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Advances in Geometric Morphometrics

2009/03/23 by Philipp Mitterœcker, Philipp Mitteroecker, Philipp Gunz · 1,324 citations
Earth and Planetary Sciences · Mathematics · #Active shape model #Artificial intelligence #Centroid #Computer science #Evolution and Paleontology Studies #Geometric analysis #Geometric shape #Geometry #Landmark #Mathematical analysis #Mathematics #Morphological variations and asymmetry #Morphometrics #Orientation (vector space) #Pattern recognition (psychology) #Point distribution model #Principal component analysis #Procrustes analysis #Shape analysis (program analysis) #Statistics #Tangent space

paper · pdf · doi:10.1007/s11692-009-9055-x

published in Evolutionary Biology 36(2), 235-247 (Springer Science+Business Media)

openalex publication_date 2009/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

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.

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