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Modeling the local surface geometry is challenging in 3D point cloudunderstanding due to the lack of connectivity information. Most prior worksmodel local geometry using various convolution operations. We observe that theconvolution can be equivalently decomposed as a weighted combination of a localand a global component. With this observation, we explicitly decouple these twocomponents so that the local one can be enhanced and facilitate the learning oflocal surface geometry. Specifically, we propose Laplacian Unit (LU), a simpleyet effective architectural unit that can enhance the learning of localgeometry. Extensive experiments demonstrate that networks equipped with LUsachieve competitive or superior performance on typical point cloudunderstanding tasks. Moreover, through establishing connections between themean curvature flow, a further investigation of LU based on curvatures is madeto interpret the adaptive smoothing and sharpening effect of LU. The code willbe available.

Enhancing Local Geometry Learning for 3D Point Cloud via Decoupling Convolution