25 June 1999 Multiresolution approach to the estimation of the shape of a 3D compact object from its radiographic data
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Abstract
We consider the estimation of a 3D compact homogeneous object from a few number of its gamma ray tomographic projections. This problem is encountered in nondestructive testing applications, in which the number of projections is very limited. We model this shape by a deformable polyhedron, which we estimate directly from the data. The coordinates of the vertices of the polyhedral shape are modeled as a first order vectorial Markov random field and estimated in the Bayesian MAP estimation framework. The energy functional is not convex, hence its minimization requires the use of a stochastic scheme strategy. To reduce the computational cost of the estimate and to propose a practical method, a multiresolution approach is considered in which the number of vertices of the polyhedron is increased as the resolution becomes finer and finer. The algorithm is initialized by a convex polyhedron at a very coarse resolution. Then, at each finer resolution the Bayesian criterion is optimized in the neighborhood of the solution obtained previously. Some simulation results in 2D and 3D cases illustrate the performances of the proposed method.
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Charles Soussen, Charles Soussen, Ali Mohammad-Djafari, Ali Mohammad-Djafari, } "Multiresolution approach to the estimation of the shape of a 3D compact object from its radiographic data", Proc. SPIE 3816, Mathematical Modeling, Bayesian Estimation, and Inverse Problems, (25 June 1999); doi: 10.1117/12.351310; https://doi.org/10.1117/12.351310
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