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.
Highlights
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 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
That a visualization where the effects of a shape difference are concentrated in one or a few landmarks appeals more to viewers than one where changes are distributed over many landmarks seems to relate to a widespread preference for simple characterizations of shape changes
Summary
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). The two icons are superimposed so that a maximum number of landmarks (in most cases, all but one) coincide precisely and all the change appears in the remaining ones (Fig. 1a), whereas for the other, the two icons are superimposed using least-squares Procrustes superimposition (e.g., Fig. 1b) Because both visualizations in each comparison include icons from the same pair of shapes, both visualizations of the shape difference in each comparison are equivalent. Palci and Lee (2019) presented a different variant of the critique of Procrustes superimposition invoking the Pinocchio effect They present an example using two abstract configurations: rectangles with “spines” on the two long sides, constructed so that all the landmarks can coincide, except for the tip of one of the spines, which makes that spine bigger or smaller. This makes this type of study rather different from most morphometric studies
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