The Statistical Theory of Shape

In general terms, the shape of an object, data set, or image can be de­ fined as the total of all information that is invariant under translations, rotations, and isotropic rescalings. Thus two objects can be said to have the same shape if they are similar in the sense of Euclidean geometry. For example, all equilateral triangles have the same shape, and so do all cubes. In applications, bodies rarely have exactly the same shape within measure­ ment error. In such cases the variation in shape ca