Closed surface reconstruction in X-ray tomography

We study the 3D reconstruction of a binary scene from X-ray tomographic data. In the special case of a compact and uniform object lying in a uniform background, the scene is entirely defined by the object surface. Then, we select parametric surface models, and we directly estimate their parameters from the data. After showing the ability of spherical harmonics and first order splines (polyhedra) to recover complex shapes, we develop an original method to estimate their parameters without using a voxel representation of the scene (object and background). Reconstructions are based on the optimization of regularized criteria, which account for the surfaces local smoothness. We use local optimization schemes, and we put the stress on their algorithmic aspects. We finally show the performance of the method on a set of incomplete synthetic data.