Reconstruction of the shape of a compact object from few

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

Ken Sauer
Department of Electrical Engineering  
University of Notre Dame,  Notre Dame, IN 46556, USA

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.