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.
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