Learning Significant Persistent Homology Features for 3D Shape Understanding

2026-02-15

AI Summary

This work addresses the lack of topological information in existing 3D shape datasets, which hinders joint geometric and topological learning. To bridge this gap, the authors introduce the first topologically enriched versions of the ModelNet40 and ShapeNet benchmark datasets by incorporating persistent homology features. They propose TopoGAT, an end-to-end graph attention network architecture that employs a learnable mechanism to select the most salient persistence diagram points, thereby automatically extracting discriminative topological features. Evaluated on 3D point cloud classification and part segmentation tasks, TopoGAT significantly outperforms conventional handcrafted topological feature methods, demonstrating the critical role of topological information in enhancing both model performance and robustness.

Technology Category

• Machine Learning: Learning with Manifolds
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Computer Vision: Generative Adversarial Networks (GANs) for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Large pretrained models with web data

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.

Problem

• persistent homology
• 3D shape understanding
• topological structure
• point cloud analysis
• geometry-topology learning

Innovation

• persistent homology
• topological data analysis
• 3D shape understanding
• deep learning
• TopoGAT