How Exactly Did the Nose Get That Long? A Critical Rethinking of the Pinocchio Effect and How Shape Changes Relate to La
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How Exactly Did the Nose Get That Long? A Critical Rethinking of the Pinocchio Effect and How Shape Changes Relate to Landmarks Christian Peter Klingenberg1 Received: 9 July 2020 / Accepted: 22 October 2020 © The Author(s) 2020
Abstract The Pinocchio effect has long been discussed in the literature on geometric morphometrics. It denotes the observation that Procrustes superimposition tends to distribute shape changes over many landmarks, even though a different superimposition may exist for the same landmark configurations that concentrates changes in just one or a few landmarks. This is widely seen as a flaw of Procrustes methods. Visualizations illustrating the Pinocchio effect use a comparison of the same pair of shapes superimposed in two different ways: in a resistant-fit superimposition that concentrates the shape difference in just one or a few landmarks, and in Procrustes superimposition, which distributes differences over most or all landmarks. Because these superimpositions differ only in the non-shape aspects of size, position and orientation, they are equivalent from the perspective of shape analysis. Simulation studies of the Pinocchio effect usually generate data, either single pairs or larger samples of landmark configurations, in a particular superimposition so that differences occur mostly or exclusively at just one or a few landmarks, but no steps are taken to remove variation from size, position and orientation. When these configurations are then compared with Procrustes-superimposed data, differences appear and are attributed to the Pinocchio effect. Overall, it is ironic that all manifestations of the Pinocchio effect in one way or another rely on differences in the non-shape properties of position and orientation. Rigorous thinking about shape variation and careful choice of visualization methods can prevent confusion over this issue. Keywords Geometric morphometrics · Landmarks · Pinocchio effect · Procrustes superimposition · Shape
Introduction Superimposition methods have an important role in geometric morphometrics for quantifying the differences between pairs of shapes or for aligning landmark configurations to the respective shape (tangent) spaces (Klingenberg 2020). Because shape is defined as all the geometric features in a configuration of landmarks except for its size, position, and orientation, superimposition methods are used to find a standardization of size, position, and orientation that minimizes some criterion quantifying the differences in the positions of landmarks relative to each other. Discrepancies in the positions of landmarks that remain after this standardization step can be ascribed to shape differences between the * Christian Peter Klingenberg [email protected] 1
School of Biological Sciences, University of Manchester, Michael Smith Building, Oxford Road, Manchester M13 9PT, UK
respective landmark configurations. The most widely used method is Procrustes superimposition, where the criterion being minimized is the sum of squared dist
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