  Recent progresses in 3D deep learning has shown that it is possible to design
special convolution operators to consume point cloud data. However, a typical
drawback is that rotation invariance is often not guaranteed, resulting in
networks being trained with data augmented with rotations. In this paper, we
introduce a novel convolution operator for point clouds that achieves rotation
invariance. Our core idea is to use low-level rotation invariant geometric
features such as distances and angles to design a convolution operator for
point cloud learning. The well-known point ordering problem is also addressed
by a binning approach seamlessly built into the convolution. This convolution
operator then serves as the basic building block of a neural network that is
robust to point clouds under 6DoF transformations such as translation and
rotation. Our experiment shows that our method performs with high accuracy in
common scene understanding tasks such as object classification and
segmentation. Compared to previous works, most importantly, our method is able
to generalize and achieve consistent results across different scenarios in
which training and testing can contain arbitrary rotations.
