Statistical assessment of bilateral symmetry of shapes

By Kanti V. Mardia, Fred L. Bookstein, Ian J. Moreton. 2000

414 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/5a6be99aeefab4b4d495337d0e41a723d2934776

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In Geometry and Topology

Citations in the corpus

Fluctuating Asymmetry: Methods, Theory, and Applications (2010, background): “Bilateral symmetry can be either matching symmetry or object symmetry [63].”
Principles for the virtual reconstruction of hominin crania. (2009, methodology): “This requires the specification of paired (bilateral) and unpaired (‘‘midsagittal’’) points (Mardia et al., 2000; Bookstein and Mardia, 2003; Bookstein, 2005).”
The Concept of Morphospaces in Evolutionary and Developmental Biology: Mathematics and Metaphors (2009, background): “The full shape space can also be partitioned into different subspaces based on statistical and geometrical criteria such as symmetric versus asymmetric shape variation, functional significance, integrated versus modular variation, or the geometric scale of shape variation (Bookstein 1989; Rasskin-Gu”
MorphoJ: an integrated software package for geometric morphometrics (2011, background): “Symmetric structures, such as vertebrate skulls, are frequently used in morphometric studies and pose some special challenges (Mardia et al. 2000; Klingenberg et al. 2002).”
Developmental instability as a research tool: using patterns of fluctuating asymmetry to infer the developmental origins of morphological integration. (2003, methodology): “…asymmetry, reflection is removed by transforming all configurations from one body side to their mirror images (for matching symmetry; Klingenberg and McIntyre 1998) or by including both the originals and mirror images of all configurations to the analysis (for object symmetry; Mardia et al. 2000).”
Advances in Geometric Morphometrics (2009, methodology): “The actual computation is based on a Procrustes superimposition of the landmark configurations together with their relabeled reflections (Bookstein 1991; Klingenberg and McIntyre 1998; Mardia et al. 2000).”
A field comes of age: geometric morphometrics in the 21 st century (2013, methodology): “Subsequently, a mathematical decomposition of shape variation into its symmetry components (for bilaterally symmetric shapes) was derived (Mardia et al., 2000; Kent and Mardia, 2001), and recent extensions of the approach have been proposed for other types of symmetry (Savriama and Klingenberg,…”
MORPHOLOGICAL AND ECOLOGICAL VARIATION WITHIN THE ACHNANTHIDIUM MINUTISSIMUM (BACILLARIOPHYCEAE) SPECIES COMPLEX 1 (2007, background): “Central nodule, Voigt faults, vestigial raphe slits in developing rapheless valves, copulae, and chiplike cuts in the valve mantle, described by Mayama and Kobayasi (1989) for Achnanthes minutissima var. saprophila, are weakly expressed or poorly developed valve characters of limited to no value in…”
Fluctuating asymmetry and exogenous stress in fishes: a review (2011, neutral): “…that partitioned shape variation into components of symmetric shape and of asymmetry (Bookstein 1996; Auffray et al. 1999) with a formal test for directional asymmetry (Mardia et al. 2000; Kent and Mardia 2001), providing a framework for analyses of asymmetry for two- and three-dimensional data.”
A brief review of shape, form, and allometry in geometric morphometrics, with applications to human facial morphology (2013, methodology): “After sliding the semilandmarks, all 44 landmark configurations were superimposed by a Generalized Procrustes Analysis and symmetrized by averaging each landmark configuration with its relabeled reflection (Mardia et al., 2000; Mitteroecker and Gunz, 2009).”
Analyzing Fluctuating Asymmetry with Geometric Morphometrics: Concepts, Methods, and Applications (2015, methodology): “This approach is a direct extension of the method for object symmetry with bilateral symmetry [12,13,214].”