  In this paper a new approach is derived in the context of shape theory. The
implemented methodology is motivated in an open problem proposed in
\citet{GM93} about the construction of certain shape density involving Euler
hypergeometric functions of matrix arguments.
  The associated distribution is obtained by establishing a connection between
the required shape invariants and a known result on canonical correlations
available since 1963; as usual in statistical shape theory and the addressed
result, the densities are expressed in terms of infinite series of zonal
polynomials which involves considerable difficulties in inference. Then the
work proceeds to solve analytically the problem of computation by using the
Eulerian matrix relation of two matrix argument for deriving the corresponding
polynomial distribution in certain parametric space which allows to perform
exact inference based on exact distributions characterized for polynomials of
very low degree. A methodology for comparing correlation shape structure is
proposed and applied in handwritten differentiation.
