  This work sets the statistical affine shape theory in the context of real
normed division algebras. The general densities apply for every field: real,
complex, quaternion, octonion, and for any noncentral and non-isotropic
elliptical distribution; then the separated published works about real and
complex shape distributions can be obtained as corollaries by a suitable
selection of the field parameter and univariate integrals involving the
generator elliptical function. As a particular case, the complex normal affine
density is derived and applied in brain magnetic resonance scans of normal and
schizophrenic patients.
