Denoising 3D images: robustness of persistent homology measures

2026-07-27

AI Summary

This study addresses the challenge posed by noise in three-dimensional images, which introduces numerous short-lived topological features that interfere with persistent homology analysis. The authors systematically evaluate the robustness of various topological descriptors—including bottleneck distance, Wasserstein distance, persistence statistics, and persistence images—against spatially uncorrelated Gaussian noise in synthetic porous media images, as well as their response to denoising procedures. By combining Gaussian convolution with machine learning–based denoising techniques and computing persistent homology via sublevel and superlevel sets, the work reveals distinct sensitivities among these metrics to both noise and denoising strategies. The findings demonstrate the superior stability of certain descriptors in preserving essential topological structures, thereby offering theoretical grounding and practical guidance for reliable topological analysis of three-dimensional imaging data.

Abstract

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).

Problem

• denoising
• 3D images
• persistent homology
• topological noise
• porous media

Innovation

• persistent homology
• denoising
• 3D images
• topological robustness
• porous media