  Feature descriptors of point clouds are used in several applications, such as
registration and part segmentation of 3D point clouds. Learning discriminative
representations of 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 previous studies have
either ignored rotations or empirically studied optimal scale parameters, which
hinders 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 scale variations. Moreover, to improve representations
of the local descriptors, we propose a global aggregation method. First, we
place kernels aligned around each point in the normal direction. To avoid the
sign problem of the normal vector, we use a symmetric kernel point distribution
in the tangential plane. From each kernel point, we first projected the points
from the spatial space to the feature space, which is robust to multiple scales
and rotation, based on angles and distances. Subsequently, we perform graph
convolutions by considering local kernel point structures and long-range global
context, obtained by a global aggregation method. We experimented with our
proposed descriptors on benchmark datasets (i.e., ModelNet40 and ShapeNetPart)
to evaluate the performance of registration, classification, and part
segmentation on 3D point clouds. Our method showed superior performances when
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 with simple and
low-dimensional architectures.
