Reconstruction of the shape of a compact object from few projections

In many applications such as nondestructive testing (NDT), we search for an anomaly (air hole, inclusion) inside a homogeneous region (metal). This problem classically is done in three steps: detection, localization and characterization. The present industrial techniques do well in the two first steps, but the exact determination of the shape of the default region is still in the research domain. The computational cost of the classical tomographic reconstruction using the pixel (2D) or the voxel (3D) representation of the examined body still hinders its use in industrial applications. We propose modelling the contour (or the surface) of the default region by a polygon (or by a polyhedron) and estimating directly the coordinates of its vertices from very limited tomographic projection data.