Denoising 3D images: robustness of persistent homology measures
2026-07-27 • Computational Geometry
Computational GeometryComputer Vision and Pattern Recognition
AI summaryⓘ
The authors study how noise affects the calculation of persistent homology (PH), a method used to understand shapes in 3D images, especially for porous materials. Noise creates many small, short-lived features that make PH computations and analysis difficult. They compare different ways to measure PH and test how well these measurements handle noisy data and denoising methods like Gaussian blurring and machine learning filtering. Their goal is to find robust approaches for analyzing PH in the presence of noise.
persistent homologysub-level setsuper-level settopological generatorsbottleneck distanceWasserstein distanceGaussian noisedenoisingmachine learningporous media
Authors
Ebru Dagdelen, Aakash Karlekar, Manav Arora, Matthew Illingsworth, Jonathan Jaquette, Linda J. Cummings, Lou Kondic
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).