Locating Fréchet means with application to shape spaces

摘要: We use Jacobi field arguments and the contraction mapping theorem to locate Frechet means of a class probability measures on locally symmetric Riemannian manifolds with non-negative sectional curvatures. This leads, in particular, method for estimating mean shapes, respect distance function ρ determined by induced metric, Kendall's shape spaces. then combine this technique ‘horizontally lifting’ pre-shape spheres obtain an algorithm finding ρ, spaces terms vertices random shapes. gives us, example, shapes samples configurations plane which is expressed directly vertices.