  With recent success of deep learning in 2D visual recognition, deep
learning-based 3D 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 paper, 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
multi-scale 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.
