present SE(3) separable point
convolution, a novel framework that breaks down the 6D convolution into two
separable convolutional operators alternatively performed in the 3D Euclidean
and SO(3) spaces. This significantly reduces the computational cost without
compromising the performance. Second, we introduce an attention layer to
effectively harness the expressiveness of the equivariant features. While
jointly trained with the network, the attention layer implicitly derives the
intrinsic local frame in the feature space and generates attention vectors that
can be integrated into different alignment tasks. We evaluate our approach
through extensive studies and visual interpretations. The empirical results
demonstrate that our proposed model outperforms strong baselines in a variety
of benchmarks

本文提出了一个有效的 SE（3）网络，它是针对点云分析领域中 3D 形状对齐任务而设计的，可以利用等变特征来提高性能并解决相对较少探索的旋转等变特征对 3D 形状对齐任务的处理问题。我们采用一个新的框架 SE (3) 可分点卷积来降低计算成本，并在网络中引入一个注意力层来有效地利用等变特征的表达能力。通过广泛的研究和视觉解释，实证结果表明，我们提出的模型在各种基准测试中优于强基线。