Resumen
The study of convolutional neural networks for 3D point clouds is becoming increasingly popular, and the difficulty lies mainly in the disorder and irregularity of point clouds. At present, it is straightforward to propose a convolution operation and perform experimental validation. Although good results are achieved, the principles behind them are not explained?i.e., why this can solve the disorder and irregularity of point clouds?and it is difficult for the researchers to design a point cloud convolution network suitable for their needs. For this phenomenon, we propose a point convolution network framework based on spatial location correspondence. Following the correspondence principle can guide us in designing convolution networks adapted to our needs. We analyzed the intrinsic mathematical nature of the convolution operation, and we argue that the convolution operation remains the same when the spatial location correspondence between the convolution kernel points and the convolution range elements remains unchanged. Guided by this principle, we formulated a general point convolution framework based on spatial location correspondence, which explains how to handle a disordered point cloud. Moreover, we discuss different kinds of correspondence based on spatial location, including M-to-M, M-to-N, and M-to-1 relationships, etc., which explain how to handle the irregularity of point clouds. Finally, we give the example of a point convolution network whose convolution kernel points are generated based on the sample?s covariance matrix distribution according to our framework. Our convolution operation can be applied to various point cloud processing networks. We demonstrated the effectiveness of our framework for point cloud classification and semantic segmentation tasks, achieving competitive results with state-of-the-art networks.