PROCRUSTES SHAPE-ANALYSIS OF PLANAR POINT SUBSETS

Consider a set of points in the plane randomly perturbed about a mean configuration by Gaussian errors. In this paper a Procrustes statistic based on the shapes of subsets of the points is studied, and its appr oximate distribution is found for small variations. We derive various properties of the distribution including the first two moments, a cent ral limit result and a scaled chi(2)-approximation. We concentrate on the independent isotropic Gaussian error case, although the results ar e valid for general covariance structures. We investigate triangle sub sets in detail and in particular the situation where the population me an is regular (i.e. a Delaunay triangulation of the mean of the proces s is comprised of equilateral triangles of the same size). We examine the variance of the statistic for differently shaped regions and provi de an asymptotic result for general shaped regions. The results are ap plied to an investigation of regularity in human muscle fibre cross-se ctions.