G is the right space for statistics of particles.
However , the orbit space is usually curved, which makes it difficult to apply routine statistical procedures to samples composed of its elements. Now we introduce some necessary notions related to samples in the orbit space. An average can be defined as the shape whose sum of squared Procrustes distances to the other specimens is minimal. This method is also called generalized Procrustes analysis, GPA, since it is not what is now . Dryden, I. L., and K. V. Mardia.