Procrustes Procedures

Abstract

The Procrustes problem is concerned with fitting one configuration, Y, to another, X, as closely as possible. In the simplest case, X and Y have the same dimensionality and the same number of points which can be brought into a 1–1 correspondence by substantive considerations. Under orthogonal transformations, Y can only be rotated and reflected in order to approximate X. More general transformations consist of rigid motions and dilations of Y. In the oblique case, Y can also be distorted linearly. Further generalizations include an incompletely specified target configuration X, different dimensionalities of X and Y, and different numbers of points in X and Y.