of the equivalence class. This will give a manifold of dimension kn-4. Procrustes is one method of doing this with particular statistical justification. Bookstein obtains a representation of shape by fixing the position of two points called the bases line. One point will be fixed at the origin and the other at (1,0) the remaining points form the Bookstein coordinates. It is also common to consider shape and scale that is with translational and rotational components removed. Examples Shape analysis is used in biological data to identify the variations of anatomical features characterised by landmark data, for example in considering the shape of jaw bones. One study by David George Kendall examined the triangles formed by standing stones to deduce if these were often arranged in straight lines. The shape of a triangle can be represented as a point on the sphere, and the distribution of all shapes can be thought of a distribution over the sphere. The sample distribution from the standing stones was compared with the theoretical distribution to show that the occurrence of straight lines was no more than average. See also Active shape model Alignments of random points Biometrics Generalized Procrustes analysis Image registration Kent distribution Morphometrics Orthogonal Procrustes problem Procrustes References F.L. Bookstein, Morphometric tools for landmark data, Cambridge University Press, (1991). J.C. Gower, G.B. Dijksterhuis, Procrustes Problems, Oxford University Press (2004). I.L.Dryden, K.V. Mardia, Statistical Shape Analysis, Wiley, Chichester, (1998). External links Extensions to continuum of points and distributions Procrustes Methods, Shape Recognition, Similarity and Docking, by Michel Petitjean. Multivariate statistics Euclidean symmetries Biometrics Greek mythology studies Greek words and phrases