# Learning Significant Persistent Homology Features for 3D Shape Understanding

arXiv: https://arxiv.org/abs/2602.14228 · HTML: https://mlsanity.com/paper/2602.14228/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 27 references that are in the map.
- First posted on arXiv 15 Feb 2026.

## Builds on (most cited first, 13 of 13)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [A Topological Loss Function for Deep-Learning based Image Segmentation using Persistent Homology](https://mlsanity.com/paper/1910.01877/) (2019)
- [PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures](https://mlsanity.com/paper/1904.09378/) (2019)
- [Topological Deep Learning: A Review of an Emerging Paradigm](https://mlsanity.com/paper/2302.03836/) (2023)
- [RipsNet: a general architecture for fast and robust estimation of the persistent homology of point clouds](https://mlsanity.com/paper/2202.01725/) (2022)
- [Topology-Aware Latent Diffusion for 3D Shape Generation](https://mlsanity.com/paper/2401.17603/) (2024)
- [Can neural networks learn persistent homology features?](https://mlsanity.com/paper/2011.14688/) (2020)
- [Topological Methods in Machine Learning: A Tutorial for Practitioners](https://mlsanity.com/paper/2409.02901/) (2024)
- [Computing Wasserstein Distance for Persistence Diagrams on a Quantum Computer](https://mlsanity.com/paper/1809.06433/) (2018)
- [The Flood Complex: Large-Scale Persistent Homology on Millions of Points](https://mlsanity.com/paper/2509.22432/) (2025)
- [Synthetic Data Generation and Deep Learning for the Topological Analysis of 3D Data](https://mlsanity.com/paper/2309.16968/) (2023)
- [STITCH: Surface reconstrucTion using Implicit neural representations with Topology Constraints and persistent Homology](https://mlsanity.com/paper/2412.18696/) (2024)

## Built on by (most cited first, 3 of 3)

- [A Persistent Homology Design Space for 3D Point Cloud Deep Learning](https://mlsanity.com/paper/2604.04299/) (2026)
- [Auditing Training-Free 3D Shape Retrieval with Diffused Geodesic Moments](https://mlsanity.com/paper/2605.29004/) (2026)
- [HyperShadow: A Benchmark for Detecting 3D Projections of Higher-Dimensional Spatial Objects](https://mlsanity.com/paper/2607.14419/) (2026)

## Abstract (arXiv)

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, textitTopoGAT, 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.