Unveiling topology in imaging problems via quasi-isometry and persistent homology

Mathematics > Algebraic Topology [Submitted on 16 Jun 2026] Title:Unveiling topology in imaging problems via quasi-isometry and persistent homology View PDFAbstract:We show that the topological structures, such as loops, voids, and higher-dimensional holes of unknown objects (of flow of an object in space-time) can be recovered from noisy and indirect measurements. More precisely, we describe how the part of the persistent homology of a space can be determined from a noise-prone and discretized model space when there is a quasi-isometry between the original space and the space modeling indirect measurements. The result not only guarantees the existence of the structures but also provides size bounds for them. The structure is studied using persistent homology, and the results assume the existence of a quasi-isometry between a model space and the noisy measurements. We explore imaging problems, particularly X-ray imaging and EIT, that are well-suited to this framework. References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.