  Modeling the local surface geometry is challenging in 3D point cloud
understanding due to the lack of connectivity information. Most prior works
model local geometry using various convolution operations. We observe that the
convolution can be equivalently decomposed as a weighted combination of a local
and a global component. With this observation, we explicitly decouple these two
components so that the local one can be enhanced and facilitate the learning of
local surface geometry. Specifically, we propose Laplacian Unit (LU), a simple
yet effective architectural unit that can enhance the learning of local
geometry. Extensive experiments demonstrate that networks equipped with LUs
achieve competitive or superior performance on typical point cloud
understanding tasks. Moreover, through establishing connections between the
mean curvature flow, a further investigation of LU based on curvatures is made
to interpret the adaptive smoothing and sharpening effect of LU. The code will
be available.
