  Let $X$ be a set of points whose coordinates are known with limited accuracy;
our aim is to give a characterization of the vanishing ideal $I(X)$ independent
of the data uncertainty. We present a method to compute a polynomial basis $B$
of $I(X)$ which exhibits structural stability, that is, if $\widetilde X$ is
any set of points differing only slightly from $X$, there exists a polynomial
set $\widetilde B$ structurally similar to $B$, which is a basis of the
perturbed ideal $ I(\widetilde X)$.
