  Research in point cloud analysis with deep neural networks has made rapid
progress in recent years. The pioneering work PointNet offered a direct
analysis of point clouds. However, due to its architecture PointNet is not able
to capture local structures. To overcome this drawback, the same authors have
developed PointNet++ by applying PointNet to local areas. The local areas are
defined by center points and their neighbors. In PointNet++ and its further
developments the center points are determined with a Farthest Point Sampling
(FPS) algorithm. This has the disadvantage that the center points in general do
not have meaningful local areas. In this paper, we introduce the neural
Local-Area-Learning Network (LocAL-Net) which places emphasis on the selection
and characterization of the local areas. Our approach learns critical points
that we use as center points. In order to strengthen the recognition of local
structures, the points are given additional metric properties depending on the
local areas. Finally, we derive and combine two global feature vectors, one
from the whole point cloud and one from all local areas. Experiments on the
datasets ModelNet10/40 and ShapeNet show that LocAL-Net is competitive for part
segmentation. For classification LocAL-Net outperforms the state-of-the-arts.
