  Let $\hat \Omega \subset \mathbb R^2$ be a bounded domain with smooth
boundary and $\hat \sigma$ a smooth anisotropic conductivity on $\hat \Omega$.
Starting from the Dirichlet-to-Neumann operator $\Lambda_{\hat \sigma}$ on
$\partial \hat \Omega$, we give an explicit procedure to find a unique domain
$\Omega$, an isotropic conductivity $\sigma$ on $\Omega$ and the boundary
values of a quasiconformal diffeomorphism $F:\hat \Omega \to \Omega$ which
transforms $\hat \sigma$ into $\sigma$.
