Palate shape information was extracted from the landmark coordinates using a General Procrustes Analysis GPAa), a procedure that superimposes configurations of landmarks and adjusts for the effects of orientation and scale (Dryden and Mardia, 1998).
General Procrustes Analysis GPAa), a procedure that superimposes configurations of landmarks by shifting them to a common position, rotating and scaling them to a standard size until a best fit of corresponding landmarks is achieved, was used to extract shape information (Dryden and Mardia, 1998).
Finally, a Procrustes fit is used to superimpose all configurations simultaneously and components of variation around the consensus shape can be extracted.
In order to switch the FOVs, three different optical configurations are superimposed and all three configurations are optimized.
The solution trajectory from t = 0 to t = 0.0004 is plotted by superimposing multiple configurations within this interval in Fig. 27.
GPA superimposes landmark configurations in that it minimizes the sum of squared distances between corresponding landmarks by scaling, translating and rotating specimens onto a mean consensus configuration calculated from all specimens.
Then, the centroid of each configuration was superimposed onto the centroid of the consensus configuration, and the configurations were rotated so as to minimize the distances between the corresponding landmarks.
The landmark configurations were superimposed according to a least squares criterion (Procrustes superimposition) [ 77- 79], first calculating a mean for each species and then superimposing all configurations to calculate a grand average.
(2) Translation: the centroids (centers of gravity) of the configurations are superimposed onto each other by translation.
The landmark configurations were superimposed using a generalized Procrustes analysis (Rohlf and Slice, 1990; Mitteroecker and Gunz, 2009) and projected into Procrustes tangent space (Rohlf, 1999).
