Reconstruction of the shape of a compact object from few projections Authors: Ali Mohammad--Djafari Laboratoire des Signaux et Syst\`emes (CNRS--SUPELEC--UPS) \'Ecole Sup\'erieure d'\'Electricit\'e Plateau de Moulon, 91192 Gif--sur--Yvette Cedex, France lss.supelec.fr and Ken Sauer Department of Electrical Engineering University of Notre Dame, Notre Dame, IN 46556, USA Summary: In many applications such as non destructive 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. In this work, we propose to model the contour (in 2D case) or the surface (in 3D case) of the fault region by a polygon (or by a polyhedron) and to estimate directly the coordinates of its vertices from very limited tomographic projection data.