  We propose an octree guided neural network architecture and spherical
convolutional kernel for machine learning from arbitrary 3D point clouds. The
network architecture capitalizes on the sparse nature of irregular point
clouds, and hierarchically coarsens the data representation with space
partitioning. At the same time, the proposed spherical kernels systematically
quantize point neighborhoods to identify local geometric structures in the
data, while maintaining the properties of translation-invariance and asymmetry.
We specify spherical kernels with the help of network neurons that in turn are
associated with spatial locations. We exploit this association to avert dynamic
kernel generation during network training that enables efficient learning with
high resolution point clouds. The effectiveness of the proposed technique is
established on the benchmark tasks of 3D object classification and
segmentation, achieving new state-of-the-art on ShapeNet and RueMonge2014
datasets.
