We present a novel algorithm for point cloud segmentation. Our approach
transforms unstructured point clouds into regular voxel grids, and further uses
a kernel-based interpolated variational autoencoder (VAE) architecture to
encode the local geometry within each voxel. Traditionally, the voxel
representation only comprises Boolean occupancy information which fails to
capture the sparsely distributed points within voxels in a compact manner. In
order to handle sparse distributions of points, we further employ radial basis
functions (RBF) to compute a local, continuous representation within each
voxel. Our approach results in a good volumetric representation that
effectively tackles noisy point cloud datasets and is more robust for learning.
Moreover, we further introduce group equivariant CNN to 3D, by defining the
convolution operator on a symmetry group acting on $\mathbb{Z}^3$ and its
isomorphic sets. This improves the expressive capacity without increasing
parameters, leading to more robust segmentation results. We highlight the
performance on standard benchmarks and show that our approach outperforms
state-of-the-art segmentation algorithms on the ShapeNet and S3DIS datasets.

本研究提出了一种基于变分自编码器和径向基函数的点云分割算法，并引入了具有对称性的卷积神经网络进行形状分割，实验表明，在 ShapeNet 和 S3DIS 数据集上，该方法的性能优于当前的主流算法。