Procrustes analysis

This chapter provides a more comprehensive treatment of Procrustes methods suitable for two and higher dimensional shape analysis. Procrustes analysis involves matching configurations with similarity transformations to be as close as possible according to Euclidean distance, using least squares techniques. The chapter begins by describing ordinary Procrustes analysis (OPA) which is used for matching two configurations. When at least two configurations are available we can use the technique of generalized Procrustes analysis (GPA) to obtain an average shape. To carry out GPA in the shapes package in R one can use the command procGPA. This function is perhaps the most useful of all the commands in the shapes library, and computes the Procrustesmean, and various summary statistics. Finally, the chapter highlights some similarities with principal component analysis (PCA) in shape analysis with PCA in multivariate analysis. As for shape analysis we can carry out PCA in the tangent space to size-and-shape space.