Planar Symmetry Detection and Quantification using the Extended Persistent Homology Transform

Nicholas Bermingham, Vanessa Robins, Katharine Turner

    Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

    Abstract

    Symmetry is ubiquitous throughout nature and can often give great insights into the formation, structure and stability of objects studied by mathematicians, physicists, chemists and biologists. However, perfect symmetry occurs rarely so quantitative techniques must be developed to identify approximate symmetries. To facilitate the analysis of an independent variable on the symmetry of some object, we would like this quantity to be a smoothly varying real parameter rather than a boolean one. The extended persistent homology transform is a recently developed tool which can be used to define a distance between certain kinds of objects. Here, we describe how the extended persistent homology transform can be used to visualise, detect and quantify certain kinds of symmetry and discuss the effectiveness and limitations of this method.

    Original languageEnglish
    Title of host publicationProceedings - 2023 Topological Data Analysis and Visualization, TopoInVis 2023
    PublisherInstitute of Electrical and Electronics Engineers Inc.
    Pages1-9
    Number of pages9
    ISBN (Electronic)9798350329643
    DOIs
    Publication statusPublished - 2023
    Event2023 Topological Data Analysis and Visualization, TopoInVis 2023 - Hybrid, Melbourne, Australia
    Duration: 22 Oct 2023 → …

    Publication series

    NameProceedings - 2023 Topological Data Analysis and Visualization, TopoInVis 2023

    Conference

    Conference2023 Topological Data Analysis and Visualization, TopoInVis 2023
    Country/TerritoryAustralia
    CityHybrid, Melbourne
    Period22/10/23 → …

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