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.

翻译：由于缺乏连通性信息,当地地表几何学模型在3D点云理解方面具有挑战性。大多数以前的工作模型都是使用各种卷变操作的地方几何学模型。我们观察到,这种演化可以等同于当地部分和全球部分的加权组合。我们通过观察,明确分离这两个组成部分,以便当地部分能够得到加强,便于学习当地的地表几何学。具体地说,我们提议拉普拉西亚单位(LU),这是一个简单而有效的建筑单位,可以加强当地几何学。广泛的实验表明,配备LU的网络在典型点云理解任务上取得了竞争性或优异性。此外,通过在平均曲线流之间建立联系,根据曲线对LU进行进一步调查,以解释LU的适应性光滑和锐化效果。代码将可用。