Extensions of the Procrustes Method for the Optimal Superimposition of Landmarks

Abstract

Superimposition methods for comparing configurations of landmarks in two or more specimens are reviewed. These methods show differences in shape among specimens as residuals after rotation, translation, and scaling them so that they align as well as possible. A new method is presented that generalizes Siegel and Benson's (1982) resistant-fit theta-rho analysis so that more than two objects can be compared at the same time. Both least-squares and resistant-fit approaches are generalized to allow for affine transformations (uniform shape change). The methods are compared, using artificial data and data on 18 landmarks on the wings of 127 species of North American mosquitoes. Graphical techniques are also presented to help summarize the patterns of differences in shape among the objects being compared.