# Synthetic Data Generation and Deep Learning for the Topological Analysis of 3D Data

arXiv: https://arxiv.org/abs/2309.16968 · HTML: https://mlsanity.com/paper/2309.16968/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 41 references that are in the map.
- First posted on arXiv 29 Sep 2023.

## Builds on (most cited first, 16 of 16)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [Deep Learning for 3D Point Clouds: A Survey](https://mlsanity.com/paper/1912.12033/) (2019)
- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [A roadmap for the computation of persistent homology](https://mlsanity.com/paper/1506.08903/) (2015)
- [Deep Learning with Topological Signatures](https://mlsanity.com/paper/1707.04041/) (2017)
- [Surface Representation for Point Clouds](https://mlsanity.com/paper/2205.05740/) (2022)
- [RipsNet: a general architecture for fast and robust estimation of the persistent homology of point clouds](https://mlsanity.com/paper/2202.01725/) (2022)
- [PI-Net: A Deep Learning Approach to Extract Topological Persistence Images](https://mlsanity.com/paper/1906.01769/) (2019)
- [A persistent homology approach to heart rate variability analysis with an application to sleep-wake classification](https://mlsanity.com/paper/1908.06856/) (2019)
- [TDA-Net: Fusion of Persistent Homology and Deep Learning Features for COVID-19 Detection in Chest X-Ray Images](https://mlsanity.com/paper/2101.08398/) (2021)
- [Can neural networks learn persistent homology features?](https://mlsanity.com/paper/2011.14688/) (2020)
- [Repulsive Surfaces](https://mlsanity.com/paper/2107.01664/) (2021)
- [Deep Learning with Persistent Homology for Orbital Angular Momentum (OAM) Decoding](https://mlsanity.com/paper/1911.06858/) (2019)

## Built on by (most cited first, 4 of 4)

- [Learning Significant Persistent Homology Features for 3D Shape Understanding](https://mlsanity.com/paper/2602.14228/) (2026)
- [Noise-Robust Topology Estimation of 2D Image Data via Neural Networks and Persistent Homology](https://mlsanity.com/paper/2509.09140/) (2025)
- [Generating Topologically and Geometrically Diverse Manifold Data in Dimensions Four and Below](https://mlsanity.com/paper/2410.07115/) (2024)
- [Challenges in 3D Data Synthesis for Training Neural Networks on Topological Features](https://mlsanity.com/paper/2511.04972/) (2025)

## Abstract (arXiv)

This research uses deep learning to estimate the topology of manifolds represented by sparse, unordered point cloud scenes in 3D. A new labelled dataset was synthesised to train neural networks and evaluate their ability to estimate the genus of these manifolds. This data used random homeomorphic deformations to provoke the learning of visual topological features. We demonstrate that deep learning models could extract these features and discuss some advantages over existing topological data analysis tools that are based on persistent homology. Semantic segmentation was used to provide additional geometric information in conjunction with topological labels. Common point cloud multi-layer perceptron and transformer networks were both used to compare the viability of these methods. The experimental results of this pilot study support the hypothesis that, with the aid of sophisticated synthetic data generation, neural networks can perform segmentation-based topological data analysis. While our study focused on simulated data, the accuracy achieved suggests a potential for future applications using real data.