# Denoising 3D images: robustness of persistent homology measures

arXiv: https://arxiv.org/abs/2607.24579 · HTML: https://mlsanity.com/paper/2607.24579/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 55 references that are in the map.
- First posted on arXiv 27 Jul 2026.

## Builds on (most cited first, 9 of 9)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [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)
- [Loss Functions and Metrics in Deep Learning](https://mlsanity.com/paper/2307.02694/) (2023)
- [Reconstruction of three-dimensional porous media using generative adversarial neural networks](https://mlsanity.com/paper/1704.03225/) (2017)
- [Persistence Homology of Networks: Methods and Applications](https://mlsanity.com/paper/1907.08708/) (2019)
- [The persistence landscape and some of its properties](https://mlsanity.com/paper/1810.04963/) (2018)
- [On the choice of weight functions for linear representations of persistence diagrams](https://mlsanity.com/paper/1807.03678/) (2018)

## Abstract (arXiv)

When computing sub/super-level-set persistent homology (PH), the effect of noise may introduce millions of (short-lived) topological generators, presenting an obstacle to both the computation of PH of large 3D images, and any analysis of PH that incorporates the number of generators. As such, it is often necessary to denoise the data before computing its PH. We analyze the PH of synthetic 3D images of porous media in the presence of spatially uncorrelated noise, and perform a comparative analysis of various topological measures (e.g. bottleneck distance, Wasserstein distance, persistence statistics and persistence images) to assess their robustness to both noise and the denoising process (i.e. adding spatially uncorrelated Gaussian noise, and denoising by either a Gaussian convolution or a machine learning approach).