Stable border basis for ideals of points

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, starting from X, a polynomial basis B of I(X) which exhibits structural stability, that is, if XP is any set of points differing only slightly from X, there exists a polynomial set BP structurally similar to B, which is a basis of the perturbed ideal I(XP).