Learning Significant Persistent Homology Features for 3D Shape Understanding

Abstract: Geometry and topology constitute complementary descriptors of three-dimensional shape, yet existing benchmark datasets primarily capture geometric information while neglecting topological structure. This work addresses this limitation by introducing topologically-enriched versions of ModelNet40 and ShapeNet, where each point cloud is augmented with its corresponding persistent homology features. These benchmarks with the topological signatures establish a foundation for unified geometry-topology learning and enable systematic evaluation of topology-aware deep learning architectures for 3D shape analysis. Building on this foundation, we propose a deep learning-based significant persistent point selection method, \textit{TopoGAT}, that learns to identify the most informative topological features directly from input data and the corresponding topological signatures, circumventing the limitations of hand-crafted statistical selection criteria. A comparative study verifies the superiority of the proposed method over traditional statistical approaches in terms of stability and discriminative power. Integrating the selected significant persistent points into standard point cloud classification and part-segmentation pipelines yields improvements in both classification accuracy and segmentation metrics. The presented topologically-enriched datasets, coupled with our learnable significant feature selection approach, enable the broader integration of persistent homology into the practical deep learning workflows for 3D point cloud analysis.