Abstract
The various types of mathematical spaces used in morphometrics are reviewed with emphasis given to the distinctions between the physical space of the organism, shape space and tangent spaces. The effects of linear transformations of the coordinates of the landmarks (on the specimens or the reference) on various statistical analyses and estimates of the uniform and nonaffine components of shape variation are presented. It is shown why statistical analyses of the estimates of the nonaffine components of shape variation are sensitive to affine transformations of the reference or the specimens (which may seem counterintuitive). Some implications of these results on the choices of methods for the study of shape are discussed.
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Rohlf, F.J. (1996). Morphometric Spaces, Shape Components and the Effects of Linear Transformations. In: Marcus, L.F., Corti, M., Loy, A., Naylor, G.J.P., Slice, D.E. (eds) Advances in Morphometrics. NATO ASI Series, vol 284. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9083-2_11
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