# The Impact of Changes in Resolution on the Persistent Homology of Images

arXiv: https://arxiv.org/abs/2111.05663 · HTML: https://mlsanity.com/paper/2111.05663/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 28 references that are in the map.
- First posted on arXiv 10 Nov 2021.

## Builds on (most cited first, 2 of 2)

- [giotto-tda: A Topological Data Analysis Toolkit for Machine Learning and Data Exploration](https://mlsanity.com/paper/2004.02551/) (2020)
- [Homotopy Reconstruction via the Cech Complex and the Vietoris-Rips Complex](https://mlsanity.com/paper/1903.06955/) (2019)

## Built on by (most cited first, 2 of 2)

- [Capturing Shape Information with Multi-Scale Topological Loss Terms for 3D Reconstruction](https://mlsanity.com/paper/2203.01703/) (2022)
- [Noise-Robust Topology Estimation of 2D Image Data via Neural Networks and Persistent Homology](https://mlsanity.com/paper/2509.09140/) (2025)

## Abstract (arXiv)

Digital images enable quantitative analysis of material properties at micro and macro length scales, but choosing an appropriate resolution when acquiring the image is challenging. A high resolution means longer image acquisition and larger data requirements for a given sample, but if the resolution is too low, significant information may be lost. This paper studies the impact of changes in resolution on persistent homology, a tool from topological data analysis that provides a signature of structure in an image across all length scales. Given prior information about a function, the geometry of an object, or its density distribution at a given resolution, we provide methods to select the coarsest resolution yielding results within an acceptable tolerance. We present numerical case studies for an illustrative synthetic example and samples from porous materials where the theoretical bounds are unknown.