  Recent advances in deep convolutional neural networks (CNNs) have motivated
researchers to adapt CNNs to directly model points in 3D point clouds. Modeling
local structure has been proven to be important for the success of
convolutional architectures, and researchers exploited the modeling of local
point sets in the feature extraction hierarchy. However, limited attention has
been paid to explicitly model the geometric structure amongst points in a local
region. To address this problem, we propose Geo-CNN, which applies a generic
convolution-like operation dubbed as GeoConv to each point and its local
neighborhood. Local geometric relationships among points are captured when
extracting edge features between the center and its neighboring points. We
first decompose the edge feature extraction process onto three orthogonal
bases, and then aggregate the extracted features based on the angles between
the edge vector and the bases. This encourages the network to preserve the
geometric structure in Euclidean space throughout the feature extraction
hierarchy. GeoConv is a generic and efficient operation that can be easily
integrated into 3D point cloud analysis pipelines for multiple applications. We
evaluate Geo-CNN on ModelNet40 and KITTI and achieve state-of-the-art
performance.
