  In this paper, we address a particular case of Calder\'on's (or conductivity)
inverse problem in dimension two, namely the case of a homogeneous background
containing a finite number of cavities (i.e. heterogeneities of infinitely high
conductivities). We aim to recover the location and the shape of the cavities
from the knowledge of the Dirichlet-to-Neumann (DtN) map of the problem. The
proposed reconstruction method is non iterative and uses two main ingredients.
First, we show how to compute the so-called generalized P\'olia-Szeg\"o tensors
(GPST) of the cavities from the DtN of the cavities. Secondly, we show that the
obtained shape from GPST inverse problem can be transformed into a shape from
moments problem, for some particular configurations. However, numerical results
suggest that the reconstruction method is efficient for arbitrary geometries.
