  With the increased availability of 3D scanning technology, point clouds are
moving into the focus of computer vision as a rich representation of everyday
scenes. However, they are hard to handle for machine learning algorithms due to
their unordered structure. One common approach is to apply occupancy grid
mapping, which dramatically increases the amount of data stored and at the same
time loses details through discretization. Recently, deep learning models were
proposed to handle point clouds directly and achieve input permutation
invariance. However, these architectures often use an increased number of
parameters and are computationally inefficient. In this work, we propose basis
point sets (BPS) as a highly efficient and fully general way to process point
clouds with machine learning algorithms. The basis point set representation is
a residual representation that can be computed efficiently and can be used with
standard neural network architectures and other machine learning algorithms.
Using the proposed representation as the input to a simple fully connected
network allows us to match the performance of PointNet on a shape
classification task while using three orders of magnitude less floating-point
operations. In a second experiment, we show how the proposed representation can
be used for registering high-resolution meshes to noisy 3D scans. Here, we
present the first method for single-pass high-resolution mesh registration,
avoiding time-consuming per-scan optimization and allowing real-time execution.
