BibTeX
@MISC{Mohammad-Djafari_shapereconstruction,
author = {Ali Mohammad-Djafari},
title = {Shape Reconstruction in X-Ray Tomography},
year = {}
}
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Abstract
X-ray tomographic image reconstruction consists in determining an object function from its projections. In many ap- plications such as non destructive testing, we look for a default region (air) in a homogeneous known background (metal). The image reconstruction problem becomes then the determination of the shape of the default region. Two approaches can bc used: modelling 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 wc 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 modelled by a small number of parameters (polygonal shapes with very small number of vertices, snakes and deformable templates) and these parameters are estimated either by least squares or by maximum likelihood methods. What wc propose is to model the shape of the default region by a polygon with a great number of vertices to bc 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 rcgularizcd criterion which can also bc interpreted as a maximum a postcriori (MAP) 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 (ICM). The simulated results are very encouraging specially when the number and the angles of projections arc very limited (5 projections limited in-45 to 45 degrees). Some comparisons with classical methods are prov...
Keyphrases
default region x-ray tomography shape reconstruction default shape small number new method x-ray tomographic image reconstruction great number deformable template vertex coordinate polygonal shape object function iterated conditional mode appropriate rcgularizcd criterion simulated annealing image reconstruction problem binary markov random field maximum likelihood method special purpose deterministic algorithm polygonal disc whole pixel many ap plication bayesian estimation framework classical method simulated result non destructive testing limited number
