In order to build a deformation model of face shapes, we must first process the raw annotated data to remove components pertaining to global rigid motion. When modeling geometry in 2D, a rigid motion is often represented as a similarity transform; this includes the scale, in-plane rotation, and translation. The following image illustrates the set of permissible motion types under a similarity transform. The process of removing global rigid motion from a collection of points is called Procrustes analysis.
Mathematically, the objective of Procrustes analysis is to simultaneously find a canonical shape and similarity, and ...
