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We present a novel algorithm for point cloud segmentation. Our approachtransforms unstructured point clouds into regular voxel grids, and further usesa kernel-based interpolated variational autoencoder (VAE) architecture toencode the local geometry within each voxel. Traditionally, the voxelrepresentation only comprises Boolean occupancy information which fails tocapture the sparsely distributed points within voxels in a compact manner. Inorder to handle sparse distributions of points, we further employ radial basisfunctions (RBF) to compute a local, continuous representation within eachvoxel. Our approach results in a good volumetric representation thateffectively tackles noisy point cloud datasets and is more robust for learning.Moreover, we further introduce group equivariant CNN to 3D, by defining theconvolution operator on a symmetry group acting on $\mathbb{Z}^3$ and itsisomorphic sets. This improves the expressive capacity without increasingparameters, leading to more robust segmentation results. We highlight theperformance on standard benchmarks and show that our approach outperformsstate-of-the-art segmentation algorithms on the ShapeNet and S3DIS datasets.

VV-Net: Voxel VAE Net with Group Convolutions for Point Cloud Segmentation