  PointNet, which is the widely used point-wise embedding method and known as a
universal approximator for continuous set functions, can process one million
points per second. Nevertheless, real-time inference for the recent development
of high-performing sensors is still challenging with existing neural
network-based methods, including PointNet. In ordinary cases, the embedding
function of PointNet behaves like a soft-indicator function that is activated
when the input points exist in a certain local region of the input space.
Leveraging this property, we reduce the computational costs of point-wise
embedding by replacing the embedding function of PointNet with the
soft-indicator function by Gaussian kernels. Moreover, we show that the
Gaussian kernels also satisfy the universal approximation theorem that PointNet
satisfies. In experiments, we verify that our model using the Gaussian kernels
achieves comparable results to baseline methods, but with much fewer
floating-point operations per sample up to 92% reduction from PointNet.
