Cited by 405Morphological variations and asymmetryAdvanced Statistical Methods and ModelsStatistical Methods and Applications

Statistical assessment of bilateral symmetry of shapes

Mardia, K.·2000·Biometrika

Abstract

SUMMARY This paper formulates the problem of measuring bilateral symmetry of objects analytically for landmark data, and develops various new testing procedures and exploratory data analyses. The development is linked with the fundamental biological problem of measuring directional asymmetry and fluctuating asymmetry. We distinguish two types of symmetry, object symmetry and matching symmetry, and provide tests under assumptions of isotropic landmark variability as well as non-isotropy. The tests require novel statistical and geometrical analyses of the Procrustes shape manifold. For describing components of symmetry and asymmetry within samples, an extension of principal component analysis is introduced and illustrated by appropriate deformation techniques. Various real examples are used to illustrate the practical relevance of this work.

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Crossref · 10.1093/biomet/87.2.285

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15 of 15 references verified0 citation errors · 0 not checkable

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  • Human skulls exhibit object symmetry (the axis of symmetry passes through mid-plane, and the left and right halves are mirror images of each other).

    “Human skulls exhibit object symmetry (i.e. the axis of symmetry passes through mid-plane, and hence the left and right halves are mirror images of each other), therefore the recommendations of [100,101] were followed.”

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Authors
Mardia, K.
Affiliations
University of Leeds (GB)
Corresponding author
Mardia, K.
Venue
Biometrika
Published
2000-06-01
Volume
87
Issue
2
Pages
285-300
ISSN
  • 0006-3444 (ISSN-L)
  • 1464-3510
OpenAlex
W2130075045
Cited by
405
References
15
Citations by year
2026: 12 · 2025: 17 · 2024: 8 · 2023: 12 · 2022: 11 · 2021: 33 · 2020: 29 · 2019: 29 · 2018: 35 · 2017: 24 · 2016: 28 · 2015: 16 · 2014: 25 · 2013: 15 · 2012: 16
FWCI
7.36
Type
journal article
Language
en
Open access
closed
Locations
Biometrika (publishedVersion)
Topics
  • Physical Sciences › Mathematics › Geometry and Topology › Morphological variations and asymmetry
  • Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
Keywords
bilateral symmetry, fluctuating asymmetry, directional asymmetry, landmark data, object symmetry, shape deformation

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