The DOI matches its Crossref record; 15 of the 15 references it cites were found in a registry or an index.
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 (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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Metadata
- 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
- 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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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