Statistical assessment of bilateral symmetry of shapes
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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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.”
From Morphological consequences of artificial cranial deformation: Modularity and integration (2020) · cites this paper as [100]
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Klingenberg, C. P. (2020) · Evolutionary Biology · doi:10.1007/s11692-020-09513-x · Cited by 52 · see citing works
Giri, F., & Loy, A. (2008) · Journal of Crustacean Biology · doi:10.1651/07-2824r.1 · Cited by 53 · see citing works
White, J., Ayoub, A. F., Hosey, M. T., Bock, M., BOWMAN, A. W., Bowman, J., Siebert, J. P., & Ray, A. (2004) · The Cleft Palate-Craniofacial Journal · doi:10.1597/03-069.1 · Cited by 52 · see citing works
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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
- 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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