A Stable Numerical Method for Inverting Shape from Moments

We derive a stable technique, based upon matrix pencils, for the reconstruction of (or approximation by) polygonal shapes from moments. We point out that this problem can be considered the dual of 2 D numerical quadrature over polygonal domains. An analysis of the sensitivity of the problem is presented along with some numerical examples illustrating the relevant points. Finally, an application to the problem of gravimetry is explored where the shape of a gravitationally anomalous region is to be recovered from measurements of its exterior gravitational eld.