Learning geometric complexes for 3D shape classification

Geometry and topology are vital elements in discerning and describing the shape of an object. Geometric complexes constructed on the point cloud of a 3D object capture the geometry as well as topological features of the underlying shape space. Leveraging this aspect of geometric complexes, we present an attention-based dual stream graph neural network (DS-GNN) for 3D shape classification. In the first stream of DS-GNN, we introduce spiked skeleton complex (SSC) for learning the shape patterns through comprehensive feature integration of the point cloud’s core structure. SSC is a novel and concise geometric complex comprising principal plane-based cluster centroids complemented with per-centroid spatial locality information. The second stream of DS-GNN consists of alpha complex which facilitates the learning of geometric patterns embedded in the object shapes via higher dimensional simplicial attention. To evaluate the model’s response to different shape topologies, we perform a persistent homology-based object segregation that groups the objects based on the underlying topological space characteristics quantified through the second Betti number. Our experimental study on benchmark datasets such as ModelNet40 and ScanObjectNN shows the potential of the proposed GNN for the classification of 3D shapes with different topologies and offers an alternative to the current evaluation practices in this domain. • Propose a novel dual-stream graph attention-based neural network to extract global and local features from the geometric complex representation of the point cloud for point cloud classification. • Introduce a novel simplicial complex representation of point cloud for non-local feature aggregation for point cloud classification. • Present two feature fusion schemes to effectively combine the features of complementary simplicial complex representations for enhanced overall performance and robustness of the model. • Present grouping of ModelNet40 dataset classes based on topology and rectilinearity. Topological segregation of objects is based on zero Vs non-zero second Betti number of point clouds. Rectilinear segregation is based on the angle between the planes fitted on the point clouds. • Conduct comprehensive evaluations on various benchmarks and segregated datasets to present comparative analysis with state-of-the-art results.