  The objective of electrical impedance tomography (EIT) is to reconstruct the
internal conductivity of a physical body based on current and voltage
measurements at the boundary of the body. In many medical applications the
exact shape of the domain boundary and contact impedances are not available.
This is problematic as even small errors in the boundary shape of the
computation domain or in the contact impedance values can produce large
artifacts in the reconstructed images which results in a loss of relevant
information. A method is proposed that simultaneously reconstructs the
conductivity, the contact impedances and the boundary shape from EIT data. The
approach consists of three steps: first, the unknown contact impedances and an
anisotropic conductivity reproducing the measured EIT data in a model domain
are computed. Second, using isothermal coordinates, a deformation is
constructed that makes the conductivity isotropic. The final step minimizes the
error of true and reconstructed known geometric properties (like the electrode
lengths) using conformal deformations. The feasibility of the method is
illustrated with experimental EIT data, with robust and accurate
reconstructions of both conductivity and boundary shape.
