Heiss, TeresaTymochko, SarahStory, BrittanyGarin, AdélieBui, HoaBleile, BeaRobins, Vanessa2025-06-242025-06-249781665439022http://www.scopus.com/inward/record.url?scp=85125316096&partnerID=8YFLogxKhttps://hdl.handle.net/1885/733764542Digital 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.The authors thank the Mathematical Sciences Institute at ANU, the US National Science Foundation through the award CCF-1841455, the Australian Mathematical Sciences Institute and the Association for Women in Mathematics for funding the second Workshop for Women in Computational Topology in July 2019 where this project began. The project reached completion thanks to funding from the MSRI Summer Research in Mathematics program awarded in 2020. Teresa Heiss has received funding from the ERC under the Horizon 2020 programme (No. 788183). Brittany Story has received funding from NASA Grant #80NSSC21K1700. The authors are also grateful to Kritika Singhal for her input to the first part of the project and to Mathijs Wintraecken for the idea for Remark IV.4.11enPublisher Copyright: © 2021 IEEE.image processingimage resolutionpersistent homology202110.1109/BigData52589.2021.967148385125316096