Advances in Geometric Morphometrics

By P. Mitteroecker, P. Gunz. Evolutionary biology, 2009

1,223 citations recorded by the source corpus.

Geometric morphometrics is the statistical analysis of form based on Cartesian landmark coordinates. After separating shape from overall size, position, and orientation of the landmark configurations, the resulting Procrustes shape coordinates can be used for statistical analysis. Kendall shape space, the mathematical space induced by the shape coordinates, is a metric space that can be approximated locally by a Euclidean tangent space. Thus, notions of distance (similarity) between shapes or of the length and direction of developmental and evolutionary trajectories can be meaningfully assessed in this space. Results of statistical techniques that preserve these convenient properties—such as principal component analysis, multivariate regression, or partial least squares analysis—can be visualized as actual shapes or shape deformations. The Procrustes distance between a shape and its relabeled reflection is a measure of bilateral asymmetry. Shape space can be extended to form space by augmenting the shape coordinates with the natural logarithm of Centroid Size, a measure of size in geometric morphometrics that is uncorrelated with shape for small isotropic landmark variation. The thin-plate spline interpolation function is the standard tool to compute deformation grids and 3D visualizations. It is also central to the estimation of missing landmarks and to the semilandmark algorithm, which permits to include outlines and surfaces in geometric morphometric analysis. The powerful visualization tools of geometric morphometrics and the typically large amount of shape variables give rise to a specific exploratory style of analysis, allowing the identification and quantification of previously unknown shape features.

Subfields: Geometry and Topology, Paleontology

View Paper: https://www.semanticscholar.org/paper/c5923dcf52c651642fe9017153c37766164ad149

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Citations in the corpus

Combining Geometric Morphometrics and Finite Element Analysis with Evolutionary Modeling: Towards a Synthesis (2016, background): “…over traditional tests based on parametric F-distributions or Wilks’ lambda because shape variation seldom meets the required assumptions of normality and sample sizes are seldom balanced (Manly, 1991; Zelditch et al., 2004; Mitteroecker and Gunz, 2009; Kowalewski and Novack-Gottshall, 2010).”
Linear Discrimination, Ordination, and the Visualization of Selection Gradients in Modern Morphometrics (2011, positive): “…morphometric methods mainly owes to the typically large number of shape variables and the possibility of visualizing statistical results as actual shapes or shape deformations (Bookstein 1991; O’Higgins 2000; Adams et al. 2004; Slice 2007; Mitteroecker and Gunz 2009; Lawing and Polly 2010).”
A field comes of age: geometric morphometrics in the 21 st century (2013, methodology): “Nearly a decade ago, we reviewed the field of geometric morphometrics and described the important advantages that these approaches have relative to alternative methods of shape analysis (Adams et al. 2004; for other reviews see: O’Higgins 2000; Slice 2005, 2007; Mitteroecker and Gunz 2009).”
The Concept of Morphospaces in Evolutionary and Developmental Biology: Mathematics and Metaphors (2009, background): “morphometrics, landmark-based approaches can express statistical results in terms of landmark coordinates and thus as actual morphologies or deformations of morphologies (Bookstein 1991; Slice 2005; Mitteroecker and Gunz 2009; for historical reviews see, e.g., Rohlf and Marcus 1993; Bookstein 1998).”
Evaluating modularity in morphometric data: challenges with the RV coefficient and a new test measure (2016, positive): “For both examples, landmark-based geometric morphometric methods were used for the analyses Bookstein 1991; Mitteroecker & Gunz 2009; Adams, Rohlf & Slice 2013).”
Phylogenetic Comparative Methods and the Evolution of Multivariate Phenotypes (2019, background): “…(1971)], sets of shape variables obtained from the coordinates of anatomical points [landmark-based geometric morphometrics: Adams et al. (2013), Mitteroecker & Gunz (2009)], or variables derived from anatomical curves or surfaces, often obtained from computed tomography scans or other…”
PACo: A Novel Procrustes Application to Cophylogenetic Analysis (2013, methodology): “Procrustes fitting is a well-established method in morphometrics [58] but its potential range of applications in other biological areas is very wide.”
Semilandmarks: a method for quantifying curves and surfaces (2013, methodology): “However, this redundant oversampling of morphology is critical for effective visualizations and exploratory studies, as well as for estimating missing data (Mitteroecker and Gunz, 2009; Gunz et al., 2009b).”
Principles for the virtual reconstruction of hominin crania. (2009, positive): “They can also be used to ‘‘unwarp’’ a volumetric data-set such as a CT scan (Mitteroecker and Gunz, 2009).”
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).”