Learning geometric complexes for 3D shape classification

Abstract

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.