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Uncertainty assessment for reconstructions based ondeformable geometryK.M. Hanson, G.S. Cunningham, and R.J. McKeeLos Alamos National Laboratory, MS P940Los Alamos, New Mexico 87545 USA Published in Int. J. Imaging Syst. Technol. 8, pp. 506-512, 1997. ABSTRACTDeformable geometric models can be used in the context of Bayesian analysis to solve ill-posed tomographicreconstruction problems. The uncertainties associated with a Bayesian analysis may be assessed by gen-erating a set of random samples from the posterior, which may be accomplished using a Markov-ChainMonte-Carlo (MCMC) technique. We demonstrate the combination of these techniques for a reconstructionof a two-dimensional object from two orthogonal noisy projections. The reconstructed object is modeled interms of a deformable geometrically-de ned boundary with a uniform interior density yielding a nonlinearreconstruction problem. We show how an MCMC sequence can be used to estimate uncertainties in thelocation of the edge of the reconstructed object.Keywords: Bayesian estimation, deformable geometric models, tomographic reconstruction, uncertaintyestimation, Markov Chain Monte Carlo 1. INTRODUCTIONDeformable geometric models are increasingly being used to analyze medical images. Their use is motivatedby the desire to represent natural characteristics of objects in the real world. Furthermore, deformablemodelscan provide the regularization needed to solve ill-posed problems.1,2 The smoothness of deformable modelsis typically controlled by means of a deformation energy function.3 In the context of Bayesian analysis,the probability of the corresponding geometric con guration is taken to be proportional to the negativeexponential of this energy function.4The main theme of this paper concerns the assessment of uncertainties in estimated models, a capabilitygreatly assisted by the use of Bayesian analysis. The general method we employ here to estimate uncertaintyin a reconstructed object is to generate a sequence