  A direct reconstruction algorithm based on Calder\'on's linearization method
for the reconstruction of isotropic conductivities is proposed for anisotropic
conductivities in two-dimensions. To overcome the non-uniqueness of the
anisotropic inverse conductivity problem, the entries of the unperturbed
anisotropic tensors are assumed known \emph{a priori}, and it remains to
reconstruct the multiplicative scalar field. The quasi-conformal map in the
plane facilitates the Calder\'on-based approach for anisotropic conductivities.
The method is demonstrated on discontinuous radially symmetric conductivities
of high and low contrast.
