  The use of the Factorization method for Electrical Impedance Tomography has
been proved to be very promising for applications in the case where one wants
to find inhomogeneous inclusions in a known background. In many situations, the
inspected domain is three dimensional and is made of various materials. In this
case, the main challenge in applying the Factorization method consists in
computing the Neumann Green's function of the background medium. We explain how
we solve this difficulty and demonstrate the capability of the Factorization
method to locate inclusions in realistic inhomogeneous three dimensional
background media from simulated data obtained by solving the so-called complete
electrode model. We also perform a numerical study of the stability of the
Factorization method with respect to various modelling errors.
