  Using a plane wave pseudopotential approach to density functional theory we
investigate the electron localization length in various oxides. For this
purpose, we first set up a theory of the band-by-band decomposition of this
quantity, more complex than the decomposition of the spontaneous polarization
(a related concept), because of the interband coupling. We show its
interpretation in terms of Wannier functions and clarify the effect of the
pseudopotential approximation. We treat the case of different oxides: BaO,
$\alpha$-PbO, BaTiO$_3$ and PbTiO$_3$. We also investigate the variation of the
localization tensor during the ferroelectric phase transitions of BaTiO$_3$ as
well as its relationship with the Born effective charges.
