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

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Statistical assessment of bilateral symmetry of shapes

Mardia, K.·2000·Biometrika

DOI 10.1093/biomet/87.2.285

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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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Authors: Mardia, K.
Affiliations: University of Leeds (GB)
Corresponding author: Mardia, K.
ORCID: Mardia, K.
Venue: Biometrika
Publisher: Oxford University Press (OUP)
Published: 2000-06-01
Volume: 87
Issue: 2
Pages: 285-300
ISSN: 0006-3444 (ISSN-L)
1464-3510
DOI: 10.1093/biomet/87.2.285
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: Life Sciences › Agricultural and Biological Sciences › Ecology, Evolution, Behavior and Systematics › 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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Statistical assessment of bilateral symmetry of shapes

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