PointWavelet: Learning in Spectral Domain for 3-D Point Cloud Analysis.

With recent success of deep learning in 2-D visual recognition, deep-learning-based 3-D point cloud analysis has received increasing attention from the community, especially due to the rapid development of autonomous driving technologies. However, most existing methods directly learn point features in the spatial domain, leaving the local structures in the spectral domain poorly investigated. In this article, we introduce a new method, PointWavelet, to explore local graphs in the spectral domain via a learnable graph wavelet transform. Specifically, we first introduce the graph wavelet transform to form multiscale spectral graph convolution to learn effective local structural representations. To avoid the time-consuming spectral decomposition, we then devise a learnable graph wavelet transform, which significantly accelerates the overall training process. Extensive experiments on four popular point cloud datasets, ModelNet40, ScanObjectNN, ShapeNet-Part, and S3DIS, demonstrate the effectiveness of the proposed method on point cloud classification and segmentation.