TY - GEN
T1 - Planar Symmetry Detection and Quantification using the Extended Persistent Homology Transform
AU - Bermingham, Nicholas
AU - Robins, Vanessa
AU - Turner, Katharine
N1 - Publisher Copyright:
© 2023 IEEE.
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
KW - Algebraic topology
KW - Continuous mathematics
KW - Human-centered computing
KW - Mathematics of computing
KW - Topology
KW - Visualization
KW - Visualization techniques
UR - http://www.scopus.com/inward/record.url?scp=85183594392&partnerID=8YFLogxK
U2 - 10.1109/TopoInVis60193.2023.00007
DO - 10.1109/TopoInVis60193.2023.00007
M3 - Conference contribution
T3 - Proceedings - 2023 Topological Data Analysis and Visualization, TopoInVis 2023
SP - 1
EP - 9
BT - Proceedings - 2023 Topological Data Analysis and Visualization, TopoInVis 2023
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2023 Topological Data Analysis and Visualization, TopoInVis 2023
Y2 - 22 October 2023
ER -