A Persistent Homology Design Space for 3D Point Cloud Deep Learning
This work addresses the insufficient modeling of topological structures in existing deep learning approaches for 3D point clouds, where persistent homology has largely been relegated to peripheral roles. The authors introduce 3DPHDL—the first systematic design space that deeply integrates persistent homology as a structural inductive bias throughout the entire point cloud learning pipeline. This integration encompasses six well-defined injection points spanning simplicial complex construction, filtration strategies, persistence representations, and their coordination with backbone architectures. Through controlled experiments on PointNet, DGCNN, and Point Transformer—augmented with persistence diagrams, images, and landscapes—on ModelNet40 and ShapeNetPart, the approach significantly improves accuracy in classification and segmentation, enhances part consistency, and boosts robustness to noise and sampling variations, while also revealing inherent trade-offs between representational capacity and computational complexity.