# Noise-Robust Topology Estimation of 2D Image Data via Neural Networks and Persistent Homology

arXiv: https://arxiv.org/abs/2509.09140 · HTML: https://mlsanity.com/paper/2509.09140/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 29 references that are in the map.
- First posted on arXiv 11 Sep 2025.

## Builds on (most cited first, 7 of 7)

- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists](https://mlsanity.com/paper/1710.04019/) (2017)
- [A roadmap for the computation of persistent homology](https://mlsanity.com/paper/1506.08903/) (2015)
- [RipsNet: a general architecture for fast and robust estimation of the persistent homology of point clouds](https://mlsanity.com/paper/2202.01725/) (2022)
- [DeePore: a deep learning workflow for rapid and comprehensive characterization of porous materials](https://mlsanity.com/paper/2005.03759/) (2020)
- [Synthetic Data Generation and Deep Learning for the Topological Analysis of 3D Data](https://mlsanity.com/paper/2309.16968/) (2023)
- [The Impact of Changes in Resolution on the Persistent Homology of Images](https://mlsanity.com/paper/2111.05663/) (2021)

## Built on by (most cited first, 1 of 1)

- [Analytic Torsion and Spectral Gap Capture Persistent-Laplacian Performance](https://mlsanity.com/paper/2606.16990/) (2026)

## Abstract (arXiv)

Persistent Homology (PH) and Artificial Neural Networks (ANNs) offer contrasting approaches to inferring topological structure from data. In this study, we examine the noise robustness of a supervised neural network trained to predict Betti numbers in 2D binary images. We compare an ANN approach against a PH pipeline based on cubical complexes and the Signed Euclidean Distance Transform (SEDT), which is a widely adopted strategy for noise-robust topological analysis. Using one synthetic and two real-world datasets, we show that ANNs can outperform this PH approach under noise, likely due to their capacity to learn contextual and geometric priors from training data. Though still emerging, the use of ANNs for topology estimation offers a compelling alternative to PH under structural noise.