Point Geometrical Coulomb Force: An explicit and robust embedding for point cloud analysis

Recently, most existing point cloud frameworks tend to utilize max pooling aggregation functions to aggregate local point cloud features. However, when handling data containing local high-frequency noise such as local drop, addition, and jitter, this mechanism leads to high-frequency noise that spreads from local to global and causes severe performance degradation. To address this issue, we creatively extend the concepts from the physical field, namely electrostatic field and Coulomb forceinto geometric processing. To be specific, we treat the entire point cloud placed in an electrostatic field and each point as a probe charge and then equip this field with a set of source charges according to the structure of the cloud. We endow these two types of charges with different electric quantities, which could encode informative geometrical structural information. By analogously computing the Coulomb force between the probe charge and its corresponding source charge, we finally propose an explicit embedding called Point Geometric Coulomb Force (PGCF) for each point. Due to the deep use of the structural information of the point cloud and the fact that the electrostatic field of each source charge could not be affected by the variations of the probe charges, the PGCF has been proven to provide richer geometric information while being robust to local noises. Using the PGCF combined with point coordinates as inputs can significantly improve the performances of existing 3D point cloud feature extraction frameworks, including point convolution, graph convolution, and point transformer, without additional parameters or computational overhead, thus not affecting their inference speed. Experimental results show that integrating the PGCF into existing works brings more desirable results in a wide range of 3D point cloud analysis tasks, including classification, part segmentation, and semantic segmentation.