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On the Axial Symmetry of 2D Star-Shaped Sets

Autor(es) y otros:
López Díaz, María ConcepciónAutoridad Uniovi; López Díaz, MiguelAutoridad Uniovi
Palabra(s) clave:

Kernel of a star-shaped set · Measure of axial symmetry · Radial function · Star-shaped set · Steiner point · Symmetry axis

Fecha de publicación:
2025
Versión del editor:
https://doi.org/10.1007/s10851-024-01222-w
Citación:
Journal of Mathematical Imaging and Vision, 67 (2025); doi:10.1007/s10851-024-01222-w
Resumen:

An essential aspect of the study of shapes is the symmetry because of its importance from a theoretical point of view and its applicability in multiple real-life problems. In this manuscript, the axial symmetry of 2D star-shaped sets is analyzed. For such a purpose, different measures of axial symmetry of a star-shaped set are proposed and the concept of a best symmetry axis is also introduced. By means of them, families of symmetry measures for star-shaped sets quantifying the degree of symmetry of a set of that class are introduced. All of them are discussed in detail, providing their main properties and the existence of at least a best axis of symmetry, which could be not unique, for any star-shaped set. Some examples illustrate the concepts and results of the manuscript.

An essential aspect of the study of shapes is the symmetry because of its importance from a theoretical point of view and its applicability in multiple real-life problems. In this manuscript, the axial symmetry of 2D star-shaped sets is analyzed. For such a purpose, different measures of axial symmetry of a star-shaped set are proposed and the concept of a best symmetry axis is also introduced. By means of them, families of symmetry measures for star-shaped sets quantifying the degree of symmetry of a set of that class are introduced. All of them are discussed in detail, providing their main properties and the existence of at least a best axis of symmetry, which could be not unique, for any star-shaped set. Some examples illustrate the concepts and results of the manuscript.

URI:
https://hdl.handle.net/10651/76377
DOI:
10.1007/s10851-024-01222-w
Patrocinado por:

Funding: Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. This work was supported by the Spanish Ministry of Science and Innovation (Grant numbers [MTM- PID2019-104486GB-I00] and [MCIU-22-PID2021-123461NB-C22]) and Principado de Asturias Government (Grant number [AYUD/2021/ 50897]).

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