Shape reconstruction in x-ray tomography

Ali Mohammad-Djafari

doi:10.1117/12.292825

31 October 1997 Shape reconstruction in x-ray tomography

Ali Mohammad-Djafari

Proceedings Volume 3170, Image Reconstruction and Restoration II; (1997) https://doi.org/10.1117/12.292825
Event: Optical Science, Engineering and Instrumentation '97, 1997, San Diego, CA, United States

Abstract

X-ray tomographic image reconstruction consists in determining an object function from its projections. In many applications such as non-destructive testing, we look for a default region in a homogeneous known background. The image reconstruction problem becomes then the determination of the shape of the default region. Two approaches can be used: modeling the image as a binary Markov random field and estimating the whole pixels of the image or modeling the shape of the default and estimating it directly from the projections. In this work we model the default shape by a polygonal disc and propose a new method for estimating directly the coordinates of its vertices from a very limited number of its projections. The idea is not new, but in other competing methods, in general, the default shape is modeled by a small number of parameters and these parameters are estimated either by least squares or by maximum likelihood methods. What we propose is to model the shape of the default region by a polygon with a great number of vertices to be able to model any shapes and to estimate directly its vertices coordinates from the projections by defining the solution as the minimizer of an appropriate regularized criterion which can also be interpreted as a maximum a posteriori estimate in a Bayesian estimation framework. To optimize this criterion we use either a simulated annealing or a special purpose deterministic algorithm based on iterated conditional modes. The simulated results are very encouraging specially when the number and the angels of projections are very limited. Some comparisons with classical methods are provided to show the performances of the proposed method.

Citation Download Citation

Ali Mohammad-Djafari "Shape reconstruction in x-ray tomography", Proc. SPIE 3170, Image Reconstruction and Restoration II, (31 October 1997); https://doi.org/10.1117/12.292825

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