  Image reconstruction in X ray tomography consists in determining an object
from its projections. In many applications such as non destructive testing, we
look for an image who has a constant value inside a region (default) and
another constant value outside that region (homogeneous region surrounding the
default). The image reconstruction problem becomes then the determination of
the shape of that region. In this work we model the object (the default region)
as a polygonal disc and propose a new method for the estimation of the
coordinates of its vertices directly from a very limited number of its
projections. Keywords: Computed Imaging, Tomography, Shape reconstruction, Non
destructive testing, Regularization, Bayesian estimation, Deformable contours.
