Procrustes Analysis

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In statistics, Procrustes analysis is a form of statistical shape analysis used to analyse the distribution of a set of shapes. The name Procrustes refers to a bandit from Greek mythology who made his victims fit his bed either by stretching their limbs or cutting them off. Here we just consider objects made up from a finite number k of points in n dimensions, these points are called landmark points. The shape of object can be considered as a member of an equivalence class formed by removing the translational, rotational and scaling components. For example, translational components can be removed from an object by translating the object so that the mean of all the points lies at the origin. Likewise the scale component can be removed by scaling the object so that the sum of the squared distances from the points to the origin is 1.