On the consistency of procrustean mean shapes
- 1 March 1998
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 30 (1) , 53-63
- https://doi.org/10.1239/aap/1035227991
Abstract
We discuss the uniqueness of the Fréchet mean of a class of distributions on the shape space ofklabelled points in ℝ2, the supports of which could be the entire space. From this it follows that the shape of the means is the unique Fréchet mean shape of the induced distribution with respect to an appropriate metric structure, provided the distribution ofklabelled points in ℝ2is isotropic and satisfies a further mild condition. This result implies that an increasing sequence of procrustean mean shapes defined in either of the two ways used in practice will tend almost surely to the shape of the means.Keywords
This publication has 9 references indexed in Scilit:
- Consistency of Procrustes EstimatorsJournal of the Royal Statistical Society Series B: Statistical Methodology, 1997
- Mean size-and-shapes and mean shapes: a geometric point of viewAdvances in Applied Probability, 1995
- Euclidean Distance Matrix Analysis (EDMA): Estimation of mean form and mean form differenceMathematical Geology, 1993
- A stochastic calculus approach to the shape distribution induced by a complex normal modelMathematical Proceedings of the Cambridge Philosophical Society, 1991
- Procrustes Methods in the Statistical Analysis of ShapeJournal of the Royal Statistical Society Series B: Statistical Methodology, 1991
- An alternate formulation of mean value for random geometric figures*Journal of Microscopy, 1988
- Shape Manifolds, Procrustean Metrics, and Complex Projective SpacesBulletin of the London Mathematical Society, 1984
- Riemannian center of mass and mollifier smoothingCommunications on Pure and Applied Mathematics, 1977
- A Strong Law of Large Numbers for Random Compact SetsThe Annals of Probability, 1975