PolyhedronNet: Representation Learning for Polyhedra with Surface-attributed Graph

• DOI: 10.48550/arxiv.2502.01814
• Publication Date: 2025-02-03
• Authors: Dazhou Yu; Ganchao Zhang; Liang Zhao
• Keywords: Polyhedron; Representation

Ubiquitous geometric objects can be precisely and efficiently represented as polyhedra. The transformation of a polyhedron into vector, known polyhedra representation learning, is crucial for manipulating these shapes with mathematical statistical tools tasks like classification, clustering, generation. Recent years have witnessed significant strides in this domain, yet most efforts focus on the vertex sequence polyhedron, neglecting complex surface modeling real-world polyhedral objects. This study proposes \textbf{PolyhedronNet}, general framework tailored learning representations 3D We propose concept surface-attributed graph to seamlessly model vertices, edges, faces, their interrelationships within polyhedron. To effectively learn entire graph, we first break it down local rigid each region's relative positions against remaining regions without information loss. Subsequently, PolyhedronGNN hierarchically aggregate via intra-face inter-face message passing modules, obtain global that minimizes loss while maintaining rotation translation invariance. Our experimental evaluations four distinct datasets, encompassing both classification retrieval tasks, substantiate PolyhedronNet's efficacy capturing comprehensive informative Code data are available at {https://github.com/dyu62/3D_polyhedron}.