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]
Citations
Cites
Principal warps: thin-plate splines and the decomposition of deformations
Bookstein, F. L. (1989) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.24792 · Cited by 4,906
Morphometric Tools for Landmark Data
Bookstein, F. L. (1992) · Cambridge University Press eBooks · doi:10.1017/cbo9780511573064 · Cited by 4,481
Procrustes Methods in the Statistical Analysis of Shape
Goodall, C. R. (1991) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1991.tb01825.x · Cited by 2,069
FLUCTUATING ASYMMETRY: Measurement, Analysis, Patterns
Palmer, A. R., & Strobeck, C. (1986) · Annual Review of Ecology and Systematics · doi:10.1146/annurev.es.17.110186.002135 · Cited by 1,701
Shape Manifolds, Procrustean Metrics, and Complex Projective Spaces
Kendall, D. G. (1984) · Bulletin of the London Mathematical Society · doi:10.1112/blms/16.2.81 · Cited by 1,453
A STUDY OF FLUCTUATING ASYMMETRY
Valen, L. V. (1962) · Evolution · doi:10.1111/j.1558-5646.1962.tb03206.x · Cited by 687
Morphometric Tools for Landmark Data: Geometry and Biology
Lele, S. R., & Bookstein, F. L. (1999) · Journal of the American Statistical Association · doi:10.2307/2669711 · Cited by 377
Shape and the Information in Medical Images: A Decade of the Morphometric Synthesis
Bookstein, F. L. (1997) · Computer Vision and Image Understanding · doi:10.1006/cviu.1997.0607 · Cited by 270
The Complex Bingham Distribution and Shape Analysis
Kent, J. T. (1994) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1994.tb01978.x · Cited by 263
Fluctuating asymmetry in the honey bee,
Smith, D. R., Crespi, B. J., & Bookstein, F. L. (1997) · Journal of Evolutionary Biology · doi:10.1007/s000360050041 · Cited by 134
Multivariate Aspects of Shape Theory
Goodall, C. R., & Mardia, K. V. (1993) · The Annals of Statistics · doi:10.1214/aos/1176349154 · Cited by 99
Self-citationCerebral asymmetry and cerebellar atrophy in schizophrenia: a controlled postmortem study
Luchins, D. J., Morihisa, J. M., Weinberger, D. R., & Wyatt, R. J. (1981) · American Journal of Psychiatry · doi:10.1176/ajp.138.11.1501 · Cited by 60
Fluctuating asymmetry measurement
Sullivan, M., Robertson, P., & Aebischer, N. J. (1993) · Nature · doi:10.1038/361409b0 · Cited by 52
Three dimensional MR-based morphometric comparison of schizophrenic and normal cerebral ventricles
Dean, D., Buckley, P. F., Bookstein, F. L., Kamath, J., Kwon, D. N., Friedman, L., & Lys, C. (1996) · Lecture notes in computer science · doi:10.1007/bfb0046975 · Cited by 35
Buckley, P. F., Dean, D., Bookstein, F. L., Friedman, L., Kwon, D. N., Lewin, J. S., Kamath, J., & Lys, C. (1999) · Biological Psychiatry · doi:10.1016/s0006-3223(98)00067-5 · Cited by 31
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Morpho J: an integrated software package for geometric morphometrics
Klingenberg, C. P. (2010) · Molecular Ecology Resources · doi:10.1111/j.1755-0998.2010.02924.x · Cited by 3,784
Geometric morphometrics: Ten years of progress following the ‘revolution’
Adams, D. C., Rohlf, F. J., & Slice, D. E. (2004) · The European Zoological Journal · doi:10.1080/11250000409356545 · Cited by 2,281
Advances in Geometric Morphometrics
Mitterœcker, P., & Gunz, P. (2009) · Evolutionary Biology · doi:10.1007/s11692-009-9055-x · Cited by 1,416
Shape analysis of symmetric structures: quantifying variation among individuals and asymmetry
Klingenberg, C. P., Barluenga, M., & Meyer, A. (2002) · Evolution · doi:10.1111/j.0014-3820.2002.tb00117.x · Cited by 1,109
A field comes of age: geometric morphometrics in the 21 st century
Adams, D. C., Rohlf, F. J., & Slice, D. E. (2013) · Bollettino del CILEA (CILEA) · doi:10.4404/hystrix-24.1-6283 · Cited by 719
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
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