HGNet: Learning Hierarchical Geometry from Points, Edges, and Surfaces

Parsing an unstructured point set into constituent local geometry structures (e.g., edges or surfaces) would be helpful for understanding and representing point clouds. This motivates us to design a deep architecture to model the hierarchical geometry from points, edges, surfaces (triangles), to super-surfaces (adjacent surfaces) for the thorough analysis of point clouds. In this paper, we present a novel Hierarchical Geometry Network (HGNet) that integrates such hierarchical geometry structures from supersurfaces, surfaces, edges, to points in a top-down manner for learning point cloud representations. Technically, we first construct the edges between every two neighbor points. A point-level representation is learnt with edge-topoint aggregation, i.e., aggregating all connected edges into the anchor point. Next, as every two neighbor edges compose a surface, we obtain the edge-level representation of each anchor edge via surface-to-edge aggregation over all neighbor surfaces. Furthermore, the surface-level representation is achieved through super-surface-to-surface aggregation by transforming all super-surfaces into the anchor surface. A Transformer structure is finally devised to unify all the point-level, edge-level, and surface-level features into the holistic point cloud representations. Extensive experiments on four point cloud analysis datasets demonstrate the superiority of HGNet for 3D object classification and part/semantic segmentation tasks. More remarkably, HGNet achieves the overall accuracy of 89.2% on ScanOb-jectNN, improving PointNeXt-S by 1.5%.