Shape Reconstruction from Moments and applications


Abstract:
In this talk, we describe methods for constructing 2D bodies from
data.  In particular we describe several algorithms for fitting
ellipses to data. And we show that several obvious algorithms do not
work well in practice.  Several numeral examples will be given.

In addition, we shall discuss the reconstruction of polygons in the
complex domain from a finite set of moments, using the theory of
quadrature.  These techniques can be used in tomographic applications.
The numerical computations involved in the algorithm can be very
ill-conditioned. We have managed to improve the algorithms used, and
to recognize when the problem will be ill-conditioned. Some numerical
results will be given.

The methods we describe are heavily dependent upon the tools of
numerical linear algebra.