ON THE CONSISTENCY OF PROCRUSTEAN MEAN SHAPES

We discuss the uniqueness of the Frechet mean of a class of distributi ons on the shape space of k labelled points in R-2, the supports of wh ich could be the entire space. From this it follows that the shape of the means is the unique Frechet mean shape of the induced distribution with respect to an appropriate metric structure, provided the distrib ution of k labelled points in R-2 is isotropic and satisfies a further mild condition. This result implies that an increasing sequence of pr ocrustean mean shapes defined in either of the two ways used in practi ce will tend almost surely to the shape of the means.