We consider the spin injection from Fe into ZnSe and GaAs in the ballistic limit. By means of the ab initio SKKR method we calculate the ground state properties of epitaxial FeJZnse and FelGaAs heterostructures for the (001), (111) and (110) orientation. Three injection processes are considered: injection of hot electrons and injection of "thermal" electrons with and without an interface barrier. The calculation of the conductance by the Landauer formula shows, that (001) oriented interface acts like a nearly ideal spin filter, while the other orientations give only small injection efficiencies. The high spin polarization can be traced back to the symmetry of the band structure of Fe(001) for normal incidence.