Robust Kernel-based Feature Representation for 3D Point Cloud Analysis via Circular Graph Convolutional Network

Feature descriptor of the point cloud is used in many applications such as registration and part segmentation from 3D point clouds. Discriminative representations of the local geometric features is unquestionably the most important task for accurate point cloud analyses. However, it is challenging to develop rotation or scale invariant descriptors. Most of the previous works have either ignored rotations or empirically studied optimal scale parameters, which hinder the applicability of the methods for real-world datasets. In this paper, we present a new local feature description method that is robust to rotation, density, and scales. Moreover, to improve representations of the local descriptors, we propose a global aggregation method. First, we place kernels aligned around each point regarding the normal direction. To avoid the sign problem of the normal vector, we use symmetric kernel point distribution regarding the tangent plane. From each kernel point, we first projected the points from the spatial space to the feature space, which is robust to multiscale and rotation, based on angles and distances. Subsequently, we perform graph convolutions by considering local kernel point structures and long-ranged global context, obtained by a global aggregation method. We experimented with our proposed descriptors on the benchmark datasets (i.e., ModelNet40 and ShapeNetPart) to evaluate the performance of registration, classification, and part segmentation on 3D point clouds. Our methods showed superior performances compared to the state-of-the-art methods by reducing 70$\%$ of the rotation and translation errors in the registration task. Our method also showed comparable performance in the classification and part segmentation tasks without any external data augmentations.