  Recently, various convolutions based on continuous or discrete kernels for
point cloud processing have been widely studied, and achieve impressive
performance in many applications, such as shape classification, scene
segmentation and so on. However, they still suffer from some drawbacks. For
continuous kernels, the inaccurate estimation of the kernel weights constitutes
a bottleneck for further improving the performance; while for discrete ones,
the kernels represented as the points located in the 3D space are lack of rich
geometry information. In this work, rather than defining a continuous or
discrete kernel, we directly embed convolutional kernels into the learnable
potential fields, giving rise to potential convolution. It is convenient for us
to define various potential functions for potential convolution which can
generalize well to a wide range of tasks. Specifically, we provide two simple
yet effective potential functions via point-wise convolution operations.
Comprehensive experiments demonstrate the effectiveness of our method, which
achieves superior performance on the popular 3D shape classification and scene
segmentation benchmarks compared with other state-of-the-art point convolution
methods.
