This paper aims at showing the stability of the recovery of a smooth planar
domain with a real algebraic boundary from a finite number of its generalized
polarization tensors. It is a follow-up of the work [H. Ammari et al., Math.
Annalen, 2018], where it is proved that the minimal polynomial with real
coefficients vanishing on the boundary can be identified as the generator of a
one dimensional kernel of a matrix whose entries are obtained from a finite
number of generalized polarization tensors. The recovery procedure is
implemented without any assumption on the regularity of the domain to be
reconstructed and its performance and limitations are illustrated