  Analyzing the orbital structure and lattice distortions in the CE phase of
half-doped manganites, we demonstrate that the usual approach directly relating
the orbital occupation of Jahn-Teller ions to the displacements of neighboring
ligands may be misleading. For the correct identification of orbital structure,
it is necessary to take self-consistently into account the electron-lattice
interactions, kinetic energy of charge carriers, and crystal-field effects. In
certain situations, e.g. in the CE phase of single-layered manganite
La$_{0.5}$Sr$_{1.5}$MnO$_4$, the type of orbital ordering strongly deviates
from that, which one would deduce from the local lattice distortions.
